Investigation of a Learning Control System with Interpolation

An on-line learning control system involving the control of processes whose mathematical description is incomplete or insufficiently known to the controller is investigated. The controller does not identify the process but finds instead from its own accumulated experience a number of points on hypersurfaces which gradually approach the control law of the system. These hypersurfaces are approximated by a number of piecewise linear hyperplanes whose equations are found after occurrence of adequate learning by interpolation methods. Due to the approximations involved, the learned control law is suboptimal. In the case of insufficient information the control vector is calculated by means of various search procedures. The results of simulation of a single-variable and a multivariable learning control system on a digital computer are presented. The results obtained indicate the achievement of adequate control with relatively small memory and real-time requirements. The feasibility of this learning control method is determined by the number of inputs and outputs of the process and the dimension of the measurement vector involved.