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Title: Nonlinear control of underactuated horizontal double pendulum.
Creator: Popescu, Cristian., Florida Atlantic University, Wang, Yuan, Roth, Zvi S.
Abstract/Description: Underactuated mechanical systems are those possessing fewer actuators than degrees of freedom, making the class a rich one from a control standpoint. The double inverted pendulum is a particular underactuated system and a well-known benchmark case for which many solutions have been offered in the literature. The control objective is to bring the system to its unstable top equilibrium point. The underactuated horizontal double pendulum is a two-link planar robot with only one actuator either...
Show moreUnderactuated mechanical systems are those possessing fewer actuators than degrees of freedom, making the class a rich one from a control standpoint. The double inverted pendulum is a particular underactuated system and a well-known benchmark case for which many solutions have been offered in the literature. The control objective is to bring the system to its unstable top equilibrium point. The underactuated horizontal double pendulum is a two-link planar robot with only one actuator either at the shoulder or the elbow. Almost no work was done on the underactuated horizontal pendulum, mainly due to the lack of controllability of such a system. The fundamental difference between a double inverted pendulum and an underactuated horizontal double pendulum is that in the latter gravity effects do not exist. Gravity is important to the controllability of the system. Thus, in search for a "gravity substitute," we added springs in the underactuated horizontal double pendulum in order to create a source of potential energy. Two different types of such systems are analyzed: spring coupled underactuated horizontal double pendulums and underactuated horizontal double pendulums with spring-loaded sliding bar constraint. The main contribution of the thesis is in proving that the zero state of the spring coupled systems is globally asymptotically stabilizable. Explicit control laws were developed.
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Date Issued: 2002
PURL: http://purl.flvc.org/fcla/dt/12894
Subject Headings: Double pendulums, Nonlinear control theory
Format: Document (PDF)

Title: Automatic design of nonlinear controllers with optimal global performance using best estimate-directed search and continued propagation cell mapping.
Creator: Rizk, Charbel George., Florida Atlantic University, Smith, Samuel M., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: The problem at hand is developing a controller design methodology that is generally applicable to autonomous systems with fairly accurate models. The controller design process has two parts: synthesis and analysis. Over the years, many synthesis and analysis methods have been proposed. An optimal method for all applications has not yet been found. Recent advances in computer technology have made computational methods more attractive and practical. The proposed method is an iterative...
Show moreThe problem at hand is developing a controller design methodology that is generally applicable to autonomous systems with fairly accurate models. The controller design process has two parts: synthesis and analysis. Over the years, many synthesis and analysis methods have been proposed. An optimal method for all applications has not yet been found. Recent advances in computer technology have made computational methods more attractive and practical. The proposed method is an iterative computational method that automatically generates non-linear controllers with specified global performance. This dissertation describes this method which consists of using an analysis tool, continued propagation cell mapping (CPCM), as feedback to the synthesis tool, best estimate directed search (BEDS). Optimality in the design can be achieved with respect to time, energy, and/or robustness depending on the performance measure used. BEDS is based on a novel search concept: globally directing a random search. BEDS has the best of two approaches: gradient (or directed) search and random search. It possesses the convergence speed of a gradient search and the convergence robustness of a random search. The coefficients of the best controller at the time direct the search process until either a better controller is found or the search is terminated. CPCM is a modification of simple cell mapping (SCM). CPCM maintains the simplicity of SCM but provides accuracy near that of a point map (PM). CPCM evaluates the controller's complete and global performance efficiently and with easily tunable accuracy. This CPCM evaluation guarantees monotonic progress in the synthesis process. The method is successfully applied to the design of a TSK-type fuzzy logic (FL) controller and a Sliding Mode-type controller for the uncertain non-linear system of an inverted pendulum on a cart for large pole angles (+/-86 degrees). The resulting controller's performance compares favorably to other established methods designed with dynamic programing (DP) and genetic algorithms (GA). When CPCM is used as feedback to BEDS, the resulting design method quickly and automatically generates non-linear controllers with good global performance and without much a priori information about the desired control actions.
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Date Issued: 1997
PURL: http://purl.flvc.org/fcla/dt/12523
Subject Headings: Nonlinear control theory, Cellular mappings, Fuzzy logic
Format: Document (PDF)

Title: Nonlinear stochastic systems.
Creator: Cai, Guo-Qiang, Florida Atlantic University, Lin, Y. K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: This thesis is concerned with nonlinear dynamical systems subject to random or combined random and deterministic excitations. To this end, a systematic procedure is first developed to obtain the exact stationary probability density for the response of a nonlinear system under both additive and multiplicative excitations of Gaussian white noises. This procedure is applicable to a class of systems called the class of generalized stationary potential. The basic idea is to separate the...
Show moreThis thesis is concerned with nonlinear dynamical systems subject to random or combined random and deterministic excitations. To this end, a systematic procedure is first developed to obtain the exact stationary probability density for the response of a nonlinear system under both additive and multiplicative excitations of Gaussian white noises. This procedure is applicable to a class of systems called the class of generalized stationary potential. The basic idea is to separate the circulatory probability flow from the noncirculatory flow, thus obtaining two sets of equations for the probability potential. It is shown that previously published exact solutions are special cases of this class. For those nonlinear systems not belonging to the class of generalized stationary potential, an approximate solution technique is developed on the basis of weighted residuals. The original system is replaced by the closest system belonging to the class of generalized stationary potential, in the sense that the statistically weighted residuals are zero for some suitably selected weighting functions. The consistency of the approximation technique is proved in terms of certain statistical moments. The above exact and approximate solution techniques are extended to two types of nonlinear systems: one subjected to non-Gaussian impulsive noise excitations and another subjected to combined harmonic and broad-band random excitations. Approximation procedures are devised to obtain stationary probabilistic solutions for these two types of problems. Monte Carlo simulations are performed to substantiate the accuracy of the approximate solution procedures.
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Date Issued: 1992
PURL: http://purl.flvc.org/fcla/dt/12293
Subject Headings: Nonlinear theories, Stochastic systems, Stochastic processes
Format: Document (PDF)

Title: Studies on nonlinear activity and cross-entropy considerations in neural networks.
Creator: Abusalah, Salahalddin Tawfiq., Florida Atlantic University, Neelakanta, Perambur S., College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description: The objectives of this research as deliberated in this dissertation are two-folded: (i) To study the nonlinear activity in the neural complex (real and artificial) and (ii) to analyze the learning processe(s) pertinent to an artificial neural network in the information-theoretic plane using cross-entropy error-metrics. The research efforts envisaged enclave the following specific tasks: (i) Obtaining a general solution for the Bernoulli-Riccati equation to represent a single parameter family...
Show moreThe objectives of this research as deliberated in this dissertation are two-folded: (i) To study the nonlinear activity in the neural complex (real and artificial) and (ii) to analyze the learning processe(s) pertinent to an artificial neural network in the information-theoretic plane using cross-entropy error-metrics. The research efforts envisaged enclave the following specific tasks: (i) Obtaining a general solution for the Bernoulli-Riccati equation to represent a single parameter family of S-shaped (sigmoidal) curves depicting the nonlinear activity in the neural network. (ii) Analysis of the logistic growth of output versus input values in the neural complex (real and artificial) under the consideration that the boundaries of the sets constituting the input and output entities are crisp and/or fuzzy. (iii) Construction of a set of cross-entropy error-metrics (known as Csiszar's measures) deduced in terms of the parameters pertinent to a perceptron topology and elucidation of their relative effectiveness in training the network optimally towards convergence. (iv) Presenting the methods of symmetrizing and balancing the aforesaid error-entropy measures (in the information-theoretic plane) so as to make them usable as error-metrics in the test domain. (v) Description and analysis of the dynamics of neural learning process in the information-theoretic plane for both crisp and fuzzy attributes of input values. Relevant to these topics portraying the studies on nonlinear activity and cross-entropy considerations vis-a-vis neural networks, newer and/or exploratory inferences are made, logical conclusions are enumerated and relative discussions are presented along with the scope for future research to be pursued.
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Date Issued: 1996
PURL: http://purl.flvc.org/fcla/dt/12447
Subject Headings: Neural networks (Computer science), Entropy (Information theory), Nonlinear control theory
Format: Document (PDF)

Title: Sobolev Inequalities.
Creator: Kalis, Jan, Florida Atlantic University, Milman, Mario, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Recently a rich theory of Sobolev spaces on metric spaces has been developed. It. turas out that many relevant results from the classical theory have their counterparts in the mcnic setting ( cf. [P. Hajlasz and P. Koskela. Sobokv met Poincare), Mern. Arner. Math. Soc. 145 (2000), no. 6888, x+101pp]). In this thesis we prove sharp Sobolev inequalities in the context of metric spaces. Our approach is ba....,ed on two recent papers, [J. Baster·o and M. Milman and F. Ruiz, A note on L(oc, q)...
Show moreRecently a rich theory of Sobolev spaces on metric spaces has been developed. It. turas out that many relevant results from the classical theory have their counterparts in the mcnic setting ( cf. [P. Hajlasz and P. Koskela. Sobokv met Poincare), Mern. Arner. Math. Soc. 145 (2000), no. 6888, x+101pp]). In this thesis we prove sharp Sobolev inequalities in the context of metric spaces. Our approach is ba....,ed on two recent papers, [J. Baster·o and M. Milman and F. Ruiz, A note on L(oc, q) spaces and Sobolev embeddings, Indiana Univ. Math. J. 52 (2003), no. 5, 1215- 1230] and [J. Martfn and M. Milman and E. Pustylnik, Sobolev inequalities: symmetrization and self improvement via truncation, to appear in J. Funct. Anal.]. These authors establish sharp Sobolev embeddings in the Euclidean setting using symmetrization. Using suitable maximal operators and covering lemmas we show that these symmetrization inequalities of Bastero-Milman-Ruiz remain valid m the metric setting. We also show that the symmetrization by truncation method of Martfn-Milman-Pustylnik can be implemented in our generalized setting. Furthermore we also show that our methods can be adapted to deal with non-doubling measures.
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Date Issued: 2007
PURL: http://purl.flvc.org/fau/fd/FA00000863
Subject Headings: Sobolev spaces, Inequalities (Mathematics), Nonlinear theories, Potential theory (Mathematics)
Format: Document (PDF)

Title: Karhunen-Loeve decomposition for non stationary propulsor flow noise.
Creator: Kersulec, Jean-Luc., Florida Atlantic University, Glegg, Stewart A. L., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: The aim of this thesis is to develop a theory for non stationary propulsor flow noise. The model which is proposed is based on Amiet's paper "Acoustic Radiation from an Airfoil in a Turbulent Stream" [1], which describes broad band noise when a simple model of airfoil interacts with a turbulent flow, under the assumption of stationarity. The Karhunen-Loeve method provides a set of modes which describe the turbulent flow without the assumption of stationarity. A method is described to obtain...
Show moreThe aim of this thesis is to develop a theory for non stationary propulsor flow noise. The model which is proposed is based on Amiet's paper "Acoustic Radiation from an Airfoil in a Turbulent Stream" [1], which describes broad band noise when a simple model of airfoil interacts with a turbulent flow, under the assumption of stationarity. The Karhunen-Loeve method provides a set of modes which describe the turbulent flow without the assumption of stationarity. A method is described to obtain broad band noise calculations when the mean turbulent flow varies with time and produces non stationary turbulence. A comparison of the numerical results obtained with the results from the paper of reference [1] shows the characteristics of time varying sound radiation. The various mathematical formulae will give a starting point to the analysis of real time varying flows, which are not considered in this thesis.
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Date Issued: 2005
PURL: http://purl.flvc.org/fcla/dt/13233
Subject Headings: Aerodynamic noise, Turbulence, Aerofoils, Unsteady flow (Aerodynamics), Nonlinear control theory, Differential equations, Nonlinear
Format: Document (PDF)

Title: Remarks on stability analysis for delayed systems with applications.
Creator: Tiwari, Shanaz, Wang, Yuan, Graduate College
Date Issued: 2011-04-08
PURL: http://purl.flvc.org/fcla/dt/3164800
Subject Headings: Nonlinear control theory, Lyapunov functions, Time delay systems
Format: Document (PDF)

Title: Synchronization of coupled semiconductor lasers.
Creator: London, Michael S., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: The synchronization of coupled semiconductor lasers with delay is investigated by numerical simulations of the nonlinear dynamic models complemented by a stability analysis of the linearized system. The equations used in the dissertation are based on the well known "Lang-Kobayashi" model modified to include unidirectional and bidirectional coupling. Stability diagrams are calculated and supplemented by numerically integrated time series. Synchronization is determined and quantified by...
Show moreThe synchronization of coupled semiconductor lasers with delay is investigated by numerical simulations of the nonlinear dynamic models complemented by a stability analysis of the linearized system. The equations used in the dissertation are based on the well known "Lang-Kobayashi" model modified to include unidirectional and bidirectional coupling. Stability diagrams are calculated and supplemented by numerically integrated time series. Synchronization is determined and quantified by computing the cross-correlation function. It is found that synchronized states are achievable for a wide range of coupling constants and delay times. These findings have implications for experiment and technological applications, notably in cryptography.
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Date Issued: 2011
PURL: http://purl.flvc.org/FAU/3318673
Subject Headings: Semiconductor lasers, Optical bistability, Nonlinear theories, Diodes, Semiconductor, Mathematical models
Format: Document (PDF)

Title: Simulations and feedback control of nonlinear coupled electromechanical oscillators for energy conversion applications.
Creator: Psarrou, Dimitrios., Dhanak, Manhar R., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: This thesis discusses the coupling of a mechanical and electrical oscillator, an arrangement that is often encountered in mechatronics actuators and sensors. The dynamics of this coupled system is mathematically modeled and a low pass equivalent model is presented. Numerical simulations are then performed, for various input signals to characterize the nonlinear relationship between the electrical current and the displacement of the mass. Lastly a framework is proposed to estimate the mass...
Show moreThis thesis discusses the coupling of a mechanical and electrical oscillator, an arrangement that is often encountered in mechatronics actuators and sensors. The dynamics of this coupled system is mathematically modeled and a low pass equivalent model is presented. Numerical simulations are then performed, for various input signals to characterize the nonlinear relationship between the electrical current and the displacement of the mass. Lastly a framework is proposed to estimate the mass position without the use of a position sensor, enabling the sensorless control of the coupled system and additionally providing the ability for the system to act as an actuator or a sensor. This is of value for health monitoring, diagnostics and prognostics, actuation and power transfer of a number of interconnected machines that have more than one electrical system, driving corresponding mechanical subsystems while being driven by the same voltage source and at the same time being spectrally separated and independent.
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Date Issued: 2011
PURL: http://purl.flvc.org/FAU/3320109
Subject Headings: Renewable energy sources, Mechatronics, Nonlinear theories, Oscillators, System analysis
Format: Document (PDF)

Title: Design of an adaptive nonlinear controller for an autonomous underwater vehicle equipped with a vectored thruster.
Creator: Morel, Yannick., Florida Atlantic University, Leonessa, Alexander, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: The tasks Autonomous Underwater Vehicles (AUVs) are expected to perform are becoming more and more challenging. Thus, to be able to address such tasks, we implemented a high maneuverability propulsion system: a vectored thruster. The design of a vehicle equipped with such a propulsion system will be presented, from a mechanical, electronic and software point of view. The motion control of the resulting system is fairly complex, and no suitable controller is available in the literature....
Show moreThe tasks Autonomous Underwater Vehicles (AUVs) are expected to perform are becoming more and more challenging. Thus, to be able to address such tasks, we implemented a high maneuverability propulsion system: a vectored thruster. The design of a vehicle equipped with such a propulsion system will be presented, from a mechanical, electronic and software point of view. The motion control of the resulting system is fairly complex, and no suitable controller is available in the literature. Accordingly, we will present the derivation of a novel tracking controller, whose adaptive properties will compensate for the lack of knowledge of the system's parameters. Computer simulations are provided and show the performance and robustness of the proposed control algorithm to external perturbations, unmodelled dynamics and dynamics variation. We finally illustrate the advantage of using an adaptive controller by comparing the presented controller to a Proportional Integral Derivative controller.
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Date Issued: 2002
PURL: http://purl.flvc.org/fcla/dt/12986
Subject Headings: Hydrodynamics, Nonlinear control theory, Adaptive control systems, Oceanographic submersibles
Format: Document (PDF)

Title: Input-to-state stability properties for discrete-time nonlinear systems.
Creator: Gao, Kehan, Florida Atlantic University, Wang, Yuan, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In this thesis, we study the input-to-state stability (scISS) property and related characterizations for discrete-time nonlinear systems. Variations of scISS property were employed in solving particular control problems. The main contribution of this work is to provide a detailed analysis on the relations among various types of notations related to system stability and show that most scISS results for continuous-time nonlinear system can be extended to discrete-time case.
Date Issued: 1999
PURL: http://purl.flvc.org/fcla/dt/15688
Subject Headings: Discrete-time systems, Nonlinear systems, Stability, Control theory
Format: Document (PDF)

Title: Hamiltonian Methods in the Quantization of Gauge Systems.
Creator: Vaulin, Ruslan, Florida Atlantic University, Miller, Warner A., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: The new formalism for quantization of gauge systems based on the concept of the dynamical Hamiltonian recently introduced as a basis for the canonical theory of quantum gravity was considered in the context of general gauge theories. This and other Hamiltonian methods, that include Dirac's theory of extended Hamiltonian and the Hamiltonian reduction formalism were critically examined. It was established that the classical theories of constrained gauge systems formulated within the framework...
Show moreThe new formalism for quantization of gauge systems based on the concept of the dynamical Hamiltonian recently introduced as a basis for the canonical theory of quantum gravity was considered in the context of general gauge theories. This and other Hamiltonian methods, that include Dirac's theory of extended Hamiltonian and the Hamiltonian reduction formalism were critically examined. It was established that the classical theories of constrained gauge systems formulated within the framework of either of the approaches are equivalent. The central to the proof of equivalence was the fact that the gauge symmetries resuIt in the constraints of the first class in Dirac's terminology that Iead to redundancy of equations of motion for some of the canonica variables. Nevertheless, analysis of the quantum theories showed that in general, the quantum theory of the dynamical Hamiltonian is inequivalent to those of the extended Hamiltonian and the Hamiltonian reduction. The new method of quantization was applied to a number of gauge systems, including the theory of relativistic particle, the Bianchi type IX cosmological model and spinor electrodynamics along side with the traditional methods of quantization. In all of the cases considered the quantum theory of the dynamical Hamiltonian was found to be well-defined and to possess the appropriate classical limit. In particular, the quantization procedure for the Bianchi type IX cosmological spacetime did not run into any of the known problems with quantizing the theory of General Relativity. On the other hand, in the case of the quantum electrodynamics the dynamical Hamiltonian approach led to the quantum theory with the modified self-interaction in the matter sector. The possible consequence of this for the quantization of the full theory of General Relativity including the matter fields are discussed.
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Date Issued: 2006
PURL: http://purl.flvc.org/fau/fd/FA00000882
Subject Headings: Quantum field theory, Mathematical physics, Evolution equations, Nonlinear, Hamiltonian systems
Format: Document (PDF)

Title: Nonlinear Phenomena from a Reinjected Horseshoe.
Creator: Fontaine, Marcus, Kalies, William D., Naudot, Vincent, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: A geometric model of a reinjected cuspidal horseshoe is constructed, that resembles the standard horseshoe, but where the set of points that escape are now reinjected and contribute to richer dynamics. We show it is observed in the unfolding of a three-dimensional vector field possessing an inclination-flip homoclinic orbit with a resonant hyperbolic equilibrium. We use techniques from classical dynamical systems theory and rigorous computational symbolic dynamics with algebraic topology to...
Show moreA geometric model of a reinjected cuspidal horseshoe is constructed, that resembles the standard horseshoe, but where the set of points that escape are now reinjected and contribute to richer dynamics. We show it is observed in the unfolding of a three-dimensional vector field possessing an inclination-flip homoclinic orbit with a resonant hyperbolic equilibrium. We use techniques from classical dynamical systems theory and rigorous computational symbolic dynamics with algebraic topology to show that for suitable parameters the flow contains a strange attractor.
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Date Issued: 2016
PURL: http://purl.flvc.org/fau/fd/FA00004591
Subject Headings: Nonlinear theories., Computational dynamics., Attractors (Mathematics), Chaotic behavior in systems., Mathematical physics.
Format: Document (PDF)

Title: Nonlinear control of an unmanned amphibious vehicle.
Creator: Alvarez, Jose L., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: The DUCKW-Ling is an 8.3 foot long, amphibious water plane area twin hull (SWATH) concept vehicle which is propelled by a pair of crawler tracks on land and dual propellers when water-borne. In its operational zone, the vehicle's dynamics change dramatically as it transitions from being completely water-borne and buoyancy supported to being completely land-borne and track supported. In the water environment, a cascaded, first-order sliding mode controller was used to control the surge and...
Show moreThe DUCKW-Ling is an 8.3 foot long, amphibious water plane area twin hull (SWATH) concept vehicle which is propelled by a pair of crawler tracks on land and dual propellers when water-borne. In its operational zone, the vehicle's dynamics change dramatically as it transitions from being completely water-borne and buoyancy supported to being completely land-borne and track supported. In the water environment, a cascaded, first-order sliding mode controller was used to control the surge and heading of the vehicle, and was capable of having a faster response when compared to using a proportional controller. Additionally, field trials of the DUKW-Ling show the capability of the vehicle to navigate and track predetermined waypoints in both terrestrial and aquatic terrains. In the transitional zone, the electric motor current from the tracks was used as the feedback mechanism to adequately actuate the propellers and tracks in the system as the dynamics of the vehicle change.
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Date Issued: 2013
PURL: http://purl.flvc.org/fcla/dt/3362334
Subject Headings: Nonlinear control theory, Feedback control systems, Motor vehicles, Amphibious, Design and construction, Adaptive signal processing
Format: Document (PDF)

Title: Intelligent Supervisory Switching Control of Unmanned Surface Vehicles.
Creator: Bertaska, Ivan Rodrigues, von Ellenrieder, Karl, Florida Atlantic University, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: novel approach to extend the decision-making capabilities of unmanned surface vehicles (USVs) is presented in this work. A multi-objective framework is described where separate controllers command different behaviors according to a desired trajectory. Three behaviors are examined – transiting, station-keeping and reversing. Given the desired trajectory, the vehicle is able to autonomously recognize which behavior best suits a portion of the trajectory. The USV uses a combination of a...
Show morenovel approach to extend the decision-making capabilities of unmanned surface vehicles (USVs) is presented in this work. A multi-objective framework is described where separate controllers command different behaviors according to a desired trajectory. Three behaviors are examined – transiting, station-keeping and reversing. Given the desired trajectory, the vehicle is able to autonomously recognize which behavior best suits a portion of the trajectory. The USV uses a combination of a supervisory switching control structure and a reinforcement learning algorithm to create a hybrid deliberative and reactive approach to switch between controllers and actions. Reinforcement learning provides a deliberative method to create a controller switching policy, while supervisory switching control acts reactively to instantaneous changes in the environment. Each action is restricted to one controller. Due to the nonlinear effects in these behaviors, two underactuated backstepping controllers and a fully-actuated backstepping controller are proposed for each transiting, reversing and station-keeping behavior, respectively, restricted to three degrees of freedom. Field experiments are presented to validate this system on the water with a physical USV platform under Sea State 1 conditions. Main outcomes of this work are that the proposed system provides better performance than a comparable gain-scheduled nonlinear controller in terms of an Integral of Absolute Error metric. Additionally, the deliberative component allows the system to identify dynamically infeasible trajectories and properly accommodate them.
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Date Issued: 2016
PURL: http://purl.flvc.org/fau/fd/FA00004671, http://purl.flvc.org/fau/fd/FA00004671
Subject Headings: Adaptive control systems, Artificial intelligence, Engineering mathematics, Intelligent control systems, Mechatronics, Nonlinear control theory, Transportation engineering
Format: Document (PDF)

Title: Stability analysis for nonlinear systems with time-delays.
Creator: Tiwari, Shanaz, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In this work, we investigate input-to-state stability (ISS) and other related stability properties for control systems with time-delays. To overcome the complexity caused by the presence of the delays, we adopt a Razumikhin approach. The underlying idea of this approach is to treat the delayed variables as system uncertainties. The advantage of this approach is that one works in the more familiar territory of stability analysis for delay-free systems in the context of ISS instead of carrying...
Show moreIn this work, we investigate input-to-state stability (ISS) and other related stability properties for control systems with time-delays. To overcome the complexity caused by the presence of the delays, we adopt a Razumikhin approach. The underlying idea of this approach is to treat the delayed variables as system uncertainties. The advantage of this approach is that one works in the more familiar territory of stability analysis for delay-free systems in the context of ISS instead of carrying out stability analysis on systems of functional differential equations. Our first step is to provide criteria on ISS and input-to-input stability properties based on the Razumikhin approach. We then turn our attention to large-scale interconnected systems. It has been well recognized that the small-gain theory is a powerful tool for stability analysis of interconnected systems. Using the Razumikhin approach, we develop small-gain theorems for interconnected systems consisting of two or more subs ystems with time-delays present either in the interconnection channels or within the subsystems themselves. As an interesting application, we apply our results to an existing model for hematopoesis, a blood cell production process,and improve the previous results derived by linear methods. Another important stability notion in the framework of ISS is the integral ISS (iISS) property. This is a weaker property than ISS, so it supplies to a larger class of systems. As in the case of ISS, we provide Razumikhin criteria on iISS for systems with delays. An example is presented to illustrate that though very useful in practice, the Razumikhin approach only provides sufficient conditions, not equivalent conditions. Finally, we address stability of time-varying systems with delays in the framework of ISS., In particular, we consider Lyapunov-Razumikhin functions whose decay rates are affected by time-varying functions that can be zero or even negative on some sets of non-zero measure. Our motivation is that it is often less demanding to find or construct such a Lyapunov function than one with a uniform decay rate. We also extend our small-gain theorems to the time-varying case by treating the time-varying system as an auxiliary time-invariant system.
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Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3352880
Subject Headings: Nonlinear systems, Simulation methods, Control theory, Stability, Mathematical models, Mathematical optimization
Format: Document (PDF)

Title: Leveled flight control of an unmanned underwater vehicle operating in a wave induced environment.
Creator: Potesta, Joshua J., An, Edgar, Florida Atlantic University, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: Autonomous Underwater Vehicle (AUV) depth control methods typically use a pressure sensor to measure the depth, which results in the AUV following the trajectory of the surface waves. Through simulations, a controller is designed for the Ocean Explorer AUV with the objective of the AUV holding a constant depth below the still water line while operating in waves. This objective is accomplished by modeling sensors and using filtering techniques to provide the AUV with the depth below the still...
Show moreAutonomous Underwater Vehicle (AUV) depth control methods typically use a pressure sensor to measure the depth, which results in the AUV following the trajectory of the surface waves. Through simulations, a controller is designed for the Ocean Explorer AUV with the objective of the AUV holding a constant depth below the still water line while operating in waves. This objective is accomplished by modeling sensors and using filtering techniques to provide the AUV with the depth below the still water line. A wave prediction model is simulated to provide the controller with knowledge of the wave disturbance before it is encountered. The controller allows for depth keeping below the still water line with a standard deviation of 0.04 and 0.65 meters for wave amplitudes of 0.1-0.25 and 0.5-2 meters respectively and wave frequencies of 0.35-1.0 𝑟𝑎𝑑⁄𝑠𝑒𝑐, and the wave prediction improves the depth control on the order of 0.03 meters.
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Date Issued: 2014
PURL: http://purl.flvc.org/fau/fd/FA00004149, http://purl.flvc.org/fau/fd/FA00004149
Subject Headings: Feedback control systems, Nonlinear control theory, Remote submersibles -- Design and construction, Vehicles, Remotely piloted -- Mathematical models
Format: Document (PDF)

Title: Design and tuning of fuzzy control surface with Bezier functions.
Creator: Wongsoontorn, Songwut., Florida Atlantic University, Zhuang, Hanqi, College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description: Design and Tuning a fuzzy logic controller (FLCs) are usually done in two stages. In the first stage, the structure of a FLC is determined based on physical characteristics of the system. In the second stage, the parameters of the FLC are selected to optimize the performance of the system. The task of tuning FLCs can be performed by a number of methods such as adjusting control gains, changing membership functions, modifying control rules and varying control surfaces. A method for the design...
Show moreDesign and Tuning a fuzzy logic controller (FLCs) are usually done in two stages. In the first stage, the structure of a FLC is determined based on physical characteristics of the system. In the second stage, the parameters of the FLC are selected to optimize the performance of the system. The task of tuning FLCs can be performed by a number of methods such as adjusting control gains, changing membership functions, modifying control rules and varying control surfaces. A method for the design and tuning of FLCs through modifying their control surfaces is presented in this dissertation. The method can be summarized as follows. First, fuzzy control surfaces are modeled with Bezier functions. Shapes of the control surface are then adjusted through varying Bezier parameters. A Genetic Algorithm (GA) is used to search for the optimal set of parameters based on the control performance criteria. Then, tuned control surfaces are sampled to create rule-based FLCs. To further improve the system performance, continuity constraints of the curves are imposed. Under the continuity constraints with the same number of tunable parameters, one can obtain more flexible curves that have the potential to improve the overall system performance. An important issue is to develop a new method to self-tune a fuzzy PD controller. The method is based on two building blocks: (I) Bezier functions used to model the control surfaces of the fuzzy PD controller; and, shapes of control surfaces are then adjusted by varying Bezier parameters. (II) The next step involves using a gradient-based optimization algorithm with which the input scaling factors and Bezier parameters are on-line tuned until the controller drives the output of the process as close as possible to the reference position. To protect vendors and consumers from being victimized, various trust models have been used in e-commerce practices. However, a strict verification and authentication process may pose unnecessary heavy cost to the vendor. As an application of the control strategy proposed, this dissertation presents a solution to the reduction of costs of a vendor. With two fuzzy variables (price, credit-history), a trust-surface can be tuned to achieve an optimal solution in terms of profit margin of the vendor. With this new approach, more realistic trust decisions can be reached.
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Date Issued: 2005
PURL: http://purl.flvc.org/fcla/dt/12172
Subject Headings: Fuzzy systems, Nonlinear control theory, Process control--Data processing, Fuzzy logic, Intelligent control systems
Format: Document (PDF)

Title: High performance and robust control.
Creator: Xu, Min., Florida Atlantic University, Smith, Samuel M., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: It is desirable to have robust high performance nonlinear control with a model-free design approach for the real time automatic control of practical industrial processes. The field has seen the application of Sliding Mode Controllers (SMCs). SMCs are nonlinear robust controllers, however most design approaches related to SMCs are model-based approaches. PID controllers and some Fuzzy Logic Controllers (FLCs) are model-free controllers, however their robustness is not integrated into their...
Show moreIt is desirable to have robust high performance nonlinear control with a model-free design approach for the real time automatic control of practical industrial processes. The field has seen the application of Sliding Mode Controllers (SMCs). SMCs are nonlinear robust controllers, however most design approaches related to SMCs are model-based approaches. PID controllers and some Fuzzy Logic Controllers (FLCs) are model-free controllers, however their robustness is not integrated into their design parameters directly. This dissertation presents two new types of robust high performance nonlinear controllers with model-free design approaches. One introduces fuzzy logic to a model-free SMC which is a simple saturation function incorporating three design parameters. Due to the interpolative nature of fuzzy control, a TSK type FLC with the model-free SMCs as its rule's consequents will produce a controller with a nonlinear sliding curve and a nonlinear boundary layer. We call this controller a Fuzzy Sliding Controller (FSC). The other uses a new type of Variable Structure Controller (VSC), which intentionally switches from one controller to another controller during a step response. In conventional approaches to VSC, the control surface does not change its shape during a step response. The new type of VSC intentionally changes the shape of the control surface during the step response. This technique is analogous to that technique employed in image processing called "morphing" where a given image gradually changes over time to the image of a different entity. In order to avoid confusion with the conventional approach to a VSC, we use the term "Morphological" Controller (MC) for the VSC of the new type. The performance and robustness with respect to parameter variations, disturbances and slow sample rates of the proposed controllers are studied in detail with a DC motor and an Inverted Pendulum System. As a means to verify the proposed controllers in practical cases, we design the model-free SMC, the FSC and the MC for the highly nonlinear and uncertain dynamics of an Autonomous Underwater Vehicle, Ocean Voyager II. It is shown that the proposed controllers are high performance and high robustness controllers.
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Date Issued: 1996
PURL: http://purl.flvc.org/fcla/dt/12446
Subject Headings: Nonlinear control theory, Automatic control, Feedback control systems, Feedforward control systems
Format: Document (PDF)

Title: Nonlinear resonance: determining maximal autoresonant response and modulation of spontaneous otoacoustic emissions.
Creator: Witkov, Carey., Charles E. Schmidt College of Science, Center for Complex Systems and Brain Sciences
Abstract/Description: Sustained resonance in a linear oscillator is achievable with a drive whose constant frequency matches the resonant frequency of the oscillator. In oscillators with nonlinear restoring forces, i.e., Dung-type oscillators, resonant frequency changes with amplitude, so a constant frequency drive generates a beat oscillation instead of sustained resonance. Dung-type oscillators can be driven into sustained resonance, called autoresonance (AR), when drive frequency is swept in time to match the...
Show moreSustained resonance in a linear oscillator is achievable with a drive whose constant frequency matches the resonant frequency of the oscillator. In oscillators with nonlinear restoring forces, i.e., Dung-type oscillators, resonant frequency changes with amplitude, so a constant frequency drive generates a beat oscillation instead of sustained resonance. Dung-type oscillators can be driven into sustained resonance, called autoresonance (AR), when drive frequency is swept in time to match the changing resonant frequency of the oscillator. It is found that near-optimal drive linear sweep rates for autoresonance can be estimated from the beat oscillation resulting from constant frequency excitation. Specically, a least squares estimate of the slope of the Teager-Kaiser instantaneous frequency versus time plot for the rising half-cycle of the beat response to a stationary drive provides a near-optimal estimate of the linear drive sweep rate that sustains resonance in the pendulum, Dung and Dung-Van der Pol oscillators. These predictions are confirmed with model-based numerical simulations. A closed-form approximation to the AM-FM nonlinear resonance beat response of a Dung oscillator driven at its low-amplitude oscillator frequency is obtained from a solution to an associated Mathieu equation. AR time responses are found to evolve along a Mathieu equation primary resonance stability boundary. AR breakdown occurs at sweep rates just past optimal and map to a single stable point just off the Mathieu equation primary resonance stability boundary. Optimal AR sweep rates produce oscillating phase dierences with extrema near 90 degrees, allowing extended time in resonance. AR breakdown occurs when phase difference equals 180 degrees. Nonlinear resonance of the van der Pol type may play a role in the extraordinary sensitivity of the human ear., The mechanism for maintaining the cochlear amplifier at its critical point is currently unknown. The possibility of open-loop control of cochlear operating point, maintaining criticality on average through periodically varying damping (super-regeneration) motivates a study of spontaneous otoacoustic emission (SOAE) amplitude modulation on a short (msec) time scale. An example of periodic amplitude modulation within a wide filter bandwidth is found that appears to be a beat oscillation of two SOAEs.
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Date Issued: 2011
PURL: http://purl.flvc.org/FAU/3174314
Subject Headings: Otoacoustic emissions, Chaotic behavior in systems, Nonlinear theories, Pattern recognition systems
Format: Document (PDF)

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