7. Several Special Optimal Feedback Control Designs Based on ADP

In this chapter, several special optimal feedback control schemes will be investigated. In the first part, the optimal feedback control problem of affine nonlinear switched systems is studied. To seek optimal solutions, a novel two-stage adaptive dynamic programming (TSADP) method is developed. The algorithm can be divided into two stages: first, for each possible mode, calculate the associated value function, and then select the optimal mode for each state. In the second and third parts, the near-optimal controllers for nonlinear descriptor systems and singularly perturbed systems are solved by iterative DHP and HDP algorithms, respectively. In the fourth part, the near-optimal state-feedback control problem of nonlinear constrained discrete-time systems is solved via a single network ADP algorithm. At each step of the iterative algorithm, a neural network is utilized to approximate the costate function, and then the optimal control policy of the system can be computed directly according to the costate function, which removes the action network appearing in the ordinary ADP method.