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Computation of Lyapunov Functions under State Constraints using Semidefinite Programming Hierarchies *
- Source :
- Proceedings of 21st IFAC World Congress, Jul 2020, Berlin, Germany
- Publication Year :
- 2020
-
Abstract
- We provide algorithms for computing a Lyapunov function for a class of systems where the state trajectories are constrained to evolve within a closed convex set. The dynamical systems that we consider comprise a differential equation which ensures continuous evolution within the domain, and a normal cone inclusion which ensures that the state trajectory remains within a prespecified set at all times. Finding a Lyapunov function for such a system boils down to finding a function which satisfies certain inequalities on the admissible set of state constraints. It is well-known that this problem, despite being convex, is computationally difficult. For conic constraints, we provide a discretization algorithm based on simplicial partitioning of a sim-plex, so that the search of desired function is addressed by constructing a hierarchy (associated with the diameter of the cells in the partition) of linear programs. Our second algorithm is tailored to semi-algebraic sets, where a hierarchy of semidefinite programs is constructed to compute Lyapunov functions as a sum-of-squares polynomial.
- Subjects :
- Mathematics - Optimization and Control
Subjects
Details
- Database :
- arXiv
- Journal :
- Proceedings of 21st IFAC World Congress, Jul 2020, Berlin, Germany
- Publication Type :
- Report
- Accession number :
- edsarx.2009.06885
- Document Type :
- Working Paper