GAME CONTROL OF A FILTER WITH A RANDOM JUMP STRUCTURE

Abstract

The game problem of synthesis of information-control algorithms of filtering of two opposing sides is considered. The opponents’ control objects are described by multidimensional linear stochastic recurrent equations. Each side controls the covariance of the output signals of its object and the covariance of additive signals in the channels of the enemy object meters. Covariances of noise signals of an object characterize the power of disturbances, and covariances of noise signals of meters characterize the power of interference.The goal of each player’s management is to reduce the filtering error of their system and at the same time increase the filtering error of the opponent’s system. The criterion of optimal control of one player is the minimax, and the other is the maximin of the average value of the quality indicator for a finite period of time. Quality indicators consist of a linear combination of three particular indicators, the first of which is the probability of one of the two states of the Markov jump structure, and the other two are restrictions on the probabilities of transitions of the Markov chain. Observation systems consist of structure indicators and meters of one-time coordinates. Each information-control algorithm is a set of five interconnected blocks: a structure classifier, a structure indicator, a regulator, a dispersiometer and a filter. The obtained information-control algorithms are described by a closed system of recurrent equations. The algorithms are based on the methods of the theory of multistep antagonistic games, the theory of systems with a random jump structure, stochastic dynamic programming and Bayesian filtering. An example of the construction of game information-control algorithms of two unmanned aerial vehicles of the opposing sides, aimed at the objects of the opponents, is considered.