Adaptive Critics Design with Support Vector Machine for Spacecraft Finite-Horizon Optimal Control

In this study, an adaptive critics design based on a support vector machine (SVM) is adopted to design a finite-horizon optimal feedback controller. The adaptive critics design consists of actor and critic networks. The actor (control input) and critic (cost-to-go) network are trained off-line with respect to various initial states and final times within a finite step. Using the well-trained actor-critic, the near-optimal feedback control solution can be obtained online. In the process of applying SVM to the adaptive critics, an adequate kernel function and parameters depending on the kernel function must be selected. In this study, a polynomial function and radial basis function are used for the SVM kernel function to implement the algorithm. A minimum control effort problem with final constraints for spacecraft rendezvous is considered to demonstrate the performance of the proposed the developed algorithm with respect to each kernel function and to show its potential for designing an optimal controller.