Inclusion functions and global optimization 11
Mathematical Programming: Series A and B
Subdivision Direction Selection in Interval Methods for Global Optimization
SIAM Journal on Numerical Analysis
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
Quantified constraints under perturbation
Journal of Symbolic Computation
Search Heuristics for Box Decomposition Methods
Journal of Global Optimization
Continuous First-Order Constraint Satisfaction
AISC '02/Calculemus '02 Proceedings of the Joint International Conferences on Artificial Intelligence, Automated Reasoning, and Symbolic Computation
Rigorous Lower and Upper Bounds in Linear Programming
SIAM Journal on Optimization
Automatic Generation of Polynomial Loop Invariants: Algebraic Foundations
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Safe bounds in linear and mixed-integer linear programming
Mathematical Programming: Series A and B
Computing polynomial program invariants
Information Processing Letters
Efficient solving of quantified inequality constraints over the real numbers
ACM Transactions on Computational Logic (TOCL)
Hybrid Systems: Computation and Control: 8th International Workshop, HSCC 2005, Zurich, Switzerland, March 9-11, 2005, Proceedings (Lecture Notes in Computer Science)
CONTROL'07 Proceedings of the 3rd WSEAS/IASME international conference on Dynamical systems and control
Model checking of hybrid systems: from reachability towards stability
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Primal–dual tests for safety and reachability
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Generating polynomial invariants for hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Survey paper: Set invariance in control
Automatica (Journal of IFAC)
Computation of Lyapunov functions for smooth nonlinear systems using convex optimization
Automatica (Journal of IFAC)
Algebraic analysis on asymptotic stability of continuous dynamical systems
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Computing a basin of attraction to a target region by solving bilinear semi-definite problems
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
Algebraic analysis on asymptotic stability of switched hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Verifiable conditions on asymptotic stabilisability for a class of planar switched linear systems
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Stabhyli: a tool for automatic stability verification of non-linear hybrid systems
Proceedings of the 16th international conference on Hybrid systems: computation and control
Discovering polynomial Lyapunov functions for continuous dynamical systems
Journal of Symbolic Computation
| Hi-index | 0.00 |
In this paper, we present a method for computing a basin of attraction to a target region for polynomial ordinary differential equations. This basin of attraction is ensured by a Lyapunov-like polynomial function that we compute using an interval based branch-and-relax algorithm. This algorithm relaxes the necessary conditions on the coefficients of the Lyapunov-like function to a system of linear interval inequalities that can then be solved exactly. It iteratively refines these relaxations in order to ensure that, whenever a nondegenerate solution exists, it will eventually be found by the algorithm. Application of an implementation to a range of benchmark problems shows the usefulness of the approach.