An efficient iterative method for the optimal control of discrete nonlinear interconnected dynamical systems

This article introduces an iterative method for solving discrete optimal control problems involving interconnected nonlinear systems. Using this approach, the discrete and coupled nonlinear boundary value problem (BVP) obtained from the necessary optimality conditions transforms into a sequence of linear time invariant BVPs. Furthermore, the linear BVP at each iteration of the proposed method consists of several decoupled sub-problems, which can be solved in parallel and are unrelated to each other. The solution of these problems, employing common techniques for solving linear difference equations, leads to an optimal control law in a converging series form with uniform convergence. Moreover, a practical approach is presented to extend the designed optimal control to a feedback form. Subsequently, the implementation of the proposed method involves the design of a highly accurate iterative algorithm with low computational complexity, ensuring that the suboptimal control law is obtained with a minimal number of iterations. Finally, the efficacy of this technique is demonstrated through simulation and the solution of various numerical examples.