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In this paper, we revised an adaptive fuzzy sliding mode control algorithm applied to a two-degree-of-freedom robotic manipulator. Stability of the overall system for the revised algorithm is proven in a Lyapunov sense. A discussion on the proof of Lyapunov stability for different algorithms is presented.

We extend the potential-based shaping method from Markov decision processes to multi-player general-sum stochastic games. We prove that the Nash equilibria in a stochastic game remains unchanged after potential-based shaping is applied to the environment. The property of policy invariance provides a possible way of speeding convergence when learning to play a stochastic game.

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