On Receding Horizon Extensions and Control Lyapunov Functions

Jim Primbs-CDS Graduate Student, CDS, Caltech

Two well known approaches to nonlinear control involve the use of control Lyapunov functions (CLFs) and receding horizon control (RHC), also known as model predictive control (MPC). Although both can be viewed as methods to approximate optimal controllers, in this talk we use this observation as a starting point to establish deeper connections between these two techniques.

Control Lyapunov function methodologies extend the Lyapunov methodology to control systems providing global, stability oriented control laws. We will highlight a variation of Sontag's formula, which is a special case of a more general class of so-called CLF based pointwise min-norm controllers. These control laws have been recognized for the property of being inverse optimal, and in particular, Sontag's formula has direct connections with the Hamilton-Jacobi-Bellman formulation of optimal control.

On the other hand, receding horizon control relies on the relative computational simplicity of the Euler-Lagrange approach to optimal control. Trajectory optimizations emanating from the current state measurement are solved on-line at every sampling instance to provide a state feedback control law. In this sense, RHC is performance oriented, but in general lacks the stability guarantees of CLF techniques.

We propose a new framework for the nonlinear optimal control design process that recognizes and exploits the complementary nature of CLF and RHC techniques. CLF based pointwise min-norm controllers, which provide guarantees of stability, can be viewed as the limiting case of a receding horizon control scheme. This receding horizon scheme inherits stability properties from the CLF, while at the same time taking advantage of the performance properties of receding horizon control. Not only does this yield a more unified view of the competing approaches to optimal control, but it results in a more flexible use of on-line computing power, facilitating practical implementation as well.