A game theory approach to mixed H2/H∞ control for a class of stochastic time-varying systems with randomly occurring nonlinearities

Copyright @ 2011 Elsevier B.V. This is the author’s version of a work that was accepted for publication in Systems and Control Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published and may be accessed at the link below.This paper is concerned with the mixed H2/H∞ control problem for a class of stochastic time-varying systems with nonlinearities. The nonlinearities are described by statistical means and could cover several kinds of well-studied nonlinearities as special cases. The occurrence of the addressed nonlinearities is governed by two sequences of Bernoulli distributed white sequences with known probabilities. Such nonlinearities are named as randomly occurring nonlinearities (RONs) as they appear in a probabilistic way. The purpose of the problem under investigation is to design a controller such that the closed-loop system achieves the expected H2 performance requirements with a guaranteed H∞ disturbance attenuation level. A sufficient condition is given for the existence of the desired controller by means of solvability of certain coupled matrix equations. By resorting to the game theory approach, an algorithm is developed to obtain the controller gain at each sampling instant. A numerical example is presented to show the effectiveness and applicability of the proposed method

Robust H∞ control of time-varying systems with stochastic non-linearities: the finite-horizon case

The official published version can be obtained from the link below.This paper is concerned with the robust H∞ control problem for the class of uncertain non-linear discrete time-varying stochastic systems with a covariance constraint. All the system parameters are time-varying and the uncertainties enter into the state matrix. The non-linearities under consideration are described by statistical means and they cover several classes of well-studied non-linearities. The purpose of the addressed problem is to design a dynamic output-feedback controller such that, the H∞ disturbance rejection attenuation level is achieved in the finite-horizon case while the state covariance is not more than an individual upper bound at each time point. An algorithm is developed to deal with the addressed problem by means of recursive linear matrix inequalities (RLMIs). It is shown that the robust H∞ control problem is solvable if the series of RLMIs is feasible. An illustrative simulation example is given to show the applicability and effectiveness of the proposed algorithm.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Robust H-infinity sliding mode control for nonlinear stochastic systems with multiple data packet losses

This is the post-print version of this Article. The official published version can be accessed from the link below - Copyright @ 2012 John Wiley & SonsIn this paper, an ∞ sliding mode control (SMC) problem is studied for a class of discrete-time nonlinear stochastic systems with multiple data packet losses. The phenomenon of data packet losses, which is assumed to occur in a random way, is taken into consideration in the process of data transmission through both the state-feedback loop and the measurement output. The probability for the data packet loss for each individual state variable is governed by a corresponding individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete-time system considered is also subject to norm-bounded parameter uncertainties and external nonlinear disturbances, which enter the system state equation in both matched and unmatched ways. A novel stochastic discrete-time switching function is proposed to facilitate the sliding mode controller design. Sufficient conditions are derived by means of the linear matrix inequality (LMI) approach. It is shown that the system dynamics in the specified sliding surface is exponentially stable in the mean square with a prescribed ∞ noise attenuation level if an LMI with an equality constraint is feasible. A discrete-time SMC controller is designed capable of guaranteeing the discrete-time sliding mode reaching condition of the specified sliding surface with probability 1. Finally, a simulation example is given to show the effectiveness of the proposed method.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National Natural Science Foundation of China under Grant 61028008 and the Alexander von Humboldt Foundation of German

Filtering and control for unreliable communication: The discrete-time case

Copyright © 2014 Guoliang Wei 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 past decades, communication networks have been extensively employed in many practical control systems, such as manufacturing plants, aircraft, and spacecraft to transmit information and control signals between the system components. When a control loop is closed via a serial communication channel, a networked control system (NCS) is formed. NCSs have become very popular for their great advantages over traditional systems (e.g., low cost, reduced weight, and power requirements, etc.). Generally, it has been implicitly assumed that the communication between the system components is perfect; that is, the signals transmitted from the plant always arrive at the filter or controller without any information loss. Unfortunately, such an assumption is not always true. For example, a common feature of the NCSs is the presence of significant network-induced delays and data losses across the networks. Therefore, an emerging research topic that has recently drawn much attention is how to cope with the effect of network-induced phenomena due to the unreliability of the network communication. This special issue aims at bringing together the latest approaches to understand, filter, and control for discrete-time systems under unreliable communication. Potential topics include but are not limited to (a) multiobjective filtering or control, (b) network-induced phenomena, (c) stability analysis, (d) robustness and fragility, and (e) applications in real-world discrete-time systems

Robust variance-constrained filtering for a class of nonlinear stochastic systems with missing measurements

The official published version of the article can be found at the link below.This paper is concerned with the robust filtering problem for a class of nonlinear stochastic systems with missing measurements and parameter uncertainties. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution, and the nonlinearities are expressed by the statistical means. The purpose of the filtering problem is to design a filter such that, for all admissible uncertainties and possible measurements missing, the dynamics of the filtering error is exponentially mean-square stable, and the individual steady-state error variance is not more than prescribed upper bound. A sufficient condition for the exponential mean-square stability of the filtering error system is first derived and an upper bound of the state estimation error variance is then obtained. In terms of certain linear matrix inequalities (LMIs), the solvability of the addressed problem is discussed and the explicit expression of the desired filters is also parameterized. Finally, a simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK and the Alexander von Humboldt Foundation of Germany

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

A survey on gain-scheduled control and filtering for parameter-varying systems

Copyright © 2014 Guoliang Wei 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.This paper presents an overview of the recent developments in the gain-scheduled control and filtering problems for the parameter-varying systems. First of all, we recall several important algorithms suitable for gain-scheduling method including gain-scheduled proportional-integral derivative (PID) control, H 2, H ∞ and mixed H 2 / H ∞ gain-scheduling methods as well as fuzzy gain-scheduling techniques. Secondly, various important parameter-varying system models are reviewed, for which gain-scheduled control and filtering issues are usually dealt with. In particular, in view of the randomly occurring phenomena with time-varying probability distributions, some results of our recent work based on the probability-dependent gain-scheduling methods are reviewed. Furthermore, some latest progress in this area is discussed. Finally, conclusions are drawn and several potential future research directions are outlined.The National Natural Science Foundation of China under Grants 61074016, 61374039, 61304010, and 61329301; the Natural Science Foundation of Jiangsu Province of China under Grant BK20130766; the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning; the Program for New Century Excellent Talents in University under Grant NCET-11-1051, the Leverhulme Trust of the U.K., the Alexander von Humboldt Foundation of Germany