Reinforcement Solver for H-infinity Filter with Bounded Noise

Abstract

H-infinity filter has been widely applied in engineering field, but copping with bounded noise is still an open problem and difficult to solve. This paper considers the Hinfinity filtering problem for linear system with bounded process and measurement noise. The problem is first formulated as a zero-sum game where the dynamic of estimation error is nonaffine with respect to filter gain and measurement noise. A nonquadratic Hamilton-Jacobi-Isaacs (HJI) equation is then derived by employing a nonquadratic cost to characterize bounded noise, which is extremely difficult to solve due to its non-affine and nonlinear properties. Next, a reinforcement learning algorithm based on gradient descent method which can handle nonlinearity is proposed to update the gain of reinforcement filter, where measurement noise is fixed to tackle non-affine property and increase the convexity of Hamiltonian. Two examples demonstrate the convergence and effectiveness of the proposed algorithm.