Mode-independent Controller Research Articles

Feedback predictive control for constrained fuzzy systems with Markovian jumps

In this paper, a feedback model predictive control method is presented to tackle control problems with constrained multivariables for uncertain discrete-time nonlinear Markovian jump systems. An uncertain Markovian jump fuzzy system (MJFS) is obtained by employing the Takagi-Sugeno (T-S) fuzzy model to represent a discrete-time nonlinear system with norm bounded uncertainties and Markovain jump parameters. To achieve more generality, the transition probabilities of the Markov chain are assumed to be partly unknown and partly accessible. The predictive formulation adopts an on-line optimization paradigm that utilizes the closed-loop state feedback controller and is solved using the standard semi-definite programming (SDP). To reduce the on-line computational burden, a mode independent control move is calculated at every sampling time based on a stochastic fuzzy Lyapunov function (FLF) and a parallel distributed compensation (PDC) scheme. The robust mean square stability, performance minimization and constraint satisfaction properties are guaranteed under the control move for all admissible uncertainties. A numerical example is given to show the efficiency of the developed approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Robust stability, ℋ2 analysis and stabilisation of discrete-time Markov jump linear systems with uncertain probability matrix

The stability and the problem of ℋ2 guaranteed cost computation for discrete-time Markov jump linear systems (MJLS) are investigated, assuming that the transition probability matrix is not precisely known. It is generally difficult to estimate the exact transition matrix of the underlying Markov chain and the setting has a special interest for applications of MJLS. The exact matrix is assumed to belong to a polytopic domain made up by known probability matrices, and a sequence of linear matrix inequalities (LMIs) is proposed to verify the stability and to solve the ℋ2 guaranteed cost with increasing precision. These LMI problems are connected to homogeneous polynomially parameter-dependent Lyapunov matrix of increasing degree g. The mean square stability (MSS) can be established by the method since the conditions that are sufficient, eventually turns out to also be necessary, provided that the degree g is large enough. The ℋ2 guaranteed cost under MSS is also studied here, and an extension to cope with the problem of control design is also introduced. These conditions are only sufficient, but as the degree g increases, the conservativeness of the ℋ2 guaranteed costs is reduced. Both mode-dependent and mode-independent control laws are addressed, and numerical examples illustrate the results.

Orthogonal adaptation for multichannel feedforward control

In active noise control, it is desired to generate destructive interference by model-independent control. This is possible for single-channel systems to which a recently proposed method, called orthogonal adaptation, is applicable. In this study, the new method is extended to multichannel systems. An important issue is how to optimize a feedforward controller in the minimum H2 norm sense. In practice, secondary paths of some multichannel systems may be nonminimum phase. It is a difficult problem to design H2 feedforward controllers for multichannel systems with nonminimum phase secondary paths. The problem is solved analytically here with the best achievable, a practical and an economical solution. A recursive least squares algorithm is presented for online identification of multiple paths without persistent excitations. These solutions make it possible to implement noninvasive mode-independent controllers for multichannel systems. Experiment results are presented to verify the analytical results.

Robust Stability and Stabilization of Uncertain Discrete-Time Markovian Jump Linear Systems

This note deals with robust stability and control of uncertain discrete-time linear systems with Markovian jumping parameters. Systems with polytopic-type parameter uncertainty in either the state-space model matrices, or in the transition probability matrix of the Markov process, are considered. This note develops methods of robust stability analysis and robust stabilization in the mean square sense which are dependent on the system uncertainty. The design of both mode-dependent and mode-independent control laws is addressed. The proposed methods are given in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the derived results.