A rule-based neural controller for inverted pendulum system

This paper tries to demonstrate how a heuristic neural control approach can be used to solve a complex nonlinear control problem. The control task is to swing up a pendulum mounted on a cart from its stable position (vertically down) to the zero state (up right) and keep it there by applying a sequence of two opposing constant forces of equal magnitude to the mass center of the cart. In addition, the displacement of the cart itself is confined to within a preset limit during the swinging up action and it will eventually be brought to the origin of the track. This is truly a nontrivial nonlinear regulation problem and is considerably difficult compared to the pendulum balancing problem (and its variations) widely adopted as a benchmarking test system for neural controllers. Through the solution of this specific control problem, we try to illustrate a heuristic neural control approach with task decomposition, control rule extraction and neural net rule implementation as its basic elements. Specializing to the pendulum problem, the global control task is decomposed into subtasks namely pendulum positioning and cart positioning. Accordingly, three separate neural subcontrollers are designed to cater to the subtasks and their coordination, i.e., pendulum subcontroller (PSC), cart subcontroller (CSC) and the switching subcontroller (SSC). Each of the subcontrollers is designed based on the rules and guidelines obtained from the experiences of a human operator. The simulation result is included to show the actual performance of the controller.