In this paper, we study the effect of a network in the feedback loop of a control system. We use a stochastic packet-loss model for the network and note that results for discrete-time linear systems with Markovian jumping parameters can be applied. We measure performance using an H/sub /spl infin// norm and compute this norm via a necessary and sufficient matrix inequality condition. We also derive necessary and sufficient linear matrix inequality (LMI) conditions for the synthesis of the H/sub /spl infin// optimal controller for a discrete-time jump system. Finally, we apply these results to study the effect of communication losses on vehicle control.

An H/sub /spl infin// approach to networked control

This paper presents a new approach to solving the problem of stabilization for networked control systems. Mean-square asymptotic stability is derived for the closed-loop networked control systems, and based on this, a controller design procedure is proposed for stabilization purpose. An inverted pendulum system is utilized to show the effectiveness and applicability of the proposed results.

Stabilization of Networked Control Systems With a New Delay Characterization

In this paper we study the effect of communication packet losses in the feedback loop of a control system. Our motivation is derived from vehicle control problems where information is communicated via a wireless local area network. For such problems, we consider a simple packet-loss model for the communicated information and note that results for discrete-time linear systems with Markovian jumping parameters can be applied. The goal is to find a controller (if one exists) such that the closed loop is mean square stable for a given packet loss rate. A linear matrix inequality (LMI) condition is developed for the existence of a stabilizing dynamic output feedback controller. This LMI condition is used to study the effect of communication losses on a vehicle following problem. In summary, these results can be used not only to design controllers but also give a 'worst-case' performance specification (in terms of packet-loss rate) for an acceptable communications system.

Analysis of communication losses in vehicle control problems

Markovian jump systems are a special class of hybrid and stochastic systems which can be used to describe many real world applications, such as manufacturing systems, power systems, chemical systems, economic systems, communication and control, etc. In this paper, a survey on recent developments of modeling, analysis and design of Markovian jump systems is presented. First, stability issues on Markovian jump systems are addressed. Then a variety of control and filter design methods are systematically recalled. Furthermore, the new trends of Markovian jump systems with uncertain transition rates as well as semi-Markovian jump systems are also discussed.

/pdf/a-survey-on-markovian-jump-systems-modeling-and-design-4ejjpo7uau.pdf

A survey on Markovian jump systems: Modeling and design

This technical note studies the linear quadratic (LQ) performance of networked control systems where control packets are subject to loss. In particular we explore the two simplest compensation strategies commonly found in the literature: the zero-input strategy, in which the input to the plant is set to zero if a packet is dropped, and the hold-input strategy, in which the previous control input is used if packet is lost. We derive expressions for computing the optimal static gain for both strategies and we compare their performance on some numerical examples. Interestingly, none of the two can be claimed superior to the other, even for simple scalar systems, since there are scenarios where one strategy performs better then the other and scenarios where the converse occurs.

/pdf/to-zero-or-to-hold-control-inputs-with-lossy-links-2qptir33i1.pdf

To Zero or to Hold Control Inputs With Lossy Links

Markov Jump Linear Systems.- Background Material.- On Stability.- Optimal Control.- Filtering.- Quadratic Optimal Control with Partial Information.- H?-Control.- Design Techniques and Examples.

Discrete-Time Markov Jump Linear Systems

In this paper we consider the mixed / -control problem for the class of discrete-time linear systems with parameters subject to Markovian jump linear systems (MJLS's). It is assumed that both the state variable and the jump variable are available to the controller. The transition probability matrix may not be exactly known, but belongs to an appropriate convex set. For this controlled discrete-time Markovian jump linear system, the problem of interest can be stated in the following way. Find a robust (with respect to the uncertainty on the transition Markov probability matrix) mean-square stabilizing state and jump feedback controller that minimizes an upper bound for the -norm, under the restriction that the -norm is less than a prespecified value . The problem of the determination of the smallest -norm is also addressed. We present an approximate version of these problems via linear matrix inequality optimization.

http://ieeexplore.ieee.org/iel4/9/14249/00654895.pdf

Mixed / -Control of Discrete-Time Markovian Jump Linear Systems

Markov Jump Linear Systems

This paper deals with the robust Hz-control of discrete-time Markovian jump linear systems Uncertainties satisfying some norm bounded conditions are considered on the parameters of the system. An upperbound for the H2-control problem is derived in terms of an LMI optimization problem. For the case in which there are no uncertainties, we show that the convex formulation is equivalent to the existence of the mean square stabilizing solution for the set of coupled algebraic Riccati equations arising on the quadratic optimal control problem of discrete-time Markovian jump linear systems. Therefore, for the case with no uncertainties, the convex formulation considered in this paper imposes no extra conditions than those in the usual dynamic programming approach.

http://ieeexplore.ieee.org/iel4/5651/15195/00703507.pdf

Robust Hz -Control for Discrete-time Markovian Jump Linear Systems

http://ieeexplore.ieee.org/iel3/4303/12517/00577440.pdf

Oswaldo Luiz Valle do Costa

Papers

Discrete-Time Markov Jump Linear Systems

Mixed / -Control of Discrete-Time Markovian Jump Linear Systems

Markov Jump Linear Systems

Robust Hz -Control for Discrete-time Markovian Jump Linear Systems

MIXED H2/Hm CONTROL OF DISCREITE-TIME MARKOVIAN JUMP LINEAR SYSTEMS*