A receding horizon generalization of pointwise min-norm controllers.

*(English)*Zbl 0976.93024A new class of control schemes is introduced which retain the global stability properties of control Lyapunov function (CLF) methods while taking advantage of the on-line optimization techniques employed in receding horizon control (RHC). A unified picture that ties together the notions of pointwise min-norm, receding horizon, and optimal control is suggested. It is shown that the receding horizon control obtained from the proposed RHC+CLF control problem will converge to the optimal control or to the CLF-based pointwise min-norm control as the horizon extends to infinity or shrinks to zero. This observation is used to develop a CLF-based receding horizon scheme, a special case of which provides an appropriate extension of Sontag’s CLF 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. The numerous theoretical and implementation advantages of the proposed RHC+CLF control schemes over present RHC and CLF methodologies are demonstrated on a nonlinear oscillator example.

Reviewer: Ingmar Randvee (Tallinn)

##### MSC:

93B51 | Design techniques (robust design, computer-aided design, etc.) |

93D15 | Stabilization of systems by feedback |

49N35 | Optimal feedback synthesis |

93C10 | Nonlinear systems in control theory |

93D30 | Lyapunov and storage functions |