Markov game based control: Worst case design strategies for games against nature

For sequential design processes, the min-max strategy minimizes the worst-case performance cost. This is a game against nature, where the agent attempts to minimize a specified cost criterion, while nature attempts to maximize it. In this paper, we formulate the problem of decision making under uncertainty as a game in which the opponent (nature) is “disinterested” and plays at random, while the agent forces to pick a strategy that maximizes the probability of wining. The potency of proposed worst-case design strategy for games against nature has been established through simulation experiments on inverted-pendulum swing-up. Simulation results show the accelerated learning, and better relative stability of the system.