Xiangpeng Xie

Control Synthesis of Discrete-Time T–S Fuzzy Systems Based on a Novel Non-PDC Control Scheme

This paper proposes relaxed stabilization conditions of discrete-time nonlinear systems in the Takagi-Sugeno (T-S) fuzzy form. By using the algebraic property of fuzzy membership functions, a novel nonparallel distributed compensation (non-PDC) control scheme is proposed based on a new class of fuzzy Lyapunov functions. Thus, relaxed stabilization conditions for the underlying closed-loop fuzzy system are developed by applying a new slack variable technique. In particular, some existing fuzzy Lyapunov functions and non-PDC control schemes are special cases of the new Lyapunov function and fuzzy control scheme, respectively. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

Event-triggered H ∞ stabilization for networked stochastic systems with multiplicative noise and network-induced delays

This paper is concerned with event-triggered H ∞ stabilization (in the mean square sense) for networked stochastic system with multiplicative noise and network-induced delays. Firstly, a new discrete event-triggered transmission protocol (DETTP) is proposed to reduce the utilization rate of communication bandwidth. The main features of the proposed protocol involve three aspects: (1) it allows the presence of external disturbances and multiplicative noise; (2) it is more general than some existing event-triggered transmission schemes in the deterministic setting; and (3) the minimum inter-event time is implicity defined and is naturally given by the sampling period chosen for the plant. Secondly, under the DETTP, a new closed-loop stochastic networked control system model is established. Remarkably, to facilitate theoretical analysis, the resultant event-based stochastic networked control system is further transformed into a system with two successive delay components in the state, considering the effects of network-induced delays, multiplicative noise and DETTP in a unified framework. By using stochastic system theory, sufficient conditions on the existence of the desired event-based H ∞ state feedback controller are derived such that the resultant event-based stochastic networked control system is exponentially stable in the mean square sense with a prescribed H ∞ performance while reducing the number of sampled-state transmission along the feedback link as much as possible. Thirdly, a co-design algorithm for determining the parameters of the DETTP and the state feedback controller gain matrix are also proposed. Finally, two practical examples are given to illustrate the effectiveness and advantage of the proposed method over some existing results in the literature.

Observer Design of Discrete-Time T–S Fuzzy Systems Via Multi-Instant Homogenous Matrix Polynomials

This paper is concerned with the design of observer for discrete-time nonlinear systems in the Takagi-Sugeno (T-S) fuzzy form. Under the framework of multi-instant homogenous matrix polynomials, a novel fuzzy observer and a new Lyapunov function, which are homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the m-steps past-time normalized fuzzy weighting functions, are proposed for conceiving less conservative observer design conditions. Since the algebraic properties of both the current-time normalized fuzzy weighting functions and the m-steps past-time normalized fuzzy weighting functions are fully considered, the relaxation quality of the fuzzy observer design of discrete-time T-S fuzzy systems is significantly improved. In particular, some existing fuzzy Lyapunov functions and fuzzy observers are special cases of the Lyapunov function and the fuzzy observer given in this paper, respectively. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

Control Synthesis of Discrete-Time T–S Fuzzy Systems: Reducing the Conservatism Whilst Alleviating the Computational Burden

The augmented multi-indexed matrix approach acts as a powerful tool in reducing the conservatism of control synthesis of discrete-time Takagi–Sugeno fuzzy systems. However, its computational burden is sometimes too heavy as a tradeoff. Nowadays, reducing the conservatism whilst alleviating the computational burden becomes an ideal but very challenging problem. This paper is toward finding an efficient way to achieve one of satisfactory answers. Different from the augmented multi-indexed matrix approach in the literature, we aim to design a more efficient slack variable approach under a general framework of homogenous matrix polynomials. Thanks to the introduction of a new extended representation for homogeneous matrix polynomials, related matrices with the same coefficient are collected together into one sole set and thus those redundant terms of the augmented multi-indexed matrix approach can be removed, i.e., the computational burden can be alleviated in this paper. More importantly, due to the fact that more useful information is involved into control design, the conservatism of the proposed approach as well is less than the counterpart of the augmented multi-indexed matrix approach. Finally, numerical experiments are given to show the effectiveness of the proposed approach.

Event-triggered controller design of nonlinear discrete-time networked control systems in T-S fuzzy model

HighlightsWe propose a more general mixed event-triggering communication scheme.Conditions for uniform ultimately bounded stability are derived in the event-triggered fuzzy control framework.A co-design algorithm is developed to design the desired fuzzy controller and event-triggering scheme simultaneously.A premise synchronizer has been delicately constructed to ensure the same premises with uniform time scales in both fuzzy model and fuzzy controller. This article is concerned with event-triggered fuzzy control design for a class of discrete-time nonlinear networked control systems (NCSs) with time-varying communication delays. Firstly, a more general mixed event-triggering scheme (ETS) is proposed. Secondly, considering the effects of the ETS and communication delays, based on the T-S fuzzy model scheme and time delay system approach, the original nonlinear NCSs is reformulated as a new event-triggered networked T-S fuzzy systems with interval time-varying delays. Sufficient conditions for uniform ultimately bound (UUB) stability are established in terms of linear matrix inequalities (LMIs). In particular, the quantitative relation between the boundness of the stability region and the triggering parameters are studied in detail. Thirdly, a relative ETS is also provided, which can be seen as a special case of the above proposed mixed ETS. As a difference from the preceding results, sufficient conditions on the existence of desired fuzzy controller are derived to ensure the asymptotic stability of the closed-loop system with reduced communication frequency between sensors and controllers. Moreover, a co-design algorithm for simultaneously determining the gain matrices of the fuzzy controller and the triggering parameters is developed. Finally, two illustrative examples are presented to demonstrate the advantage of the proposed ETS and the effectiveness of the controller design method.

Multi-Instant Observer Design of Discrete-Time Fuzzy Systems: A Ranking-Based Switching Approach

This paper generalizes recent results on multi-instant observer design for discrete-time Takagi–Sugeno fuzzy systems through a valid ranking-based switching approach. The approach hereby develops a concentrated subdivision of spanning space composed of normalized fuzzy weighting functions and then substantially produces a new ranking-based switching mechanism. By taking advantage of this ranking-based switching mechanism, a class of new fuzzy multi-instant observers are achieved and more relaxed design conditions with respect to the recent work can be obtained for ensuring the asymptotically stability of the developed state estimation error system. Two illustrative examples are provided to validate the effectiveness of the result given in this study.

Multi-elite guide hybrid differential evolution with simulated annealing technique for dynamic economic emission dispatch

The orthogonal initialization method is integrated into differential evolution.Modified mutation operator is used to control convergence rate with simulated annealing technique.Entropy diversity method is utilized to adaptively monitor the population diversity.The results show the quality and efficiency of proposed algorithm in DEED problem. This paper proposes an improved multi-objective differential evolutionary algorithm named multi-objective hybrid differential evolution with simulated annealing technique (MOHDE-SAT) to solve dynamic economic emission dispatch (DEED) problem. The proposed MOHDE-SAT integrates the orthogonal initialization method into the differential evolution, which enlarges the population diversity at the beginning of population evolution. In addition, modified mutation operator and archive retention mechanisms are used to control convergence rate, and simulated annealing technique and entropy diversity method are utilized to adaptively monitor the population diversity as the evolution proceeds, which can properly avoid the premature convergence problem. Furthermore, the MOHDE-SAT is applied on the thermal system with a heuristic constraint handling method, and obtains more desirable results in comparison to those alternatives established recently. The obtained results also reveal that the proposed MOHDE-SAT can provide a viable way for solving DEED problems.

Observer-Based Non-PDC Control for Networked T–S Fuzzy Systems With an Event-Triggered Communication

This paper addresses the problem of an event-triggered non-parallel distribution compensation (PDC) control for networked Takagi–Sugeno (T–S) fuzzy systems, under consideration of the limited data transmission bandwidth and the imperfect premise matching membership functions. First, a unified event-triggered T–S fuzzy model is provided, in which: 1) a fuzzy observer with the imperfect premise matching is constructed to estimate the unmeasurable states of the studied system; 2) a fuzzy controller is designed following the same premise as the observer; and 3) an output-based event-triggering transmission scheme is designed to economize the restricted network resources. Different from the traditional PDC method, the synchronous premise between the fuzzy observer and the T–S fuzzy system are no longer needed in this paper. Second, by use of Lyapunov theory, a stability criterion and a stabilization condition are obtained for ensuring asymptotically stable of the studied system. On account of the imperfect premise matching conditions are well considered in the derivation of the above criteria, less conservation can be expected to enhance the design flexibility. Compared with some existing emulation-based methods, the controller gains are no longer required to be known a priori. Finally, the availability of proposed non-PDC design scheme is illustrated by the backing-up control of a truck-trailer system.This paper addresses the problem of an event-triggered non-parallel distribution compensation (PDC) control for networked Takagi-Sugeno (T-S) fuzzy systems, under consideration of the limited data transmission bandwidth and the imperfect premise matching membership functions. First, a unified event-triggered T-S fuzzy model is provided, in which: 1) a fuzzy observer with the imperfect premise matching is constructed to estimate the unmeasurable states of the studied system; 2) a fuzzy controller is designed following the same premise as the observer; and 3) an output-based event-triggering transmission scheme is designed to economize the restricted network resources. Different from the traditional PDC method, the synchronous premise between the fuzzy observer and the T-S fuzzy system are no longer needed in this paper. Second, by use of Lyapunov theory, a stability criterion and a stabilization condition are obtained for ensuring asymptotically stable of the studied system. On account of the imperfect premise matching conditions are well considered in the derivation of the above criteria, less conservation can be expected to enhance the design flexibility. Compared with some existing emulation-based methods, the controller gains are no longer required to be known a priori. Finally, the availability of proposed non-PDC design scheme is illustrated by the backing-up control of a truck-trailer system.

Finite-Frequency Model Reduction of Takagi–Sugeno Fuzzy Systems

This paper considers the model-reduction problem for continuous-time Takagi-Sugeno (T-S) fuzzy systems. Different from existing full-frequency methods, a finite-frequency model-reduction method is proposed in this paper. The proposed method can get a better approximation performance when input signals belong to a finite-frequency domain. To this end, a finite-frequency H∞ performance index is first defined. Then, a sufficient finite-frequency performance analysis condition is derived by the aid of Parsevals theorem and quadratic functions. Based on this condition and projection lemma, three model-reduction algorithms for T-S fuzzy systems with input signals in low-frequency, middle-frequency, and high-frequency domain are obtained, respectively. Finally, an example is given to illustrate the effectiveness of the proposed method.

Relaxed fuzzy control synthesis of nonlinear networked systems under unreliable communication links

HighlightsA novel fuzzy controller and a new kind of slack variable approach are developed.The criterion takes the form of an LMI which is computationally tractable.The obtained stabilization conditions are less conservative. This paper proposes relaxed conditions for control synthesis of discrete-time Takagi-Sugeno fuzzy control systems under unreliable communication links. To widen the applicability of the fuzzy control approach under network environments, a novel fuzzy controller, which is homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the multi-steps-past normalized fuzzy weighting functions, is provided to make much more use of the information of the underlying system. Moreover, a new kind of slack variable approach is also developed and thus the algebraic properties of these multi-instant normalized fuzzy weighting functions are collected into some augmented matrices. As a result, the conservatism of control synthesis of discrete-time Takagi-Sugeno fuzzy control systems under unreliable communication links can be significantly reduced. Two illustrative examples are presented to demonstrate the effectiveness of the theoretical development.