Data-Driven Suboptimal Control for Nonlinear Systems Using State-Dependent Riccati Equation

The approximate optimal control design for continuous-time nonlinear systems with partially unknown dynamics is studied in this paper. Based on the state-dependent coefficient parameterization, the dynamics of nonlinear systems are represented in a resemble linear manner. In this case, the Hamilton-Jacobi-Bellman equation can be recast in the form of the state-dependent Riccati equation (SDRE). Based on the integral reinforcement learning, an online policy iteration algorithm is developed to iteratively solve the SDRE using status and control data. In addition, it is proved that the proposed algorithm is equivalent to the traditional iterative solution of SDRE. A suboptimal control policy can be attained under proper conditions. The iterative feedback control policy has the ability to stabilize closed-loop system. The effectiveness of the presented algorithm is validated by simulation results.