Minimax estimation for hybrid systems

This paper addresses static minimax estimation for switched-linear hybrid systems, by solving a related auxiliary stochastic game where the switching variable is allowed to be random (but with unknown statistics), the disturbance terms are allowed knowledge of the switching variable, but the estimation policy is only allowed knowledge of the measurement. We provide a proof of the existence of a minimax, cost-bounding estimation policy under certain conditions and an algorithm for finding that policy. Two examples are included to illustrate the application of the stochastic game and the proposed algorithm.