Lyapunov-based switching control of nonlinear systems using high-gain observers.

*(English)*Zbl 1140.93456Summary: We consider output feedback stabilization of uniformly observable uncertain nonlinear systems when the uncertain parameters belong to a known but comparably large compact set. In a previous paper, we proposed a new logic-based switching control to improve the performance of continuous high-gain-observer-based sliding mode controllers. Our main goal here is to show that similar techniques can be exploited for solving challenging control problems for a more general class of uncertain nonlinear systems. We require neither the sign of the high-frequency gain to be known nor the system to be minimum-phase. The key idea is to split the set of parameters into smaller subsets, design a controller for each of them, and switch the controller if, after a dwell-time period, the derivative of the Lyapunov function does not satisfy a certain inequality. A high-gain observer is used to estimate the derivatives of the output as well as the derivative of the Lyapunov function. Another goal of this paper is to introduce a switching strategy that uses on-line information to decide on the controller to switch to, instead of using a pre-sorted list as in our previous work. The new strategy can improve the transient performance of the system.

##### MSC:

93D15 | Stabilization of systems by feedback |

93D30 | Lyapunov and storage functions |

93C10 | Nonlinear systems in control theory |

##### Keywords:

switching control; Lyapunov design; high-gain observers; nonlinear uncertain systems; practical stabilization
PDF
BibTeX
XML
Cite

\textit{L. B. Freidovich} and \textit{H. K. Khalil}, Automatica 43, No. 1, 150--157 (2007; Zbl 1140.93456)

Full Text:
DOI

##### References:

[1] | Angeli, D.; Mosca, E., Lyapunov-based switching supervisory control of nonlinear uncertain systems, IEEE transactions on automatic control, 47, 500-505, (2002) · Zbl 1364.93696 |

[2] | Corradini, M.L.; Orlando, G., A switching controller for the output feedback stabilization of unknown uncertain interval plants via sliding modes, IEEE transactions on automatic control, 47, 2101-2107, (2002) · Zbl 1364.93627 |

[3] | Freidovich, L.B. (2005). Logic-based switching control of nonlinear systems using high-gain observers. Ph.D. dissertation, Michigan State University. |

[4] | Freidovich, L.B.; Khalil, H.K., Logic-based switching for the robust control of minimum-phase nonlinear systems, Systems and control letters, 54, 713-727, (2005) · Zbl 1129.93412 |

[5] | Hespanha, J.P.; Liberzon, D.; Morse, A.S., Overcoming the limitations of adaptive control by means of logic-based switching, Systems and control letters, 49, 49-65, (2003) · Zbl 1157.93440 |

[6] | Khalil, H.K., Nonlinear systems, (2002), Prentice-Hall Englewood Cliffs, NJ · Zbl 0626.34052 |

[7] | Liberzon, D., Switching in systems and control, (2003), BirkhĂ¤user Boston, MA · Zbl 1036.93001 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.