A receding horizon generalization of pointwise min-norm controllers

Abstract

Abstract-Control Lyapunov functions (CLF's) are used in conjunction with receding horizon control (RHC) to develop a new class of receding horizon 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 CLF based receding horizon scheme, of which a special case provides an appropriate extension of Sontag's formula. The scheme is first presented as an idealized continuous-time receding horizon control law. The issue of implementation under discrete-time sampling is then discussed as a modification. 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. Finally, stronger connections to both optimal and pointwise min-norm control are proved in the Appendix under more restrictive technical conditions. Index Terms-Control Lyapunov functions, nonlinear optimal control, predictive control, receding horizon control.

Online Control Customization via Optimization‐Based Control

“…In Primbs et al [26], aspects of a stability guaranteeing global control Lyapunov function were used, via state and control constraints, to develop a stabilizing receding horizon scheme. Many of the nice characteristics of the CLF controller together with better cost performance were realized.…”

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“…The use of control Lyapunov functions within the context of receding horizon control is a recent one. In [15] control Lyapunov functions were utilized as explicit constraints in the auxiliary problems to guarantee that the final state x(T i + T ) lies within the level curve of the control Lyapunov function that is determined by the trajectory controlled by a minimum norm control. The analysis in [11] utilizes control Lyapunov functions as a terminal penalty as in (1.4).…”

“…Receding horizon techniques have proved to be effective numerically both for optimal control problems governed by ordinary (e.g. [3,[11][12][13]15,16]) and for partial differential equations, e.g. in the form of the instantaneous control technique for problems in fluid mechanics [2,4,5,9].…”

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“…18,19 Recently, the researches in refs. [20][21][22][23][24] show that nonlinear controllers can be used to find the terminal state region as long as a stability condition is met. The works in refs.…”