A NOVEL STABILITY CONDITION AND ITS APPLICATION TO GA-BASED FUZZY CONTROL FOR NONLINEAR SYSTEMS WITH UNCERTAINTY

In this study, we strive to combine the advantages of fuzzy theory, genetic algorithms (GA), H-infinite tracking control schemes, smooth control and adaptive laws to design an adaptive fuzzy sliding model controller for the rapid and efficient stabilization of complex and nonlinear systems. First, we utilize a reference model and a fuzzy model (both involvingrules) to describe and well-approximate an uncertain, nonlinear plant. The FLC rules and the consequent parameter are decided on via GA. A boundary-layer function is introduced into these updated laws to cover modeling errors and to guarantee that the state errors converge into a specified error bound. After this, a H-infinite tracking problem is characterized. We solve an eigenvalue problem (EVP), and derive a modified adaptive neural network controller (MANNC) to simultaneously stabilize and control the system and achieve H-infinite control performance.

In this study, we propose a method of stability analysis for a GA-Based reference ANNC capable of handling these types of problems for a nonlinear system. The initial values of the consequent parameter vector are decided via a genetic algorithm (GA) after which a modified adaptive law is derived based on Lyapunov stability theory to control the nonlinear system for tracking a user-defined reference model. The requirement of Kalman-Yacubovich lemma is fulfilling. A boundary-layer function is introduced into these updating laws to cover parameter and modeling errors, and to guarantee that the state errors converge into a specified error bound. After this, an adaptive neural network controller (ANNC) is derived to simultaneously stabilize and control the system.

Generally, the biggest difficulty when designing a neural network controller that will be capable of rapidly and efficiently controlling complex and nonlinear systems is selection of the most appropriate initial values for the parameter vector. Overcoming the coupling effects of each degree-of-freedom is also difficult in multi-variable system control. In this study, an intelligent adaptive controller is proposed to handle these behaviors. First of all, an uncertain and nonlinear plant, for the tracking of a reference trajectory, is well approximated via radial basis function networks. Next, the adjustable parameters of the intelligent system are initialized using a genetic algorithm. Then, novel online parameter tuning algorithms are developed, based on the Lyapunov stability theory. A boundary-layer function is introduced into these updating laws to cover parameter and modeling errors, and to guarantee that the state errors converge to within a specified error bound. The non-square multi-variable system can be decoupled into several reduced-order isolated square multi-variable subsystems using a singular perturbation scheme for different types of time-scale stability analysis. Following this, a decoupled adaptive neural network controller is derived simultaneously to stabilize and control the system. Finally, an example, in the form of a numerical simulation, is provided to demonstrate the effectiveness of the control methodology, which is shown to rapidly and efficiently control nonlinear multi-variable systems.

This book presents a systematic framework targeting at fuzzy modeling and fuzzy control of nonlinear systems with uncertainties. The book is organized into three major parts incorporating 13 chapters. The first part contains four chapters focusing on the modeling of nonlinear dynamical systems by using fuzzy logic. The second part includes five chapters in which fuzzy inference and control techniques are addressed. The final part consists of four chapters, which covers several advanced topics in fuzzy control ranging from controller and filter design to chaotification of fuzzy systems and feedforward fuzzy control of nonlinear systems via Fourier integrals. One of the major contributions of this book is that it presents the latest original research developments in the field. It provides rich examples and references, too. It is a valuable resource for those researchers and practitioners interested in expanding their knowledge from fuzzy logic and applications to nonlinear dynamical systems.

Many existing stability analysis methods for fuzzy logic control systems like TS fuzzy model based methods usually tackle plants that are linear with respect to control. However, these methods may be difficult to apply to plants with dead zones. This paper presents an improved stability analysis method to resolve this difficulty. Our proposed method employs a Lyapunov function to prove the stability of nonlinear fuzzy logic control systems with asymmetric dead zone and saturation. An illustrative example will be given to demonstrate the ability of the method.

On observer-based fault detection for nonlinear systems

In this paper finite-time stabilization of nonlinear affine systems, is considered. First we provide a formula for a finite-time stabilizing state feedback control law, for the last class of system. Then we extend the result to the case of a norm-bounded uncertain system and a polytopic uncertain system stabilization are given. Some numerical examples are given to illustrate the main result.

In this paper, some recent results on systematic design of model based fuzzy controllers for nonlinear systems with Takagi-Sugeno (T-S) fuzzy models are discussed. These methods are based on finding a common Lyapunov matrix and state feedback gains for the closed loop T-S fuzzy model using linear matrix inequalities. However, all of these methods assume that the states are available for measurement, while in reality this is not the case. To solve this problem, the notion of fuzzy observer is introduced and a separation theorem for the observer/controller system is stated and proof sketch is presented.

We show how frequency domain design procedures can be effectively used in nonlinear fuzzy control systems. For this purpose, theoretical justifications of the approach discussed here are provided to show that solid notions from nonlinear system and control theory can be successfully applied in the fuzzy control domain. The methodology proposed is very simple, but powerful, effective and practical. In addition, it supports systematic control system design and stability analysis in the frequency domain for systems described by mathematical, linguistic or experimental models. Several case studies are included to illustrate the usefulness of frequency response in conventional fuzzy control systems analysis and design.

A robustness design of fuzzy control is proposed in this paper to overcome the effect of modeling error between nonlinear system and Takagi-Sugeno (T-S) fuzzy model. In terms of Lyapunov's direct method, a stability criterion is derived to guarantee the asymptotic stability of nonlinear interconnected systems. Based on the decentralized control scheme and this criterion, a set of model-based fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear interconnected systems. Finally, an example is given to illustrate the concepts discussed throughout the paper.

This paper proposes shared control in wireless-based remote stabilization for nonlinear systems. Shared control that is newly named in this paper can be regarded as simultaneous stabilization of plural nonlinear systems (in different places) by a single (common) controller. This paper consists of two parts. The first part addresses the basis of wireless-based remote stabilization for a single nonlinear system with time-varying delay. We derive a delay-dependent sufficient condition for ensuring the stability of Takagi-Sugeno (T-S) fuzzy models with time-varying delays that are globally (or semiglobally at least) equivalent to nonlinear systems with wireless communication time delays. A feature of the derived condition is to be able to obtain the maximum time delay for ensuring the stability of wireless-based remote control system for given feedback gains. The second part presents shared control of plural nonlinear systems via a single controller. To design a (common) shared controller to stabilize plural nonlinear systems, we derive also a shared control version of the stability condition for T-S fuzzy models with time-varying delays. Design examples demonstrate the utility of this proposed design approach.

A genetic algorithm (GA)-based optimized hybrid controller which is suitable for controlling both linear and nonlinear systems is proposed. The proposed controller, consisting of a linear proportional-integral-derivative (PID) controller and a linear fuzzy logic controller, employs a GA to facilitate optimal tuning of controller gains. A two-input normalized fuzzy logic controller with a linearly-defined fuzzy space is developed to replace the conventional PI controller in the PID connective structure. A closed-form analysis shows that the proposed fuzzy logic controller is capable of generating nonlinear output. Simulation results for a typical second-order over-damped process and a tactical missile model demonstrate that the proposed controller outperforms other existing controllers, is robust and has great potential in many industrial applications.

The paper describes the development of two different type-2 adaptive fuzzy logic controllers and their use for the control of a non linear system that is characterized by the presence of bifurcations and parameter uncertainty. Although a type-2 fuzzy logic controller is able to handle the non linearities and the uncertainties present in a system, its robustness and effectiveness can be increased by the use of an opportune adaptive algorithm. A simulation study was conducted to compare the behavior of adaptive controllers with that of simple type-1 and type-2 fuzzy logic controllers. The system to be controlled, used for the simulation, is a continuous bioreactor for the treatment of mixed wastes in which a culture of Pseudomonas Putida is carried out while phenol and glucose are carbon and energy sources. From simulations results it can be seen that both adaptive controllers, but in particular the self tuning controller, have a better performance being able to eliminate oscillations that are present with basic fuzzy controllers.

In this paper a two-step design methodology of the near optimal Mamdani type fuzzy logic controller (FLC) has been applied to three types of systems: a linear time invariant system (LTI), a LTI system with time delay and an nonlinear system. In the first step, the tuning/learning procedure of a data base/knowledge base of the FLC is based on the model of the system using genetic algorithms (GA). The achieved solution is the optimal one with regard to the model of the system. In the second step experiments are performed on the real system at the vicinity of the optimum (achieved by GA) and using response surface methodology (RSM) control parameters are readjusted in order to achieve the near optimal solution for the real system. The proposed two step methodology gives a systematic way of the near optimal FLC tuning/learning when confronted with the real system and a very efficient combination of off-line and online part of design procedure.

Genetic algorithm is heuristic searching algorithm which based on nature selection of mechanism and nature genetic. The basic concept that inspires the genetic algorithm is that evolution theory. In the process of searching the best solution on classic genetic algorithm often occurs optimum local. Optimum local is a common problem which is often occurs in genetic algorithm, and one of the reasons is that because of the population diversity. If population diversity is too low is led to optimum local, and if it is too high caused more times to look for the best solution. Mutation operator plays an important role in the process of genetic algorithm to manage that population diversity and an important element of mutation operator is mutation rate. On classic genetic algorithm that mutation rate is set in the beginning while the process of genetic algorithm depends on how many generations are. Therefore is needed to control mutation rate in generation. Controlling mutation operator, especially mutation rate based on Fuzzy Logic Controller (FLC) to manage population diversity, not too high or too low, in order to get optimal result. Evaluation is done 10 times execution by comparing the performance of standard genetic algorithm (GA), IAG and genetic algorithm based on Fuzzy Logic Controller (FLC) and experimental results show that there is an improvement on genetic algorithm performance based on FLC. Keywords: Genetic Algorithm, Fuzzy Logic Controller (FLC), Mutation Rate