Optimum continuous control by a method of parameterization

A method is developed in this thesis which utilizes a parameter search iteration scheme to determine the continuous control which will yield an optimal cost for a multistage process. The method of parameterization presented is defined to be a technique which considers the state at any stage of the process to be a function of the state at the preceding stage, the process equations derived for the control variables, and the parameters which are chosen to yield extremal values of some cost model. The free parameters are the initial conditions for the process equations of control and the duration of the process. The process equations for the control are obtained by applying the necessary conditions for optimality and converting the problem to a two point boundary value problem. The parameters (the missing initial conditions and the duration of the process) are determined by numerically selecting a set of values such that the sum of the squares of the dissatisfactions in meeting the necessary conditions for optimality and the boundary conditions is minimized. The problems of multiburn spacecraft transfers can be solved by using the method of parameterization. An obstacle to obtaining optimal control for such problems is the discontinuity in the control which occurs when the engine is shut down or restarted. For such cases the method of parameterization converges to an optimal cost with little sensitivity to errors in the assumed initial conditions for the free parameters. [...]