An Introduction to Polar Forms
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
Nonquadratic Lyapunov functions for robust control
Automatica (Journal of IFAC)
Global qualitative description of a class of nonlinear dynamical systems
Artificial Intelligence
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Automatica (Journal of IFAC)
Computing Differential Invariants of Hybrid Systems as Fixedpoints
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Box invariance in biologically-inspired dynamical systems
Automatica (Journal of IFAC)
Automatic invariant generation for hybrid systems using ideal fixed points
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Symbolic model checking of hybrid systems using template polyhedra
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Formal verification of hybrid systems
EMSOFT '11 Proceedings of the ninth ACM international conference on Embedded software
Survey paper: Set invariance in control
Automatica (Journal of IFAC)
Brief On absolute stability analysis by polyhedral Lyapunov functions
Automatica (Journal of IFAC)
Synthesizing switching controllers for hybrid systems by generating invariants
Theories of Programming and Formal Methods
Hi-index | 22.14 |
This paper deals with the computation of polytopic invariant sets for polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state space such that if the state of the system belongs to the set at a given instant, it will remain in the set forever in the future. Polytopic invariants for polynomial systems can be verified by solving a set of optimization problems involving multivariate polynomials on bounded polytopes. Using the blossoming principle together with properties of multi-affine functions on rectangles and Lagrangian duality, we show that certified lower bounds of the optimal values of such optimization problems can be computed effectively using linear programs. This allows us to propose a method based on linear programming for verifying polytopic invariant sets of polynomial dynamical systems. Additionally, using sensitivity analysis of linear programs, one can iteratively compute a polytopic invariant set. Finally, we show using a set of examples borrowed from biological applications, that our approach is effective in practice.