Chess Review November 21, 2005 Berkeley, CA Edited and presented by Optimal Control of Stochastic Hybrid Systems Robin Raffard EECS Berkeley.

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Presentation transcript:

Chess Review November 21, 2005 Berkeley, CA Edited and presented by Optimal Control of Stochastic Hybrid Systems Robin Raffard EECS Berkeley

Chess Review, Nov. 21, 2005Control of Stochastic Hybrid Systems, Robin Raffard2 Introduction - Motivations: Present a new method for optimal control of Stochastic Hybrid Systems. More flexible than Hamilton-Jacobi, because handles more problem formulations. In implementation, up to dimension 4-5 in the continuous state.

Chess Review, Nov. 21, 2005Control of Stochastic Hybrid Systems, Robin Raffard3 Problem Formulation: standard Brownian motion. continuous state. Solves an SDE whose jumps are governed by the discrete state. discrete state: continuous time Markov chain. control.

Chess Review, Nov. 21, 2005Control of Stochastic Hybrid Systems, Robin Raffard4 Applications: Engineering: Maintain dynamical system in safe domain for maximum time. Systems biology: Parameter identification. Finance: Optimal portfolio selection

Chess Review, Nov. 21, 2005Control of Stochastic Hybrid Systems, Robin Raffard5 Method: 1 st step 1.Derive a PDE satisfied by the objective function in terms of the generator: Example 1: If then Example 2: If then

Chess Review, Nov. 21, 2005Control of Stochastic Hybrid Systems, Robin Raffard6 Method: 2.Rewrite original problem as deterministic PDE optimization program 3.Solve PDE optimization program using adjoint method Simple and robust…