TS fuzzy approach for modeling, analysis and design of non-smooth dynamical systems

There has been growing interest in the past two decades in studying the physical model of dynamical systems that can be described by nonlinear, non-smooth differential equations, i.e. non-smooth dynamical systems. These systems exhibit more colourful and complex dynamics compared to their smooth counterparts; however, their qualitative analysis and design are not yet fully developed and still open to exploration. At the same time, Takagi-Sugeno (TS) fuzzy systems have been shown to have a great ability to represent a large class of nonlinear systems and approximate their inherent uncertainties. This thesis explores an area of TS fuzzy systems that have not been considered before; that is, modelling, stability analysis and design for non-smooth dynamical systems. TS fuzzy model structures capable of representing or approximating the essential dis- continuous dynamics of non-smooth systems are proposed in this thesis. It is shown that by incorporating discrete event systems, the proposed structure for TS fuzzy models, which we will call non-smooth TS fuzzy models, can accurately represent the smooth (or contin- uous) as well as non-smooth (or discontinuous) dynamics of different classes of electrical and mechanical non-smooth systems including (sliding and non-sliding) Filippov's systems and impacting systems. The different properties of the TS fuzzy modelling (or formalism) are discussed. It is highlighted that the TS fuzzy formalism, taking advantage of its simple structure, does not need a special platform for its implementation. Stability in its new notion of structural stability (stability of a periodic solution) is one of the most important issues in the qualitative analysis of non-smooth systems. An important part of this thesis is focused on addressing stability issues by extending non- smooth Lyapunov theory for verifying the stability of local orbits, which the non-smooth TS fuzzy models can contain. Stability conditions are proposed for Filippov-type and impacting systems and it is shown that by formulating the conditions as Linear Matrix inequalities (LMIs), the onset of non-smooth bifurcations or chaotic phenomena can be detected by solving a feasibility problem. A number of examples are given to validate the proposed approach. Stability robustness of non-smooth TS fuzzy systems in the presence of model uncertainties is discussed in terms of non-smoothness rather than traditional observer design. The LMI stabilization problem is employed as a building block for devising design strategies to suppress the unwanted chaotic behaviour in non-smooth TS fuzzy models. There have been a large number of control applications in which the overall closed-loop sys tem can be stabilized by switching between pre-designed sub-controllers. Inspired by this idea, the design part of this thesis concentrates on fuzzy-chaos control strategies for Filippov-type systems. These strategies approach the design problem by switching be- tween local state-feedback controllers such that the closed-loop TS fuzzy system of interest rapidly converges to the stable periodic solution of the system. All control strategies are also automated as a design problem recast on linear matrix inequality conditions to be solved by modern optimization techniques. Keywords: Takagi-Sugeno fuzzy systems, non-smooth Lyapunov theory, non-smooth dy- namical systems, piecewise-smooth dynamical systems, structural stability, discontinuity- induced bifurcation, chaos controllers, dc-dc converters, Filippov's system, impacting system, linear matrix inequalities.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Fuzzy synchronization of chaotic systems with hidden attractors

Chaotic systems are hard to synchronize, and no general solution exists. The presence of hidden attractors makes finding a solution particularly elusive. Successful synchronization critically depends on the control strategy, which must be carefully chosen considering system features such as the presence of hidden attractors. We studied the feasibility of fuzzy control for synchronizing chaotic systems with hidden attractors and employed a special numerical integration method that takes advantage of the oscillatory characteristic of chaotic systems. We hypothesized that fuzzy synchronization and the chosen numerical integration method can successfully deal with this case of synchronization. We tested two synchronization schemes: complete synchronization, which leverages linearization, and projective synchronization, capitalizing on parallel distributed compensation (PDC). We applied the proposal to a set of known chaotic systems of integer order with hidden attractors. Our results indicated that fuzzy control strategies combined with the special numerical integration method are effective tools to synchronize chaotic systems with hidden attractors. In addition, for projective synchronization, we propose a new strategy to optimize error convergence. Furthermore, we tested and compared different Takagi-Sugeno (T-S) fuzzy models obtained by tensor product (TP) model transformation. We found an effect of the fuzzy model of the chaotic system on the synchronization performance

Contributions to fuzzy polynomial techniques for stability analysis and control

The present thesis employs fuzzy-polynomial control techniques in order to improve the stability analysis and control of nonlinear systems. Initially, it reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems, such as the more relevant results about polynomial and fuzzy polynomial systems. The basic framework uses fuzzy polynomial models by Taylor series and sum-of-squares techniques (semidefinite programming) in order to obtain stability guarantees. The contributions of the thesis are: ¿ Improved domain of attraction estimation of nonlinear systems for both continuous-time and discrete-time cases. An iterative methodology based on invariant-set results is presented for obtaining polynomial boundaries of such domain of attraction. ¿ Extension of the above problem to the case with bounded persistent disturbances acting. Different characterizations of inescapable sets with polynomial boundaries are determined. ¿ State estimation: extension of the previous results in literature to the case of fuzzy observers with polynomial gains, guaranteeing stability of the estimation error and inescapability in a subset of the zone where the model is valid. ¿ Proposal of a polynomial Lyapunov function with discrete delay in order to improve some polynomial control designs from literature. Preliminary extension to the fuzzy polynomial case. Last chapters present a preliminary experimental work in order to check and validate the theoretical results on real platforms in the future.Pitarch Pérez, JL. (2013). Contributions to fuzzy polynomial techniques for stability analysis and control [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34773TESI

Design of Intelligent PID Controller for AVR System Using an Adaptive Neuro Fuzzy Inference System

This paper presents a hybrid approach involving signal to noise ratio (SNR) and particle swarm optimization (PSO) for design the optimal and intelligent proportional-integral-derivative (PID) controller of an automatic voltage regulator (AVR) system with uses an adaptive neuro fuzzy inference system (ANFIS). In this paper determined optimal parameters of PID controller with SNR-PSO approach for some events and use these optimal parameters of PID controller for design the intelligent PID controller for AVR system with ANFIS.  Trial and error method can be used to find a suitable design of anfis based an intelligent controller. However, there are many options including fuzzy rules, Membership Functions (MFs) and scaling factors to achieve a desired performance. An optimization algorithm facilitates this process and finds an optimal design to provide a desired performance. This paper presents a novel application of the SNRPSO approach to design an intelligent controller for AVR. SNR-PSO is a method that combines the features of PSO and SNR in order to improve the optimize operation. In order to emphasize the advantages of the proposed SNR-PSO PID controller, we also compared with the CRPSO PID controller. The proposed method was indeed more efficient and robust in improving the step response of an AVR system and numerical simulations are provided to verify the effectiveness and feasibility of PID controller of AVR based on SNRPSO algorithm.DOI:http://dx.doi.org/10.11591/ijece.v4i5.652

A Non-Fragile H∞ Output Feedback Controller for Uncertain Fuzzy Dynamical Systems with Multiple Time-Scales

This paper determines the designing of a non-fragile H∞ output feedback controller for a class of nonlinear uncertain dynamical systems with multiple timescales described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop a non-fragile H∞ output feedback controller which guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for this class of uncertain fuzzy dynamical systems with multiple time-scales. A numerical example is provided to illustrate the design developed in this paper

Variance-constrained multiobjective control and filtering for nonlinear stochastic systems: A survey

The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed H 2 / H ∞ control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out

Advances in Control of Power Electronic Converters

This book proposes a list of contributions in the field of control of power electronics converters for different topologies: DC-DC, DC-AC and AC-DC. It particularly focuses on the use of different advanced control techniques with the aim of improving the performances, flexibility and efficiency in the context of several operation conditions. Sliding mode control, fuzzy logic based control, dead time compensation and optimal linear control are among the techniques developed in the special issue. Simulation and experimental results are provided by the authors to validate the proposed control strategies