Robust optimal control of logical control networks with function perturbation

Optimal control is an important branch in modern control theory. In this article, the robustness of optimal control sequence is investigated for logical control networks (LCNs) subject to function perturbation. Firstly, the impact of function perturbation on the Bolza-type optimal control problem of LCNs is analyzed, and several sufficient conditions are presented for the robustness of optimal control sequence. Secondly, combining the characteristics of state transition matrix and stage cost function, a kind of optimal matrix is constructed, which brings a new way for the solvability of Bolza-type optimal control problem. Thirdly, the optimal matrix is used to measure the deviation of cost function with respect to function perturbation, and several necessary and sufficient conditions are proposed to guarantee the robustness of optimal control sequence. Finally, the robustness of optimal control sequence in the Bolza-type optimal control problem is applied to other types of finite-horizon and infinite-horizon optimal control problems of LCNs.