Optimal prescribed performance tracking control of nonlinear motor driven systems via adaptive dynamic programming

Although optimal regulation problem has been well studied, resolving optimal tracking control via adaptive dynamic programming (ADP) has not been completely resolved, particularly for nonlinear uncertain systems. In this paper, an online adaptive learning method is developed to realize the optimal tracking control design for nonlinear motor driven systems (NMDSs), which adopts the concept of ADP, unknown system dynamic estimator (USDE), and prescribed performance function (PPF). To this end, the USDE in a simple form is first proposed to address the NMDSs with bounded disturbances. Then, based on the estimated unknown dynamics, we define an optimal cost function and derive the optimal tracking control. The derived optimal tracking control is divided into two parts, that is, steady-state control and optimal feedback control. The steady-state control can be obtained with the tracking commands directly. The optimal feedback control can be obtained via the concept of ADP based on the PPF; this contributes to improving the convergence of critic neural network (CNN) weights and tracking accuracy of NMDSs. Simulations are provided to display the feasibility of the designed control method.