Radial basis function neural networks for optimal control with model reduction and transfer learning

Anni Zhao, Siyuan Xing, Xi Wang, Jian-Qiao Sun

Abstract: This paper proposes a method to compute the solutions of linear optimal control expressed in terms of the radial basis function neural networks with Gaussian activation functions for multi-degree-of-freedom dynamic systems. Hamilton–Jacobi–Bellman equation is adopted to formulate the optimal control problem. The radial basis function neural networks are proposed to approximate the value function to solve the Hamilton–Jacobi–Bellman equation with a policy iteration algorithm. A dominant stabilizing control is proposed as an initial control to start the policy iteration that guarantees the convergence of the iteration, particularly for open-loop unstable dynamic systems. The balanced truncation technique is applied to the multi-degree-of-freedom dynamic system to reduce the dimension of the original system, which provides multiple advantages when applying the radial basis function neural networks to unstable dynamic systems in a relatively high dimensional state space. Transfer learning is also adopted to update radial basis function neural networks with experimental data, which results in further control performance improvement. Numerical simulations and experimental studies show that the radial basis function neural networks not only find accurate optimal controls for linear systems, but also offer excellent performance in trajectory tracking and stabilization applications.