PARAMETER OPTIMIZATION FOR ESTIMATION OF LINEAR NON-STATIONARY SYSTEMS
A problem of the optimal parameters choice for the best state estimation of the linear system subject to uncertain perturbations is considered. The problem is interpreted as a differential game for the Riccati equation that arises in the process of solution of the uncertain minimax estimation. The game is realized by two players: the first player (an observer) can choose some matrices of the system at any instant of time in order to minimize the diameter of the informational set at the end of the observation interval. The second player (an opponent of the
observer) tries to maximize the diameter choosing the matrices which are multipliers at perturbations. All the choosing parameters are limited to compact sets in appropriate spaces of matrices. The perturbations in the system are subjected to integral constraints. The payoff of the game is the Euclidean norm of the inverse Riccati matrix at the end of the process. A specific case of the problem with constant matrices is considered. Methods of minimax optimization, the theory of optimum control, and the theory of differential games are used. Examples
are also given.