Optimal Control Design using Sequential Linear Programming

The focus of this paper is on the development of an iterative Linear Programming based approach for the determination of optimal controllers for nonlinear systems. The optimal control problem is posed in a Mayer form and a one-dimensional search technique such as the bisection algorithm is used on the cost function to converge to the optimal solution. A polynomial representation for the variation of the control profile is used to arrive at discrete time approximation of the perturbation dynamics about nominal trajectories. A linear program is then used to determine perturbations to the nominal control to satisfy terminal and transient constraints. The proposed technique is illustrated on some benchmark problems.