Reinforcement Solver for H-infinity Filter with Bounded Noise

TL;DR

This paper develops a reinforcement learning-based method to design H-infinity filters that effectively handle bounded noise in linear systems, overcoming the challenges of non-affine and nonlinear estimation error dynamics.

Contribution

It introduces a novel reinforcement learning algorithm to solve the nonquadratic Hamilton-Jacobi-Isaacs equation for bounded noise filtering, which is a significant advancement over traditional methods.

Findings

The proposed algorithm converges reliably in example scenarios.

It effectively handles non-affine and nonlinear properties of the filtering problem.

Simulation results demonstrate improved filtering performance 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 H-infinity 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 non-affine 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.