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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 on theme: "Chess Review November 21, 2005 Berkeley, CA Edited and presented by Optimal Control of Stochastic Hybrid Systems Robin Raffard EECS Berkeley."— Presentation transcript:

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

2 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.

3 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.

4 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

5 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

6 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…

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