Nonlinear and Optimal Control Systems
Nonlinear and Optimal Control Systems
Safety verification of hybrid systems by constraint propagation-based abstraction refinement
ACM Transactions on Embedded Computing Systems (TECS)
Condition number based complexity estimate for computing local extrema
Journal of Computational and Applied Mathematics
Region stability proofs for hybrid systems
FORMATS'07 Proceedings of the 5th international conference on Formal modeling and analysis of timed systems
Condition number based complexity estimate for solving polynomial systems
Journal of Computational and Applied Mathematics
SIAM Journal on Control and Optimization
Algebraic analysis on asymptotic stability of continuous dynamical systems
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Algebraic analysis on asymptotic stability of switched hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Discovering polynomial Lyapunov functions for continuous dynamical systems
Journal of Symbolic Computation
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In this paper, we present a sum of squares programming based method for computing a basin of attraction to a target region as large as possible by iteratively searching for Lyapunov-like functions. We start with the basic mathematical notions and show how attraction to a target region can be ensured by Lyapunov-like functions. Then, we present an initial framework for getting an increasing sequence of basins of attraction by iteratively computing Lyapunov-like functions. This framework can be realized by solving bilinear semi-definite problems based on sums of squares decomposition. We implement our algorithm and test it on some interesting examples. The computation results show the usefulness of our method.