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Reinforcement Solver for H-infinity Filter with Bounded Noise

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Document pages: 6 pages

Abstract: H-infinity filter has been widely applied in engineering field, but coppingwith bounded noise is still an open problem and difficult to solve. This paperconsiders the H-infinity filtering problem for linear system with boundedprocess and measurement noise. The problem is first formulated as a zero-sumgame where the dynamic of estimation error is non-affine with respect to filtergain and measurement noise. A nonquadratic Hamilton-Jacobi-Isaacs (HJI)equation is then derived by employing a nonquadratic cost to characterizebounded noise, which is extremely difficult to solve due to its non-affine andnonlinear properties. Next, a reinforcement learning algorithm based ongradient descent method which can handle nonlinearity is proposed to update thegain of reinforcement filter, where measurement noise is fixed to tacklenon-affine property and increase the convexity of Hamiltonian. Two examplesdemonstrate the convergence and effectiveness of the proposed algorithm.

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