OPTIMAL CONTROL FOR A CLASS OF SINGULAR SYSTEMS USING NEURAL NETWORK

In this paper we address the optimal LQR and tracking problems for continuous linear time invariant singular systems which have only a finite dynamic mode. We use the HamiltonJaccobi theory to compute the optimal control and associated trajectory. In the case of the LQR problem, a generalized Riccati equation is derived. Wethen propose three neural network structures for solving the equation. In the case of the tracking problem, in addition to the generalized Riccati equation, we obtain a singular equation. In each case, the solutions obtained by neural networks are applied to the original singular system. Simulation results demonstrate the good performance of the proposed methods.