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Continuity of Solutions of Riccati Equations for the Discrete-Time Jlqp

Czornik A., Świerniak A.

International Journal of Applied Mathematics and Computer Science

2002

Vol. 12, no 4

539-543

The continuity of the solutions of difference and algebraic coupled Riccati equations for the discrete-time Markovian jump linear quadratic control problem as a function of coefficients is verified. The line of reasoning goes through the use of the minimum property formulated analogously to the one for coupled continuous Riccati equations presented by Wonham and a set of comparison theorems.

Linear Quadratic Control Problem With Fixed Final State for Discrete-Time Distributed Systems

Chraibi L., Karrakchou J., Ouansafi A., Rachik M.

International Journal of Applied Mathematics and Computer Science

2000

Vol. 10, no 3

517-535

The problem considered is that of minimizing a quadratic cost functional for a discrete distributed system with fixed initial and final states. It is shown that under suitable controllability assumptions, there is a close relationship between this problem and that of exact controllability with minimization of a time-varying energy criterion. The HUM technique is then extended to treat the exact controllability problem in the time-varying case and applied to provide an explicit form for the optimal control and the optimal cost.