Parameterization and stabilization of the equilibrium points of affine non-linear control systems

Abstract

The paper investigates the equilibrium points of affine non-linear control systems and constructs a scheduled control law composed of a feedforward control and a family of state feedbacks. When the design of a non-linear system is decomposed into the design of a family of linear time-invariant systems, it is required to generate parameterized linear models for the plant and to develop a scheduling scheme guaranteeing stability. To solve these difficulties, we parameterized the equilibrium points of the system by constructing a coordinate transformation into a new coordinate system with the parameter coordinates. Then, the system is represented by a parameterized family of linear models along its equilibrium manifold. With these parameterized linear families, we designed a scheduled control law with a feedforward control and local linear robust controllers so that the overall feedback stabilizes the plant about the equilibrium points. The approach is illustrated by applying it to the control of an arm-driven inverted pendulum.