Continuous-time Zero-sum Games Research Articles

Online and Robust Intermittent Motion Planning in Dynamic and Changing Environments.

In this article, we propose RRT-Q X∞ , an online and intermittent kinodynamic motion planning framework for dynamic environments with unknown robot dynamics and unknown disturbances. We leverage RRT X for global path planning and rapid replanning to produce waypoints as a sequence of boundary-value problems (BVPs). For each BVP, we formulate a finite-horizon, continuous-time zero-sum game, where the control input is the minimizer, and the worst case disturbance is the maximizer. We propose a robust intermittent Q-learning controller for waypoint navigation with completely unknown system dynamics, external disturbances, and intermittent control updates. We execute a relaxed persistence of excitation technique to guarantee that the Q-learning controller converges to the optimal controller. We provide rigorous Lyapunov-based proofs to guarantee the closed-loop stability of the equilibrium point. The effectiveness of the proposed RRT-Q X∞ is illustrated with Monte Carlo numerical experiments in numerous dynamic and changing environments.

Continuous-time zero-sum games for Markov chains with risk-sensitive finite-horizon cost criterion

In this paper, we study the two-person zero-sum stochastic games for controlled continuous time Markov chains with risk-sensitive finite-horizon cost criterion. The transition and cost rates are possibly unbounded. For the zero-sum risk-sensitive stochastic game, we prove the existence of the value of the game and a Markov saddle-point equilibrium in the class of all history-dependent multi-strategies under the suitable conditions. We achieve our results by studying the corresponding risk-sensitive finite-horizon optimality equations.

Continuous-time zero-sum games with probability criterion

In this article, we investigate a zero-sum stochastic game for continuous-time Markov chain with denumerable state space and unbounded transition rates, under the probability criterion. Under suitable assumptions, we show the existence of value of the game and also characterize it as the unique solution of a pair of Shapley equations. We also establish the existence of a randomized stationary saddle point equilibrium.