Abstract
In this paper, we provide an analysis of the convergence characteristics of the dynamic programming value iteration method based on stability-theoretical results of discrete-time switched affine systems. For interval Markov decision processes subject to multiple objective functions, we reformulate the value iteration algorithm as a switched affine system with additive uncertainties. Building on this change of perspective, we adopt a Lyapunov-based strategy for designing a control policy by finding a switching law that stabilizes the system towards an invariant set of attraction centered at a desired target value. The results provide insights into the convergence of the value iteration algorithm and the feasibility of desired target values. The results are demonstrated on two case studies.
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