Optimal control of satellite attitude acquisition by a random search algorithm on a hybrid computer

Computer implemented parameter search techniques for optimization problems have become useful engineering design tools over the past few years. Many, if not most of the techniques, are based on deterministic schemes which have inherent limitations when the system is nonlinear. Random search techniques have been suggested which propose to overcome some of the difficulties. References 1--3 give good general discussions of the merits of random techniques. Reference 4 develops an algorithm, based on random methods, to solve the difficult mixed two-point boundary value problem that results from an application of the Maximum Principle. The method was shown to be remarkably effective in solving a fairly complex fifth-order, nonlinear orbital-transfer problem. The purpose of this paper is to discuss the application of the random search algorithm to a still more complex problem to demonstrate its feasibility. The example chosen was the three-dimensional, large-angle, single-axis attitude acquisition control problem in which it is desired to minimize fuel expenditure to accomplish the acquisition. The equations are highly nonlinear since small angle assumptions cannot be made; the control torques are assumed to be limited. This problem is more complex than the orbit-transfer problem in that the dimension of the state vector is greater by 1 and the number of degrees of freedom allowed the control action is greater. The same acquisition problem was discussed in Reference 5 but a proportional control law was assumed. A random parameter search was used in that paper to find the optimal set of feedback constants for the given control system structure so as to minimize system performance (fuel). Systems performances will be compared to indicate the striking improvement in performance with optimal nonlinear control.