Numerical construction of nonsmooth control Lyapunov functions. (English) Zbl 1414.93168

Baier, Robert; Braun, Philipp; Grüne, Lars; Kellett, Christopher M.

Giselsson, Pontus (ed.) et al., Large-scale and distributed optimization. Contributions of the workshop, Lund, Sweden, June 14–16, 2017. Cham: Springer. Lect. Notes Math. 2227, 343-373 (2018).

Lyapunov control functions are computed by means of linear programming and mixed integer linear programming. A mixed integer linear program based on a discretization of the state space is proposed, where a continuous piecewise affine control Lyapunov function can be recovered from the solution of the optimization problem. Differences to previous work are stressed, in particular the role of the considered semiconcavity. The new results are illustrated on the example of Artstein’s circles and on a two-dimensional system with two inputs, the underlying optimization problems being solved in Gurobi.
For the entire collection see [Zbl 1407.90006].

Reviewer: Sorin-Mihai Grad (Vienna)

MSC:

93D30	Lyapunov and storage functions
90C11	Mixed integer programming
93D05	Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
90C05	Linear programming

Keywords:

control Lyapunov functions; mixed integer programming; dynamical systems

Software:

Gurobi