An Integrated Dynamics Approach for Optimal Control

In this paper, an integrated dynamics approach is used to convert a constrained nonlinear optimal control problem to an unconstrained nonlinear optimal control problem. This is achieved by numerically integrating the system dynamics based on knowledge of the control functions, control parameters, and the system's initial conditions. The integrated dynamics are then substituted directly into the performance index, avoiding the need for Lagrange multipliers. The necessary conditions for optimality of the unconstrained control problem are derived. The necessary conditions are then expanded into useful formulas for implementation. Finally, it is shown how to implement the integrated dynamics approach using a conjugate gradient algorithm, assuming fourth-order Runge-Kutta integration.