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2 Matematyka Stosowana : matematyka dla społeczeństwa

2 1997

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Optimal control of a two-dimensional linear system with a quadratic performance index with constraints on the trajectory and the control

Biły Barbara

Matematyka Stosowana : matematyka dla społeczeństwa

1997

Nr 40

21--29

The main purpose of this note is to present a method for solving the linear-quadratic optimal regulator for discrete, linear general two-dimensional system with constant coefficients. The quadratic optimal regulator problem can be formulated: find of sequence of control vectors in fixed rectangle, which transfer the system to given final state vector and minimizes the quadratic performance index, with constraints of control and state vector. This problem, by transformation for systemand performance index is reduced to equivalent mathematical programming problem. Necessary and sufficient conditions are established for the existence of a solution to this problem. With slight modifications the considerations can be extended for 2-D systems with variable coefficient and n-D linear systems.

Optimal control for a nonstationary linear system with a quadratic cost functional

Czornik Adam

Matematyka Stosowana : matematyka dla społeczeństwa

1997

Nr 40

3--11

This paper is about optimal control of infinite-horizon nonstationary stochastic linear processes with a quadratic cost criterion. The synthesis problem of optimal control is solved under the assumptions that the criterion is an average expected cost and that the process' matrices possess limits for the time approaching infinity. Furthermore, the limit matrices are such that the "limit" process is both observable and controllable. The paper documents existence of an optimal feedback control policy. The policy is such that the gain matrix is a (scaled) solution to a Riccati stationary matrix equation. The equation is stationary in that its coefficients are the limits of the process' non-stationary matrices.