Optimal and Sub-optimal Control Design for Second Order Nonlinear Affine Systems using Krotov Sufficient Conditions

This article tackles the optimal control design problem for second order nonlinear affine systems using Krotov sufficient conditions. The computation of optimal control law(s) for nonlinear systems is usually done using the iterative methods based on the standard tools of optimal control theory which viz. Calculus of Variations (CoV), Hamilton-Jacobi-Bellman equation, Pontryagin's principle, etc. This work utilizes the Krotov sufficient conditions of global optimality to obtain non-iterative solutions. These conditions are derived by transforming the optimal control problem into another equivalent optimization problem. This translation is done via an ad-hoc selection of the so-called Krotov function. In this article, the Krotov function is chosen such that the equivalent optimization problem is solved non-iteratively to obtain optimal and sub-optimal control laws for the original optimal control problem. The proposed methodology is demonstrated by a numerical example.