On receding horizon extensions and control Lyapunov functions

Abstract

Control Lyapunov functions (CLFs) are used in conjunction with receding horizon control (RHC) to develop a new class of control schemes. In the process, strong connections between the seemingly disparate approaches are revealed, leading to a unified picture that ties together the notions of pointwise min-norm, receding horizon, and optimal control. This framework is used to develop a control Lyapunov function based receding horizon scheme, of which a special case provides an appropriate extension of a variation on Sontag's formula. These schemes are shown to possess a number of desirable theoretical and implementation properties. An example is provided, demonstrating their application to a nonlinear control problem.