Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
&egr;-approximation of differential inclusions
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Optimization: algorithms and consistent approximations
Optimization: algorithms and consistent approximations
Determinant Maximization with Linear Matrix Inequality Constraints
SIAM Journal on Matrix Analysis and Applications
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Reachability Analysis via Face Lifting
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Synthesizing Controllers for Nonlinear Hybrid Systems
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Controllers for reachability specifications for hybrid systems
Automatica (Journal of IFAC)
Controlled Invariance of Discrete Time Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Level Set Methods for Computation in Hybrid Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Semi-decidable Synthesis for Triangular Hybrid Systems
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Checking Safe Trajectories of Aircraft Using Hybrid Automata
SAFECOMP '02 Proceedings of the 21st International Conference on Computer Safety, Reliability and Security
A hierarchical approach for the synthesis of stabilizing controllers for hybrid systems
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Synthesis of quantized feedback control software for discrete time linear hybrid systems
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
On model based synthesis of embedded control software
Proceedings of the tenth ACM international conference on Embedded software
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We discuss a procedure for synthesizing controllers for safety specifications for hybrid systems. The procedure depends on the construction of the set of states of a continuous dynamical system that can be driven to a subset of the state space, avoiding another subset of the state space (the Reach-Avoid set). We present a new characterization of the Reach-Avoid set in terms of the solution of a pair of coupled Hamilton-Jacobi partial differential equations. We also discuss a computational algorithm for solving such partial differential equations and demonstrate its effectiveness on numerical examples.