On merging constraint and optimal control-Lyapunov functions

Franco Bianchini, Filippo Fabiani, Sergio Grammatico

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

1 Citation (Scopus)


Merging two Control Lyapunov Functions (CLFs) means creating a single 'new-born' CLF by starting from two parents functions. Specifically, given a 'father' function, shaped by the state constraints, and a 'mother' function, designed with some optimality criterion, the merging CLF should be similar to the father close to the constraints and similar to the mother close to the origin. To successfully merge two CLFs, the control-sharing condition is crucial: the two functions must have a common control law that makes both Lyapunov derivatives simultaneously negative. Unfortunately, it is difficult to guarantee this property a-priori, i.e., while computing the two parents functions. To create a constraint-shaped 'father' function that has the control-sharing property with the 'mother' function, we introduce a partial control-sharing i.e., the control-sharing only in the regions where the constraints are active. We show that imposing partial control-sharing is a convex optimization problem. Finally, the partial control-sharing is used to merge constraint-shaped and the Riccati-optimal functions, thus generating a CLF with bounded complexity that solves the constrained linear-quadratic stabilization problem with local optimality.

Original languageEnglish
Title of host publicationProceedings of the 57th IEEE Conference on Decision and Control (CDC 2018)
EditorsAndrew R. Teel, Magnus Egerstedt
Place of PublicationPiscataway, NJ, USA
ISBN (Electronic)978-1-5386-1395-5
Publication statusPublished - 2018
EventCDC 2018: 57th IEEE Conference on Decision and Control - Miami, United States
Duration: 17 Dec 201819 Dec 2018


ConferenceCDC 2018: 57th IEEE Conference on Decision and Control
Country/TerritoryUnited States


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