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Adaptive control for a jump linear system with quadratic cost

Czornik A.

Control and Cybernetics

2004

Vol. 33, no 1

51-69

The adaptive control problem for a jump linear system with quadratic cost functional on infinite time interval is solved in this paper. It is assumed that the coefficients of the state equation are unknown but a compact set that contains the parameters is known. A diminishing excitation accompanies the adaptive control signal, to ensure the strong consistency of the weighted least squares algorithm.

On the stability of one dimensional discrete-time jump linear systems

Czornik A., Nawrat A., Rabsztyn S.

Archives of Control Sciences

2003

Vol. 13, no. 1

81-93

In this paper we present necessary and sufficient conditions for "delta" - moment stability and almost sure stability of one-dimensional discrete-time linear systems subject is equivalent to "delta"-moment stability for certain "delta">0.

On the discrete time-varying JLQG problem

Czornik A., Świerniak A.

International Journal of Applied Mathematics and Computer Science

2002

Vol. 12, no 2

203-207

In the present paper optimal time-invariant state feedback controllers are designed for a class of discrete time-varying control systems with Markov jumping parameter and quadratic performance index. We assume that the coefficients have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Moreover, following the same line of reasoning, an adaptive controller is proposed in the case when system parameters are unknown but their strongly consistent estimators are available.

Discrete-time Markovian jump linear systems

Szajowski K., Koning W.

Control and Cybernetics

1998

Vol. 27, no 1

63-80

The paper considers a problem of optimal control of a linear system with the parameters dependent on the states of a Markov chain. The cost criterion is quadratic in the controls and states of the system. The criterion parameters also depend on the states of the Markov chain. Two models of observation of the Markov chain are adopted - delay for one step and no delay. It is shown that under appopriate mean square detectability and stabilizability conditions the infinite horizon optimal control problem for the general case of Markovian jump linear quadratic systems has a unigue mean square stabilizing solution. Necessary and sufficient conditions are given to determine if a system is mean square stabilizable.