Direct Adaptive Control using Single Network Adaptive Critic

An optimal control law for a general nonlinear system can be obtained by solving Hamilton-Jacobi-Bellman equation. However, it is difficult to obtain an analytical solution of this equation. In this paper, we propose a direct adaptive control method for affine systems where the optimal value function is approximated using a critic network and the weight update law is derived so as to satisfy the HJB equation. This provides an alternative method to solve the HJB equation in real-time and thus paves the way for introducing some notion of optimality to direct adaptive control paradigm. The efficacy of the scheme is demonstrated for a linearized mass-spring-damper system and its performance is compared with that of LQR.