# Browsing by Subject "Nonlinear control theory"

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Item Adaptive fuzzy nonlinear internal model control strategy(Texas Tech University, 1996-12) Kreesuradej, WorapojShow more Proportional-Integratal Derivative like Fuzzy Logic Controllers (PID-FLCs), have been used for a variety of nonlinear control problems. Basically, a PID-FLC contains a control algorithm in the form of linguistic fuzzy rules. The problem with PID-FLCs is that there is no systematic design for developing fuzzy rules. It is also difficult to develop the controllers to meet specific requirements on control performances. In this dissertation, a nonlinear internal model control (NIMC) structure and an adaptive fuzzy NIMC strategy have been proposed to overcome the problems of PIDFLCs. One of the attractive features of the NIMC structure is that the relations between some designed parameters and the performance of the control system can be found explicitly. Thus, this control structure allows designers to systematically construct the fuzzy control. An adaptive fuzzy NIMC strategy has been proposed. The proposed strategy has two attractive features. First, the strategy provides an on-line adaptation to improve control performance and to keep the closed-loop system stable. Second, a fuzzy basis function (FBF) expansion is used to implement the controller. The use of the FBF expansion enhances the ability of the strategy to control practical nonUnear systems whose exact mathematical models are difficult to obtain. Finally, Simulation studies of controlling four nonlinear systems (e.g., a pendulum, an inverted pendulum, a forced Van der Pol equation, and a two-link cylindrical robot manipulator) have been conducted. The simulation results show that the proposed strategy has successfully controlled the four nonlinear systems.Show more Item An incremental optimizing controller for constrained nonlinear processes(Texas Tech University, 1998-08) Natarajan, SivaShow more Chemical process control today, has its own share of problems and deficiencies and there is plenty of room for improvement. These problems and issues include nonlinearity, multivariable processes, interaction and coupling, disturbance rejection, constraint handling, computational speed, ease of design and tuning, degrees of freedom, initialization and transfers, and ill-behaved dynamics. The conventional PI/PID controller is still largely used in industrial control loops today. But, it is essentially a linear controller and requires a lot of tack-on fixes to cope with the above mentioned problems. This makes its design complex and the effort required quite laborious. Also, advanced control algorithms like Model Predictive Control entail computational complexity when it comes to dealing with process nonlinearity. In this work, a novel nonlinear control approach called Incremental Optimizing Control (IOC), has been developed. The key embodiment of this control approach is the prediction of process gains and the incremental changes based on it. Gain prediction is done using neural network models that facilitate rapid and efficient computation. Constraints and degrees of freedom issues are solved by optimization. This approach has the potential to tackle all of the problems/issues mentioned in the previous paragraph with the exception of ill-behaved dynamics. Since for a lot of chemical processes, nonlinearity rather than ill-behaved dynamics is the dominant problem, this approach should therefore have its own significant applications. Besides coping with nonlinearity, IOC has the ability to handle constraints, take care of interaction effects, provide good disturbance rejection, be simplistic in design and be computationally less expensive. The IOC approach has been developed for Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) processes, starting from basic principles. Theoretical analyses place this approach on firm fundamental ground. Excellent results have been obtained from the use of IOC on a nonlinear, multivariable, multicomponent flash process. These include very good setpoint tracking and disturbance rejection, effective decoupling and excellent constraint handling.Show more Item Analysis and Control of Non-Affine, Non-Standard, Singularly Perturbed Systems(2012-09-18) Narang, AnshuShow more This dissertation addresses the control problem for the general class of control non-affine, non-standard singularly perturbed continuous-time systems. The problem of control for nonlinear multiple time scale systems is addressed here for the first time in a systematic manner. Toward this end, this dissertation develops the theory of feedback passivation for non-affine systems. This is done by generalizing the Kalman-Yakubovich-Popov lemma for non-affine systems. This generalization is used to identify conditions under which non-affine systems can be rendered passive. Asymptotic stabilization for non-affine systems is guaranteed by using these conditions along with well-known passivity-based control methods. Unlike previous non-affine control approaches, the constructive static compensation technique derived here does not make any assumptions regarding the control influence on the nonlinear dynamical model. Along with these control laws, this dissertation presents novel hierarchical control design procedures to address the two major difficulties in control of multiple time scale systems: lack of an explicit small parameter that models the time scale separation and the complexity of constructing the slow manifold. These research issues are addressed by using insights from geometric singular perturbation theory and control laws are designed without making any assumptions regarding the construction of the slow manifold. The control schemes synthesized accomplish asymptotic slow state tracking for multiple time scale systems and simultaneous slow and fast state trajectory tracking for two time scale systems. The control laws are independent of the scalar perturbation parameter and an upper bound for it is determined such that closed-loop system stability is guaranteed. Performance of these methods is validated in simulation for several problems from science and engineering including the continuously stirred tank reactor, magnetic levitation, six degrees-of-freedom F-18/A Hornet model, non-minimum phase helicopter and conventional take-off and landing aircraft models. Results show that the proposed technique applies both to standard and non-standard forms of singularly perturbed systems and provides asymptotic tracking irrespective of the reference trajectory. This dissertation also shows that some benchmark non-minimum phase aerospace control problems can be posed as slow state tracking for multiple time scale systems and techniques developed here provide an alternate method for exact output tracking.Show more Item Control of a nonlinear multivariable system with adaptive critic designs(Texas Tech University, 1997-05) Visnevski, Nikita A.Show more A family of Adaptive Critic Designs (ACD) was proposed by Werbos (1992) as a new optimization technique combining together concepts of reinforcement learning and backpropagation. The goal of each design is to find an approximation of the cost-to-go function from the Bellman equation of dynamic programming or some function related to it, and then find the optimal solution of the problem by applying a reinforcement learning technique. In ACD we have two networks called critic and action (a substitute name for "controller" in the ACD literature), the action network trying to minimize an approximation of the cost-to-go. There are three basic implementations of ACD called Heuristic Dynamic Programming (HDP), Dual Heuristic Programming (DHP), and Globalized Dual Heuristic Programming (GDHP) (Prokhorov & Wunsch, to appear).Show more Item Identification and fuzzy logic control of nonlinear dynamical systems(Texas Tech University, 1995-05) Kaymaz, EmreShow more A generalized controller based on fuzzy clustering and fuzzy generalized predictive control has been developed for nonlinear systems. The proposed controller is particularly useful when the dynamics of the nonlinear system to be controlled are difficult to yield exact solutions and the system specification can be obtained in terms of crisp input-output pairs. It inherits the advantages of both fuzzy logic and predictive control. The identification of the nonlinear mapping of the system to be controlled is realized by a three-layer feed-forward neural network model employing the input-output data obtained from the system. The speed of convergence of the neural network is improved by the introduction of a fuzzy logic controlled backpropagation learning algorithm. The use of fuzzy clustering facilitates automatic generation of membership relations of the input-output data. Unlike the linguistic fuzzy logic controller which requires approximate knowledge of the shape and the numbers of the membership functions in the input and output universes of the discourse, this integrated neuro-fuzzy approach allows one to find the fuzzy relations and the membership functions more accurately. Furthermore, there is no need for tuning the controller. The proposed controller is applied to a nonlinear heating/cooling system and a multilink robot manipulator and it is shown that its performance is superior to the performances of the currently employed conventional controllers both in terms of accuracy and energy consumption.Show more Item Noncertainty equivalent nonlinear adaptive control and its applications to mechanical and aerospace systems(2007) Seo, Dong Eun, 1973-; Akella, Maruthi Ram, 1972-Show more Adaptive control has long focused on establishing stable adaptive control methods for various nonlinear systems. Existing methods are mostly based on the certainty equivalence principle which states that the controller structure developed in the deterministic case (without uncertain system parameters) can be used for controlling the uncertain system along by adopting a carefully determined parameter estimator. Thus, the overall performance of the regulating/tracking control depends on the performance of the parameter estimator, which often results in the poor closed-loop performance compared with the deterministic control because the parameter estimate can exhibit wide variations compared to their true values in general. In this dissertation we introduce a new adaptive control method for nonlinear systems where unknown parameters are estimated to within an attracting manifold and the proposed control method always asymptotically recovers the closed-loop error dynamics of the deterministic case control system. Thus, the overall performance of this new adaptive control method is comparable to that of the deterministic control method, something that is usually impossible to obtain with the certainty equivalent control method. We apply the noncertainty equivalent adaptive control to study application arising in the n degree of freedom (DOF) robot control problem and spacecraft attitude control. Especially, in the context of the spacecraft attitude control problem, we developed a new attitude observer that also utilizes an attracting manifold, while ensuring that the estimated attitude matrix confirms at all instants to the special group of rotation matrices SO(3). As a result, we demonstrate for the first time a separation property of the nonlinear attitude control problem in terms of the observer/controller based closed-loop system. For both the robotic and spacecraft attitude control problems, detailed derivations for the controller design and accompanying stability proofs are shown. The attitude estimator construction and its stability proof are presented separately. Numerical simulations are extensively performed to highlight closed-loop performance improvement vis-a-vis adaptive control design obtained through classical certainty equivalence based approaches.Show more Item Nonlinear continuous feedback controllers(Texas A&M University, 2004-09-30) Sitharaman, Sai GaneshShow more Packet-switched communication networks such as today's Internet are built with several interconnected core and distribution packet forwarding routers and several sender and sink transport agents. In order to maintain stability and avoid congestion collapse in the network, the sources control their rate behavior and voluntarily adjust their sending rates to accommodate other sources in the network. In this thesis, we study one class of sender rate control that is modeled using continuous first-order differential equation of the sending rates. In order to adjust the rates appropriately, the network sends continuous packet-loss feedback to the sources. We study a form of closed-loop feedback congestion controllers whose rate adjustments exhibit a nonlinear form. There are three dimensions to our work in this thesis. First, we study the network optimization problem in which sources choose utilities to maximize their underlying throughput. Each sender maximizes its utility proportional to the throughput achieved. In our model, sources choose a utility function to define their level of satisfaction of the underlying resource usages. The objective of this direction is to establish the properties of source utility functions using inequality constrained bounded sets and study the functional forms of utilities against a chosen rate differential equation. Second, stability of the network and tolerance to perturbation are two essential factors that keep communication networks operational around the equilibrium point. Our objective in this part of the thesis is to analytically understand the existence of local asymptotic stability of delayed-feedback systems under homogeneous network delays. Third, we propose a novel tangential controller for a generic maximization function and study its properties using nonlinear optimization techniques. We develop the necessary theoretical background and the properties of our controller to prove that it is a better rate adaptation algorithm for logarithmic utilities compared to the well-studied proportional controllers. We establish the asymptotic local stability of our controller with upper bounds on the increase / decrease gain parameters.Show more Item Robust non-linear control through neuroevolution(2003) Gomez, Faustino John; Miikkulainen, RistoShow more Many complex control problems require sophisticated solutions that are not amenable to traditional controller design. Not only is it difficult to model real world systems, but often it is unclear what kind of behavior is required to solve the task. Reinforcement learning approaches have made progress in such problems, but have so far not scaled well. Neuroevolution, has improved upon conventional reinforcement learning, but has still not been successful in full-scale, non-linear control problems. This dissertation develops a methodology for solving real world control tasks consisting of three components: (1) an efficient neuroevolution algorithm that solves difficult non-linear control tasks by coevolving neurons, (2) an incremental evolution method to scale the algorithm to the most challenging tasks, and (3) a technique for making controllers robust so that they can transfer from simulation to the real world. The method is faster than other approaches on a set of difficult learning benchmarks, and is used in two full-scale control tasks demonstrating its applicability to real world problems.Show more Item Structural analysis, design and optimization of nonlinear control systems using the linear algebraic equivalence of nonlinear controllers(2003) Gwak, Kwan-woong; Masada, Glenn Y.Show more