1,085 research outputs found
Automated and Sound Synthesis of Lyapunov Functions with SMT Solvers
In this paper we employ SMT solvers to soundly synthesise Lyapunov functions
that assert the stability of a given dynamical model. The search for a Lyapunov
function is framed as the satisfiability of a second-order logical formula,
asking whether there exists a function satisfying a desired specification
(stability) for all possible initial conditions of the model. We synthesise
Lyapunov functions for linear, non-linear (polynomial), and for parametric
models. For non-linear models, the algorithm also determines a region of
validity for the Lyapunov function. We exploit an inductive framework to
synthesise Lyapunov functions, starting from parametric templates. The
inductive framework comprises two elements: a learner proposes a Lyapunov
function, and a verifier checks its validity - its lack is expressed via a
counterexample (a point over the state space), for further use by the learner.
Whilst the verifier uses the SMT solver Z3, thus ensuring the overall soundness
of the procedure, we examine two alternatives for the learner: a numerical
approach based on the optimisation tool Gurobi, and a sound approach based
again on Z3. The overall technique is evaluated over a broad set of benchmarks,
which shows that this methodology not only scales to 10-dimensional models
within reasonable computational time, but also offers a novel soundness proof
for the generated Lyapunov functions and their domains of validity
Formal synthesis of stabilizing controllers for periodically controlled linear switched systems
In this paper, we address the problem of synthesizing periodic switching controllers for stabilizing a family of linear systems. Our broad approach consists of constructing a finite game graph based on the family of linear systems such that every winning strategy on the game graph corresponds to a stabilizing switching controller for the family of linear systems. The construction of a (finite) game graph, the synthesis of a winning strategy and the extraction of a stabilizing controller are all computationally feasible. We illustrate our method on an example
- …