Static analysis by policy iteration on relational domains
ESOP'07 Proceedings of the 16th European conference on Programming
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
Survey paper: Set invariance in control
Automatica (Journal of IFAC)
Discretizing affine hybrid automata with uncertainty
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Template-Based unbounded time verification of affine hybrid automata
APLAS'11 Proceedings of the 9th Asian conference on Programming Languages and Systems
Synthesizing switching controllers for hybrid systems by generating invariants
Theories of Programming and Formal Methods
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We present a technique to compute over-approximations of the time trajectories of an affine hybrid system using template polyhedra. Such polyhedra are obtained by conjoining a set of inequality templates with varying constant coefficients. Given a set of template expressions, we show the existence of a smallest template polyhedron that is a positive invariant w.r.t to the dynamics of the continuous variables, and hence, an over-approximation of the time trajectories. However, the least invariant is hard to compute efficiently. Therefore, we propose a policy iteration technique that iterates over the space of invariant certificates to converge onto a solution that is close to the least solution. We incorporate our ideas in our prototype tool TimePass for safety verification of affine hybrid systems, with promising results on benchmarks.