SUMMARYRobust λ-contractive sets have been proposed in previous literature for uncertain polytopic linear systems. It is well known that, if initial state is inside such sets, it is guaranteed to converge to the origin. This work presents the generalization of such concepts to systems whose behaviour changes among different linear models with probability given by a Markov chain. We propose sequence-dependent sets and associated controllers which can ensure a reliability bound when initial conditions are outside the maximal λ-contractive set. Such reliability bound will be understood as the probability of actually reaching the origin from a given initial condition without violating constraints. As initial condition are further away from the origin, the likelihood of reaching the origin decreases.

Predictive control of TS fuzzy systems has been addressed in prior literature with some simplifying assumptions or heuristic approaches. This paper presents a rigorous formulation of the model predictive control of TS systems, so that results are valid for any membership value (shape-independent) with a suitable account of causality (control can depend on current and past memberships and state). As in most fuzzy control results, a family of progressively better controllers can be obtained by increasing Polya-related complexity parameters, generalising over prior proposals.

Takagi-Sugeno fuzzy models are exact representations of nonlinear systems in a compact region. Guaranteed-cost linear matrix inequalities produce controllers which minimize a shape-independent bound on a quadratic cost; however, the controller has a fixed structure (possibly suboptimal), say a Parallel Distributed Compensator (PDC), and does not allow input saturation. By posing the problem as a Model Predictive Control one, the ideas of terminal set, terminal controller and feasible set can be used in order to improve the performance of usual guaranteed-cost controllers for Takagi-Sugeno systems via Quadratic Programming. A Polya-based approach has been introduced in order to (conservatively) transform the invariant set problem into a polytopic one, as well as computing the controller feasibility region. The optimal controller is computed iteratively.Index Terms-Discrete Takagi-Sugeno Fuzzy Models, Invariant sets, Contractive sets and Robust Stability.

This paper proposes a model predictive control for Markov-jump or switched linear systems (switching between a finite set of modes) when simultaneously considering prediction horizons (and realisations of the mode variable) of different length, in order to balance accuracy versus computational cost. Feasibility, stability and receding horizon issues are considered.

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This work considers fault-tolerant control (FTC) for discrete-time Markov Jump Linear System (MJLS) subject to constraints on the state an control variables. The objective is to design a control law which depends on the jump variable, minimizing an average quadratic function. Improving over previous MJLS literature, input and state constraints are enforced. The initial condition of the system and the transition probability of the Markov chain are available to the controller at each instant of time. Concepts arising from the receding horizon framework and invariant set theory are incorporated in a constrained fault-tolerant predictive control approach.