Piecewise Linear Control of Nonlinear Systems

Abstract

Using a Taylor series expansion, nonlinear control systems are approximated about desired equilibrium points in state space as linear control systems. The techniques of the linear regulator problem are then used to calculate the linear state variable feedback gains needed to keep the system at the desired equilibrium point. Liapunov's second method is the basis for determining stable regions of operation about the equilibrium points. When driving the system from one equilibrium point to another, the piecewise linearization method is also used but with intermediate equilibrium points successively utilized. Enough equilibrium points are used so that the system is stable throughout the region of interest. Thus, a nonlinear system is controlled using linear state variable feedback. A small digital computer is required to implement this strategy.