Current Search: Nonlinear theories (x)
View All Items
Pages
 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 wellknown 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 twolink 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 wellknown 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 twolink 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 springloaded 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.
Show less  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 estimatedirected 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 nonlinear 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 TSKtype fuzzy logic (FL) controller and a Sliding Modetype controller for the uncertain nonlinear 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 nonlinear controllers with good global performance and without much a priori information about the desired control actions.
Show less  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, GuoQiang, 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 nonGaussian impulsive noise excitations and another subjected to combined harmonic and broadband 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.
Show less  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 crossentropy 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 twofolded: (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 informationtheoretic plane using crossentropy errormetrics. The research efforts envisaged enclave the following specific tasks: (i) Obtaining a general solution for the BernoulliRiccati equation to represent a single parameter family...
Show moreThe objectives of this research as deliberated in this dissertation are twofolded: (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 informationtheoretic plane using crossentropy errormetrics. The research efforts envisaged enclave the following specific tasks: (i) Obtaining a general solution for the BernoulliRiccati equation to represent a single parameter family of Sshaped (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 crossentropy errormetrics (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 errorentropy measures (in the informationtheoretic plane) so as to make them usable as errormetrics in the test domain. (v) Description and analysis of the dynamics of neural learning process in the informationtheoretic plane for both crisp and fuzzy attributes of input values. Relevant to these topics portraying the studies on nonlinear activity and crossentropy considerations visavis 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.
Show less  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 BasteroMilmanRuiz remain valid m the metric setting. We also show that the symmetrization by truncation method of MartfnMilmanPustylnik can be implemented in our generalized setting. Furthermore we also show that our methods can be adapted to deal with nondoubling measures.
Show less  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
 KarhunenLoeve decomposition for non stationary propulsor flow noise.
 Creator
 Kersulec, JeanLuc., 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 KarhunenLoeve 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 KarhunenLoeve 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.
Show less  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
 20110408
 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 "LangKobayashi" 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 "LangKobayashi" 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 crosscorrelation 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.
Show less  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.
Show less  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.
Show less  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
 Inputtostate stability properties for discretetime 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 inputtostate stability (scISS) property and related characterizations for discretetime 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 continuoustime nonlinear system can be extended to discretetime case.
 Date Issued
 1999
 PURL
 http://purl.flvc.org/fcla/dt/15688
 Subject Headings
 Discretetime 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 welldefined 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 selfinteraction 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.
Show less  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 threedimensional vector field possessing an inclinationflip 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 threedimensional vector field possessing an inclinationflip 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.
Show less  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 DUCKWLing 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 waterborne. In its operational zone, the vehicle's dynamics change dramatically as it transitions from being completely waterborne and buoyancy supported to being completely landborne and track supported. In the water environment, a cascaded, firstorder sliding mode controller was used to control the surge and...
Show moreThe DUCKWLing 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 waterborne. In its operational zone, the vehicle's dynamics change dramatically as it transitions from being completely waterborne and buoyancy supported to being completely landborne and track supported. In the water environment, a cascaded, firstorder 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 DUKWLing 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.
Show less  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 decisionmaking capabilities of unmanned surface vehicles (USVs) is presented in this work. A multiobjective framework is described where separate controllers command different behaviors according to a desired trajectory. Three behaviors are examined – transiting, stationkeeping 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 decisionmaking capabilities of unmanned surface vehicles (USVs) is presented in this work. A multiobjective framework is described where separate controllers command different behaviors according to a desired trajectory. Three behaviors are examined – transiting, stationkeeping 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 fullyactuated backstepping controller are proposed for each transiting, reversing and stationkeeping 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 gainscheduled 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.
Show less  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 timedelays.
 Creator
 Tiwari, Shanaz, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

In this work, we investigate inputtostate stability (ISS) and other related stability properties for control systems with timedelays. 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 delayfree systems in the context of ISS instead of carrying...
Show moreIn this work, we investigate inputtostate stability (ISS) and other related stability properties for control systems with timedelays. 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 delayfree 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 inputtoinput stability properties based on the Razumikhin approach. We then turn our attention to largescale interconnected systems. It has been well recognized that the smallgain theory is a powerful tool for stability analysis of interconnected systems. Using the Razumikhin approach, we develop smallgain theorems for interconnected systems consisting of two or more subs ystems with timedelays 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 timevarying systems with delays in the framework of ISS., In particular, we consider LyapunovRazumikhin functions whose decay rates are affected by timevarying functions that can be zero or even negative on some sets of nonzero 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 smallgain theorems to the timevarying case by treating the timevarying system as an auxiliary timeinvariant system.
Show less  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 0.10.25 and 0.52 meters respectively and wave frequencies of 0.351.0 𝑟𝑎𝑑⁄𝑠𝑒𝑐, and the wave prediction improves the depth control on the order of 0.03 meters.
Show less  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 rulebased 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 selftune 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 gradientbased optimization algorithm with which the input scaling factors and Bezier parameters are online 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 ecommerce 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, credithistory), a trustsurface 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.
Show less  Date Issued
 2005
 PURL
 http://purl.flvc.org/fcla/dt/12172
 Subject Headings
 Fuzzy systems, Nonlinear control theory, Process controlData 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 modelfree 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 modelbased approaches. PID controllers and some Fuzzy Logic Controllers (FLCs) are modelfree controllers, however their robustness is not integrated into their...
Show moreIt is desirable to have robust high performance nonlinear control with a modelfree 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 modelbased approaches. PID controllers and some Fuzzy Logic Controllers (FLCs) are modelfree 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 modelfree design approaches. One introduces fuzzy logic to a modelfree 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 modelfree 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 modelfree 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.
Show less  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., Dungtype oscillators, resonant frequency changes with amplitude, so a constant frequency drive generates a beat oscillation instead of sustained resonance. Dungtype 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., Dungtype oscillators, resonant frequency changes with amplitude, so a constant frequency drive generates a beat oscillation instead of sustained resonance. Dungtype 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 nearoptimal 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 TeagerKaiser instantaneous frequency versus time plot for the rising halfcycle of the beat response to a stationary drive provides a nearoptimal estimate of the linear drive sweep rate that sustains resonance in the pendulum, Dung and DungVan der Pol oscillators. These predictions are confirmed with modelbased numerical simulations. A closedform approximation to the AMFM nonlinear resonance beat response of a Dung oscillator driven at its lowamplitude 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 openloop control of cochlear operating point, maintaining criticality on average through periodically varying damping (superregeneration) 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.
Show less  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)