Optimal control of discrete-time singularly perturbed systems

In this paper, we present a new algorithm for solving the optimal control of discrete-time singularly perturbed systems. The main idea of this algorithm is based on two steps. First, the Hamiltonian difference equation is reduced to the backward recursive form rather than the forward recursive form. Second, the bilinear transformation is applied to transform the derived non-symmetric discrete-time Riccati equations into continuous-time equations. In order to improve the efficiency of this scheme, two matrix permutations are introduced into this algorithm by taking into account the previous work of Gajic and Shen (1991). Therefore, substantial numerical advantages are gained; namely, computation and memory requirements. The F-8 aircraft model is used to illustrate the efficiency of the proposed method.