Real quantifier elimination is doubly exponential
Journal of Symbolic Computation
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
SIAM Review
Automatic analysis of hybrid systems
Automatic analysis of hybrid systems
Synthesizing Controllers for Hybrid Systems
HART '97 Proceedings of the International Workshop on Hybrid and Real-Time Systems
Non-linear loop invariant generation using Gröbner bases
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
QEPCAD B: a program for computing with semi-algebraic sets using CADs
ACM SIGSAM Bulletin
A Policy Iteration Technique for Time Elapse over Template Polyhedra
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Computing Differential Invariants of Hybrid Systems as Fixedpoints
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Constraint-Based Approach for Analysis of Hybrid Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Differential-algebraic Dynamic Logic for Differential-algebraic Programs
Journal of Logic and Computation
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
Synthesizing switching logic for safety and dwell-time requirements
Proceedings of the 1st ACM/IEEE International Conference on Cyber-Physical Systems
Switching logic synthesis for reachability
EMSOFT '10 Proceedings of the tenth ACM international conference on Embedded software
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
Verification and synthesis using real quantifier elimination
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Computing semi-algebraic invariants for polynomial dynamical systems
EMSOFT '11 Proceedings of the ninth ACM international conference on Embedded software
Formal verification of hybrid systems
EMSOFT '11 Proceedings of the ninth ACM international conference on Embedded software
Synthesizing switching logic using constraint solving
International Journal on Software Tools for Technology Transfer (STTT) - VMCAI 2009
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Survey paper: Set invariance in control
Automatica (Journal of IFAC)
Computation of polytopic invariants for polynomial dynamical systems using linear programming
Automatica (Journal of IFAC)
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We extend a template-based approach for synthesizing switching controllers for semi-algebraic hybrid systems, in which all expressions are polynomials. This is achieved by combining a QE (quantifier elimination)-based method for generating invariants with a qualitative approach for predefining templates. Our synthesis method is relatively complete with regard to a given family of predefined templates. Using qualitative analysis, we discuss heuristics to reduce the numbers of parameters appearing in the templates. To avoid too much human interaction in choosing templates as well as the high computational complexity caused by QE, we further investigate applications of the SOS (sum-of-squares) relaxation approach and the template polyhedra approach in invariant generation, which are both supported by modern numerical solvers.