NONLINEAR OPTIMAL CONTROL: A CONTROL LYAPUNOV FUNCTION AND RECEDING HORIZON PERSPECTIVE

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). The on-line Euler-Lagrange computation of receding horizon control is naturally viewed in terms of optimal control, whereas researchers in CLF methods have emphasized such notions as inverse optimality. We focus on a CLF variation of Sontag's formula, which also results from a special choice of parameters in the so-called pointwise minnorm formulation. Viewed this way, CLF methods have direct connections with the Hamilton-Jacobi-Bellman formulation of optimal control. A single example is used to illustrate the various limitations of each approach. Finally, we contrast the CLF and receding horizon points of view, arguing that their strengths are complementary and suggestive of new ideas and opportunities for control design. The presentation is tutorial, emphasizing concepts and connections over details and technicalities.