The derivation of optimal control laws and the synthesis of real-time optimal controllers for a class of dynamic systems

A method for the solution of a class of optimal control problems based on a modified steepest descent method is discussed. This method is suitable for the solution of problems in variational calculus of the Mayer type, and can be used to realize comparatively simple on-line optimal controllers by means of analogue computer techniques. The essence of the modified steepest descent method is to search for the optimum value of a performance function by replacing a search in function space by a search in parameter space. In general, an iterative type of search for the optimum value of the performance function is required. However, in certain classes of problems the optimal control variable can be expressed as a function of the system state variables and no iteration is necessary. Several optimal control problems for the rocket flight problem are studied and optimal control laws are derived as functions of the system state variables. Experimental results show that the method is very satisfactory. A PACE 231-R analogue computer is used to solve the sounding rocket problem. A more complex problem, the two—dimensional zero-lift rocket flight problem, is solved using the modified method of steepest descent and an electromechanical flight simulator. The experimental results obtained with the flight simulator show that the modified steepest descent method is practical and show promise of being useful in the design of real-time optimal controllers.Applied Science, Faculty ofElectrical and Computer Engineering, Department ofGraduat