Reinforcement learning-based optimized backstepping control of nonlinear strict feedback system with unknown control gain function

The article develops an optimized control via learning from the design idea of optimized backstepping (OB) technique for the nonlinear strict feedback systems containing the unknown dynamic and control gain functions. OB technique requires to deal with the actual and virtual controls of backstepping as the optimized solutions of corresponding subsystems so that the entire backstepping control is optimized. In the work, for achieving the optimization control, reinforcement learning (RL) of critic-actor structure is constructed in every backstepping step on the basis of the neural network approximation of the Hamilton-Jacobi-Bellman equation's solution. Since the unknown nonlinear control gain function is considered, the complexity of control algorithm is greatly increased. However, the proposed RL is with the simple training laws, it can greatly alleviate the algorithm complexity for the optimized control. Finally, the feasibility of the method is demonstrated by both theory and simulation.