SNAC based near-optimal controller for robotic manipulator with unknown dynamics

A near optimal control technique for robotic manipulator with completely unknown dynamics is described in this work. Obtaining the optimal control law u* depends on solving Hamilton Jacobi Bellman equation but getting an analytic solution is not possible for unknown models. It is shown that instead of solving HJB equation analytically, the optimal control law can be obtained through learning of a Single Network Adaptive Critic (SNAC). The generic nonlinear model of manipulator dynamics is represented as Takagi-Sugeno-Kang fuzzy combination of local linear models. A stabilizing fixed gain controller is designed for the TSK fuzzy system using an unconventional Lyapunov function that is used to represent the value function. Stable Lyapunov P⁽ⁱ⁾ matrices are selected using the Genetic Algorithm (GA) Toolbox in Matlab. This approach avoids the learning of initial cost that can be accumulated by an existing controller. The critic is trained to approximate the optimal cost J* by renewing the policy in iterations. Validation of the proposed technique is done through simulation on a robotic manipulator model. Results show the effectiveness of the presented work.