Solution of Highly Constrained Optimal Control Problems Using Nonlinear Programing

HIS paper considers the solution of highly constrained optimal control problems using the nonlinear programing method of Fiacco-McCormick.1 Several authors2'3 have successfully applied the technique to constrained optimal control problems of a limited scope. The present paper expands the theory to encompass a general mathematical model for trajectory optimization capable of directly handling six types of equality and inequality constraints. The user-oriented model is designed to facilitate the rapid set up of a wide range of different simulations and provides for the simultaneous optimization of design parameters and continuous control variables. Accurate and efficient methods of unconstrained function minimization and linear search required to implement the Fiacco-McCormick method are discussed. Contents The general mathematical model presented provides a flexible skeletal framework for describing a wide spectrum of complex optimal control problems in terms of problem-oriented functions. The model is capable of incorporating two classes of independent variables which are to be chosen to extremize some objective function. Independent variables which are functions of time are termed dynamic control variables and are designated by uk(t). Independent variables which are constant with respect to time are termed design variables, dp. Trajectory sectioning is a device commonly used to provide flexibility in modeling. It is a method of subdividing the time history of a trajectory simulation into parts relevant to the description of the simulation. A section is defined as any portion of the trajectory in which the mathematical model is of a given form and the state variables xt(t) are continuous functions of time. Section endpoints are chosen to coincide with points at which the differential equations of motion, the control model, or the trajectory constraints change form ; or at which the state variables experience a discontinuity. If the subscript) denotes the trajectory section, then the general optimal control problem is to