## Abstract

The problem of set-point regulation (stabilization) of mechanical port-Hamiltonian (pH) systems has been widely studied in the literature by means of energy-based methods. However, for motion control problems, where the reference signal is time-varying, it is not straightforward to design control laws for such pH systems that still provides an insightful energy interpretation of the closed-loop system. One major difficulty is that the external reference signals can induce both the closed-loop system and total energy function

to be time-varying. In this case, the closed-loop system may not be dissipative, or if it is a time-varying dissipative system, the usual La-Salle invariance principle argument can no longer be invoked for analyzing the asymptotic behavior. As an alternative, in this work, we propose a contraction based approach, to the convergence analysis of fullyactuated mechanical pH systems in closed-loop with the trajectory tracking controller. To that end, using partial contraction analysis, we construct a contracting virtual system having as two particular solutions to the time-varying desired trajectory driven by the tracking controller and the mechanical pH system itself

to be time-varying. In this case, the closed-loop system may not be dissipative, or if it is a time-varying dissipative system, the usual La-Salle invariance principle argument can no longer be invoked for analyzing the asymptotic behavior. As an alternative, in this work, we propose a contraction based approach, to the convergence analysis of fullyactuated mechanical pH systems in closed-loop with the trajectory tracking controller. To that end, using partial contraction analysis, we construct a contracting virtual system having as two particular solutions to the time-varying desired trajectory driven by the tracking controller and the mechanical pH system itself

Original language | English |
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Pages | 134 |

Number of pages | 134 |

Publication status | Published - 28-Mar-2017 |

Event | 36 th Benelux Meeting on Systems and Control - Spa, Belgium Duration: 28-Mar-2017 → 30-Apr-2017 |

### Conference

Conference | 36 th Benelux Meeting on Systems and Control |
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Country | Belgium |

City | Spa |

Period | 28/03/2017 → 30/04/2017 |