The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Formal verification of parallel programs
Communications of the ACM
An axiomatic basis for computer programming
Communications of the ACM
Synthesis of Linear Ranking Functions
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Mode Switching Synthesis for Reachability Specifications
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Convex Optimization
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Differential Dynamic Logic for Hybrid Systems
Journal of Automated Reasoning
Lost in Translation: Hybrid-Time Flows vs. Real-Time Transitions
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Constraint-Based Approach for Analysis of Hybrid Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Synthesizing Switching Logic Using Constraint Solving
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
Periodically Controlled Hybrid Systems
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Control-flow refinement and progress invariants for bound analysis
Proceedings of the 2009 ACM SIGPLAN conference on Programming language design and implementation
Approximate reachability for linear systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation 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
Survey paper: Set invariance in control
Automatica (Journal of IFAC)
Verification and synthesis using real quantifier elimination
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Synthesis of optimal switching logic for hybrid 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
Automated synthesis of symbolic instruction encodings from I/O samples
Proceedings of the 33rd ACM SIGPLAN conference on Programming Language Design and Implementation
Synthesizing switching controllers for hybrid systems by generating invariants
Theories of Programming and Formal Methods
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We consider the problem of driving a system from some initial configuration to a desired configuration while avoiding some unsafe configurations. The system to be controlled is a dynamical system that can operate in different modes. The goal is to synthesize the logic for switching between the modes so that the desired reachability property holds. In this paper, we first present a sound and complete inference rule for proving reachability properties of single mode continuous dynamical systems. Next, we present an inference rule for proving controlled reachability in multi-modal continuous dynamical systems. From a constructive proof of controlled reachability, we show how to synthesize the desired switching logic. We show that our synthesis procedure is sound and produces only non-zeno hybrid systems. In practice, we perform a constructive proof of controlled reachability by solving an Exists-Forall formula in the theory of reals. We present an approach for solving such formulas that combines symbolic and numeric solvers. We demonstrate our approach on some examples. All results extend naturally to the case when, instead of reachability, interest is in until properties.