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

Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this technical note, the globally exponential stabilization problem is investigated for a general class of stochastic systems with both Markovian jumping parameters and mixed time-delays. The mixed mode-dependent time-delays consist of both discrete and distributed delays. We aim to design a memoryless state feedback controller such that the closed-loop system is stochastically exponentially stable in the mean square sense. First, by introducing a new Lyapunov-Krasovskii functional that accounts for the mode-dependent mixed delays, stochastic analysis is conducted in order to derive a criterion for the exponential stabilizability problem. Then, a variation of such a criterion is developed to facilitate the controller design by using the linear matrix inequality (LMI) approach. Finally, it is shown that the desired state feedback controller can be characterized explicitly in terms of the solution to a set of LMIs. Numerical simulation is carried out to demonstrate the effectiveness of the proposed methods.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 973 Program of China under Grant 2009CB320600, and the Alexander von Humboldt Foundation of Germany. Recommended by Associate Editor G. Chesi

Analysis, filtering, and control for Takagi-Sugeno fuzzy models in networked systems

Copyright © 2015 Sunjie Zhang 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.The fuzzy logic theory has been proven to be effective in dealing with various nonlinear systems and has a great success in industry applications. Among different kinds of models for fuzzy systems, the so-called Takagi-Sugeno (T-S) fuzzy model has been quite popular due to its convenient and simple dynamic structure as well as its capability of approximating any smooth nonlinear function to any specified accuracy within any compact set. In terms of such a model, the performance analysis and the design of controllers and filters play important roles in the research of fuzzy systems. In this paper, we aim to survey some recent advances on the T-S fuzzy control and filtering problems with various network-induced phenomena. The network-induced phenomena under consideration mainly include communication delays, packet dropouts, signal quantization, and randomly occurring uncertainties (ROUs). With such network-induced phenomena, the developments on T-S fuzzy control and filtering issues are reviewed in detail. In addition, some latest results on this topic are highlighted. In the end, conclusions are drawn and some possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 11301118 and 61174136, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130017, the Fundamental Research Funds for the Central Universities of China under Grant CUSF-DH-D-2013061, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Robust H∞ control for a class of nonlinear discrete time-delay stochastic systems with missing measurements

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2009 Elsevier LtdThis paper is concerned with the problem of robust H∞ output feedback control for a class of uncertain discrete-time delayed nonlinear stochastic systems with missing measurements. The parameter uncertainties enter into all the system matrices, the time-varying delay is unknown with given low and upper bounds, the nonlinearities satisfy the sector conditions, and the missing measurements are described by a binary switching sequence that obeys a conditional probability distribution. The problem addressed is the design of an output feedback controller such that, for all admissible uncertainties, the resulting closed-loop system is exponentially stable in the mean square for the zero disturbance input and also achieves a prescribed H∞ performance level. By using the Lyapunov method and stochastic analysis techniques, sufficient conditions are first derived to guarantee the existence of the desired controllers, and then the controller parameters are characterized in terms of linear matrix inequalities (LMIs). A numerical example is exploited to show the usefulness of the results obtained.This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor Dragan Nešic under the direction of Editor Hassan K. Khalil. 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 City University of Hong Kong under Grant 7001992, the Royal Society of the U.K. under an International Joint Project, the Natural Science Foundation of Jiangsu Province of China under Grant BK2007075, the National Natural Science Foundation of China under Grant 60774073, and the Alexander von Humboldt Foundation of Germany

Stabilisation of hybrid stochastic differential equations by delay feedback control

This paper is concerned with the exponential mean-square stabilisation of hybrid stochastic differential equations (also known as stochastic dierential equations with Markovian switching) by delay feedback controls. Although the stabilisation by non-delay feedback controls for such equations has been discussed by several authors, there is so far little on the stabilisation by delay feedback controls and our aim here is mainly to close the gap. To make our theory more understandable as well as to avoid complicated notations, we will restrict our underlying hybrid stochastic dierential equations to a relatively simple form. However our theory can certainly be developed to cope with much more general equations without any diculty

Dynamic output feedback sliding mode control for uncertain linear systems

In this paper, a class of uncertain linear systems with unmatched disturbances is considered, where the nominal system representation is allowed to be non-minimum phase. A sliding surface is designed which is dependent on the system output, observed state, and estimated uncertain parameters. A linear coordinate transformation is introduced so that the stability analysis of the reduced-order sliding mode dynamics can be conveniently performed. A robust output feedback sliding mode control (OFSMC) is then designed to drive the considered system state to reach the sliding surface in finite time and maintain a sliding motion thereafter. A simulation example for a high incidence research model (HIRM) aircraft is used to demonstrate the effectiveness of the proposed method

STABILITY AND PERFORMANCE OF NETWORKED CONTROL SYSTEMS

Network control systems (NCSs), as one of the most active research areas, are arousing comprehensive concerns along with the rapid development of network. This dissertation mainly discusses the stability and performance of NCSs into the following two parts. In the first part, a new approach is proposed to reduce the data transmitted in networked control systems (NCSs) via model reduction method. Up to our best knowledge, we are the first to propose this new approach in the scientific and engineering society. The "unimportant" information of system states vector is truncated by balanced truncation method (BTM) before sending to the networked controller via network based on the balance property of the remote controlled plant controllability and observability. Then, the exponential stability condition of the truncated NCSs is derived via linear matrix inequality (LMI) forms. This method of data truncation can usually reduce the time delay and further improve the performance of the NCSs. In addition, all the above results are extended to the switched NCSs. The second part presents a new robust sliding mode control (SMC) method for general uncertain time-varying delay stochastic systems with structural uncertainties and the Brownian noise (Wiener process). The key features of the proposed method are to apply singular value decomposition (SVD) to all structural uncertainties, to introduce adjustable parameters for control design along with the SMC method, and new Lyapunov-type functional. Then, a less-conservative condition for robust stability and a new robust controller for the general uncertain stochastic systems are derived via linear matrix inequality (LMI) forms. The system states are able to reach the SMC switching surface as guaranteed in probability 1 by the proposed control rule. Furthermore, the novel Lyapunov-type functional for the uncertain stochastic systems is used to design a new robust control for the general case where the derivative of time-varying delay can be any bounded value (e.g., greater than one). It is theoretically proved that the conservatism of the proposed method is less than the previous methods. All theoretical proofs are presented in the dissertation. The simulations validate the correctness of the theoretical results and have better performance than the existing results

Sliding mode and shaped input vibration control of flexible systems

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the vibration reduction problem is investigated for a flexible spacecraft during attitude maneuvering. A new control strategy is proposed, which integrates both the command input shaping and the sliding mode output feedback control (SMOFC) techniques. Specifically, the input shaper is designed for the reference model and implemented outside of the feedback loop in order to achieve the exact elimination of the residual vibration by modifying the existing command. The feedback controller, on the other hand, is designed based on the SMOFC such that the closed-loop system behaves like the reference model with input shaper, where the residual vibrations are eliminated in the presence of parametric uncertainties and external disturbances. An attractive feature of this SMOFC algorithm is that the parametric uncertainties or external disturbances of the system do not need to satisfy the so-called matching conditions or invariance conditions provided that certain bounds are known. In addition, a smoothed hyperbolic tangent function is introduced to eliminate the chattering phenomenon. Compared with the conventional methods, the proposed scheme guarantees not only the stability of the closed-loop system, but also the good performance as well as the robustness. Simulation results for the spacecraft model show that the precise attitudes control and vibration suppression are successfully achieved