Optimal Preview Control of Markovian Jump Linear Systems

In this paper, we investigate the design of controllers, for discrete-time Markovian jump linear systems, that achieve optimal reference tracking in the presence of preview (reference look-ahead). For a quadratic cost and given a reference sequence, we obtain the optimal solution for the full information case. The optimal control policy consists of the additive contribution of two terms: a feedforward term and a feedback term. We show that the feedback term is identical to the standard optimal linear quadratic regulator for Markovian jump linear systems. We provide explicit formulas for computing the feedforward term, including an analysis of convergence

Stabilization of markovian systems via probability rate synthesis and output feedback

This technical note is concerned with the stabilization problem of Markovian jump linear systems via designing switching probability rate matrices and static output-feedback gains. A novel necessary and sufficient condition is established to characterize the switching probability rate matrices that guarantee the mean square stability of Markovian jump linear systems. Based on this, a necessary and sufficient condition is provided for the existence of desired controller gains and probability rate matrices. Extensions to the polytopic uncertain case are also provided. All the conditions are formulated in terms of linear matrix inequalities with some equality constraints, which can be solved by two modified cone complementarity linearization algorithms. Examples are given to show the effectiveness of the proposed method. © 2010 IEEE.published_or_final_versio

Fault Compensation Controller for Markovian Jump Linear Systems

In this paper, we tackle the fault-compensation controller in the context of Marko- vian Jump Linear Systems (MJLS). More specifically, we propose the design of H∞ Fault- Compensation Controllers under the MJLS formulation, which is provided in terms of linear matrices inequalities optimization problems. These particular controllers have as the main motivation the network communication loss which is inherent to any automation process. We present a numerical example of a coupled tank system, where a Monte Carlo simulation illustrates the feasibility of the proposed solution. The results show that the proposed approach is indeed a valuable alternative to compensate for the fault occurrence

Static output-feedback stabilization of discrete-time Markovian jump linear systems: a system augmentation approach

This paper studies the static output-feedback (SOF) stabilization problem for discrete-time Markovian jump systems from a novel perspective. The closed-loop system is represented in a system augmentation form, in which input and gain-output matrices are separated. By virtue of the system augmentation, a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities, which possess a monotonic structure for a linearized computation, and a convergent iteration algorithm is given to solve such inequalities. In addition, a special property of the feasible solutions enables one to further improve the solvability via a simple D-K type optimization on the initial values. An extension to mode-independent SOF stabilization is provided as well. Compared with some existing approaches to SOF synthesis, the proposed one has several advantages that make it specific for Markovian jump systems. The effectiveness and merit of the theoretical results are shown through some numerical example

Fault accommodation controller under Markovian jump linear systems with asynchronous modes

We tackle the fault accommodation control (FAC) in the Markovian jump linear system (MJLS) framework for the discrete-time domain, under the assumption that it is not possible to access the Markov chain mode. This premise brings some challenges since the controllers are no longer allowed to depend on the Markov chain, meaning that there is an asynchronism between the system and the controller modes. To tackle this issue, a hidden Markov chain ((Formula presented.), (Formula presented.)) is used where θ(k) denotes the Markov chain mode, and (Formula presented.) denotes the estimated mode. The main novelty of this work is the design of H∞ and H2 FAC under the MJLS framework considering partial observation of the Markov chain. Both designs are obtained via bilinear matrix inequalities optimization problems, which are solved using coordinate descent algorithm. As secondary results, we present simulations using a two-degree of freedom serial flexible joint robot to illustrate the viability of the proposed approach

A gradient-based iterative algorithm for solving coupled Lyapunov equations of continuous-time Markovian jump systems

In this paper, a new gradient-based iterative algorithm is proposed to solve the coupled Lyapunov matrix equations associated with continuous-time Markovian jump linear systems. A necessary and sufficient condition is established for the proposed gradient-based iterative algorithm to be convergent. In addition, the optimal value of the tunable parameter achieving the fastest convergence rate of the proposed algorithm is given explicitly. Finally, some numerical simulations are given to validate the obtained theoretical results