A novel approach with parallel processing capability to solve optimal control problem of nonlinear large-scale systems

In this paper, a novel Modal Series Representation (MSR) approach is proposed to solve the infinite horizon optimal control problem (OCP) of nonlinear interconnected large-scale systems. In this approach, the high order, coupled, nonlinear two-point boundary value problem (TPBVP) derived from the Pontryagin´s maximum principle is transformed into a sequence of decoupled linear TPBVP´s. By solving the proposed linear TPBVP sequence in a recursive manner, the optimal control law and the optimal trajectory are determined in terms of uniformly convergent series. Hence, to obtain the optimal solution, only the techniques of solving linear ordinary differential equations (ODE´s) are employed. Another important factor is that the computational structure of the proposed technique can effectively utilize the parallel processing facilities, from which a significant reduction of computational time can be obtained. Besides, a control design algorithm with low computational complexity and fast convergence rate is presented. Through the finite iterations of the algorithm, a closed-form expression is obtained for the suboptimal control law. Finally, a numerical example is included to demonstrate the computational efficiency and high accuracy of the proposed technique.