Robustness improvement of optimal control in terms of RBFNN with empirical model reduction and transfer learning

This paper proposes a method to compute solutions of optimal controls for dynamic systems in terms of radial basis function neural networks (RBFNN) with Gaussian neurons. The RBFNN is used to compute the value function from Hamilton-Jacobi-Bellman equation with the policy iteration. The concept of dominant system is introduced to create initial coefficients of the neural networks to stabilise unstable systems and guarantee the convergence of policy iteration. Model reduction and transfer learning techniques are introduced to improve robustness of RBFNN optimal control, and reduce computational time. Numerical and experimental results show that the resulting optimal control has excellent control performance in stabilisation and trajectory tracking, and much-improved robustness to disturbances and model uncertainties even when the system responses move to a domain of the state space that is larger than the domain where the neural networks are trained.