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

Nonfragile H∞Fuzzy filtering with randomly occurring gain variations and channel fadings

This paper is concerned with the nonfragile filtering problem for a class of discrete-Time Takagi-Sugeno (T-S) fuzzy systems with both randomly occurring gain variations (ROGVs) and channel fadings.The phenomenon of the ROGVs is introduced into the system model so as to account for the parameter fluctuations occurring during the filter implementation. Two sequences of random variables obeying the Bernoulli distribution are employed to describe the phenomenon of the ROGVs bounded by prescribed norms. In addition, the Rice fading model is utilized to describe the phenomena of channel fadings, where the occurrence probabilities of the random channel coefficients are allowed to time varying. Through stochastic analysis and Lyapunov functional approach, sufficient conditions are established under which the filtering error dynamics is exponentially mean-square stable with a prespecified ∞ performance. The set of the desired nonfragile ∞ filters is characterized by solving a convex optimization problem via the semidefinite programming method. An illustrative example is given to show the usefulness and effectiveness of the proposed design method in this paper.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 61203139, 61374127 and 61422301, the Hujiang Foundation of China under Grant C14002, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information

Copyright q 2012 Hongli Dong 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.In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out. © 2012 Hongli Dong et al.This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of German

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Disturbance-observer-based robust control for time delay uncertain systems

A robust control scheme is proposed for a class of systems with uncertainty and time delay based on disturbance observer technique. A disturbance observer is developed to estimate the disturbance generated by an exogenous system, and the design parameters of the disturbance observer are determined by solving linear matrix inequalities (LMIs). Based on the output of the disturbance observer, a robust control scheme is proposed for the time delay uncertain system. The disturbance-observer-based robust controller is combined of two parts: one is a linear feedback controller designed using LMIs and the other is a compensatory controller designed with the output of the disturbance observer. By choosing an appropriate Lyapunov function candidate, the stability of the closed-loop system is proved. Finally, simulation example is presented to illustrate the effectiveness of the proposed control scheme

Non-fragile estimation for discrete-time T-S fuzzy systems with event-triggered protocol

summary:This paper investigates the non-fragile state estimation problem for a class of discrete-time T-S fuzzy systems with time-delays and multiple missing measurements under event-triggered mechanism. First of all, the plant is subject to the time-varying delays and the stochastic disturbances. Next, a random white sequence, the element of which obeys a general probabilistic distribution defined on $[0,1]$, is utilized to formulate the occurrence of the missing measurements. Also, an event generator function is employed to regulate the transmission of data to save the precious energy. Then, a non-fragile state estimator is constructed to reflect the randomly occurring gain variations in the implementing process. By means of the Lyapunov-Krasovskii functional, the desired sufficient conditions are obtained such that the Takagi-Sugeno (T-S) fuzzy estimation error system is exponentially ultimately bounded in the mean square. And then the upper bound is minimized via the robust optimization technique and the estimator gain matrices can be calculated. Finally, a simulation example is utilized to demonstrate the effectiveness of the state estimation scheme proposed in this paper

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Non-fragile state estimation for discrete Markovian jumping neural networks

In this paper, the non-fragile state estimation problem is investigated for a class of discrete-time neural networks subject to Markovian jumping parameters and time delays. In terms of a Markov chain, the mode switching phenomenon at different times is considered in both the parameters and the discrete delays of the neural networks. To account for the possible gain variations occurring in the implementation, the gain of the estimator is assumed to be perturbed by multiplicative norm-bounded uncertainties. We aim to design a non-fragile state estimator such that, in the presence of all admissible gain variations, the estimation error converges to zero exponentially. By adopting the Lyapunov–Krasovskii functional and the stochastic analysis theory, sufficient conditions are established to ensure the existence of the desired state estimator that guarantees the stability of the overall estimation error dynamics. The explicit expression of such estimators is parameterized by solving a convex optimization problem via the semi-definite programming method. A numerical simulation example is provided to verify the usefulness of the proposed methods