Lyapunov-Based Robust and Adaptive Control Design for nonlinear Uncertain Systems

The control of systems with uncertain nonlinear dynamics is an important field of control science attracting decades of focus. In this dissertation, four different control strategies are presented using sliding mode control, adaptive control, dynamic compensation, and neural network for a nonlinear aeroelastic system with bounded uncertainties and external disturbance. In Chapter 2, partial state feedback adaptive control designs are proposed for two different aeroelastic systems operating in unsteady flow. In Chapter 3, a continuous robust control design is proposed for a class of single input and single output system with uncertainties. An aeroelastic system with a trailingedge flap as its control input will be considered as the plant for demonstration of effectiveness of the controller. The controller is proved to be robust by both athematical proof and simulation results. In Chapter 3, a robust output feedback control strategy is discussed for the vibration suppression of an aeroelastic system operating in an unsteady incompressible flowfield. The aeroelastic system is actuated using a combination of leading-edge (LE) and trailing-edge (TE) flaps in the presence of different kinds of gust disturbances. In Chapter 5, a neural-network based model-free controller is designed for an aeroelastic system operating at supersonic speed. The controller is shown to be able to effectively asymptotically stabilize the system via both a Lyapunov-based stability proof and numerical simulation results

Exponential ε-regulation for multi-input nonlinear systems using neural networks

This paper considers the problem of robust exponential ε-regulation for a class of multi-input nonlinear systems with uncertainties. The uncertainties appear not only in the feedback channel but also in the control channel. Under some mild assumptions, an adaptive neural network control scheme is developed such that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded and, under the control scheme with initial data starting in some compact set, the states of the closed-loop system is guaranteed to exponentially converge to an arbitrarily specified ε-neighborhood about the origin. The important contributions of the present work are that a new exponential uniformly ultimately bounded performance is proposed and that the design parameters and initial condition set can be determined easily. The development generalizes and improves earlier results for the single-input case. © 2005 IEEE.published_or_final_versio

Intelligent control of a class of nonlinear systems

The objective of this study is to improve and propose new fuzzy control algorithms for a class of nonlinear systems. In order to achieve the objectives, novel stability theorems as well as modeling techniques are also investigated. Fuzzy controllers in this work are designed based on the fuzzy basis function neural networks and the type-2 Takagi-Sugeno fuzzy models. For a class of single-input single-output nonlinear systems, a new stability condition is derived to facilitate the design process of proportional-integral Mamdani fuzzy controllers. The stability conditions require a new technique to calculate the dynamic gains of nonlinear systems represented by fuzzy basis function network models. The dynamic gain of a fuzzy basis function network can be approximated by finding the maximum of norm values of the locally linearized systems or by solving a non-smooth optimal control problem. Based on the new stability theorem, a multilevel fuzzy controller with self-tuning algorithm is proposed and simulated in a tower crane control system. For a class of multi-input multi-output nonlinear systems with measurable state variables, a new method for modeling unstructured uncertainties and robust control of unknown nonlinear dynamic systems is proposed by using a novel robust Takagi-Sugeno fuzzy controller. First, a new training algorithm for an interval type-2 fuzzy basis function network is presented. Next, a novel technique is derived to convert the interval type-2 fuzzy basis function network to an interval type-2 Takagi-Sugeno fuzzy model. Based on the interval type-2 Takagi-Sugeno and type-2 fuzzy basis function network models, a robust controller is presented with an adjustable convergence rate. Simulation results on an electrohydraulic actuator show that the robust Takagi-Sugeno fuzzy controller can reduce steady-state error under different conditions while maintaining better responses than the other robust sliding mode controllers can. Next, the study presents an implementation of type-2 fuzzy basis function networks and robust Takagi-Sugeno fuzzy controllers to data-driven modeling and robust control of a laser keyhole welding process. In this work, the variation of the keyhole diameter during the welding process is approximated by a type-2 fuzzy-basis-function network, while the keyhole penetration depth is modelled by a type-1 fuzzy basis function network. During the laser welding process, a CMOS camera integrated with the welding system was used to provide a feedback signal of the keyhole diameter. An observer was implemented to estimate the penetration depth in real time based on the adaptive divided difference filter and the feedback signal from the camera. A robust Takagi-Sugeno fuzzy controller was designed based on the fuzzy basis function networks representing the welding process with uncertainties to adjust the laser power to ensure that the penetration depth of the keyhole is maintained at a desired value. Experimental results demonstrated that the fuzzy models provided an accurate estimation of both the welding geometry and its variations due to uncertainties, and the robust Takagi-Sugeno fuzzy controller successfully reduced the penetration depth variation and improved the quality of the welding process

Nonlinear Model-Based Control for Neuromuscular Electrical Stimulation

Neuromuscular electrical stimulation (NMES) is a technology where skeletal muscles are externally stimulated by electrodes to help restore functionality to human limbs with motor neuron disorder. This dissertation is concerned with the model-based feedback control of the NMES quadriceps muscle group-knee joint dynamics. A class of nonlinear controllers is presented based on various levels of model structures and uncertainties. The two main control techniques used throughout this work are backstepping control and Lyapunov stability theory. In the first control strategy, we design a model-based nonlinear control law for the system with the exactly known passive mechanical that ensures asymptotical tracking. This first design is used as a stepping stone for the other control strategies in which we consider that uncertainties exist. In the next four control strategies, techniques for adaptive control of nonlinearly parameterized systems are applied to handle the unknown physical constant parameters that appear nonlinearly in the model. By exploiting the Lipschitzian nature or the concavity/convexity of the nonlinearly parameterized functions in the model, we design two adaptive controllers and two robust adaptive controllers that ensure practical tracking. The next set of controllers are based on a NMES model that includes the uncertain muscle contractile mechanics. In this case, neural network-based controllers are designed to deal with this uncertainty. We consider here voltage inputs without and with saturation. For the latter, the Nussbaum gain is applied to handle the input saturation. The last two control strategies are based on a more refined NMES model that accounts for the muscle activation dynamics. The main challenge here is that the activation state is unmeasurable. In the first design, we design a model-based observer that directly estimates the unmeasured state for a certain activation model. The second design introduces a nonlinear filter with an adaptive control law to handle parametric uncertainty in the activation dynamics. Both the observer- and filter-based, partial-state feedback controllers ensure asymptotical tracking. Throughout this dissertation, the performance of the proposed control schemes are illustrated via computer simulations

Analysis, filtering, and control for Takagi-Sugeno fuzzy models in networked systems

Copyright © 2015 Sunjie Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The fuzzy logic theory has been proven to be effective in dealing with various nonlinear systems and has a great success in industry applications. Among different kinds of models for fuzzy systems, the so-called Takagi-Sugeno (T-S) fuzzy model has been quite popular due to its convenient and simple dynamic structure as well as its capability of approximating any smooth nonlinear function to any specified accuracy within any compact set. In terms of such a model, the performance analysis and the design of controllers and filters play important roles in the research of fuzzy systems. In this paper, we aim to survey some recent advances on the T-S fuzzy control and filtering problems with various network-induced phenomena. The network-induced phenomena under consideration mainly include communication delays, packet dropouts, signal quantization, and randomly occurring uncertainties (ROUs). With such network-induced phenomena, the developments on T-S fuzzy control and filtering issues are reviewed in detail. In addition, some latest results on this topic are highlighted. In the end, conclusions are drawn and some possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 11301118 and 61174136, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130017, the Fundamental Research Funds for the Central Universities of China under Grant CUSF-DH-D-2013061, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany