Hybrid Kernels and Capture Basins for Impulse Constrained Systems
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Overapproximating Reachable Sets by Hamilton-Jacobi Projections
Journal of Scientific Computing
Dirichlet Problems for some Hamilton-Jacobi Equations with Inequality Constraints
SIAM Journal on Control and Optimization
Comparing forward and backward reachability as tools for safety analysis
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
A toolbox of hamilton-jacobi solvers for analysis of nondeterministic continuous and hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Controllers for reachability specifications for hybrid systems
Automatica (Journal of IFAC)
On reachability and minimum cost optimal control
Automatica (Journal of IFAC)
Computing the viability kernel using maximal reachable sets
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
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The solution of a particular Hamilton-Jacobi (HJ) partial differential equation (PDE) provides an implicit representation of reach sets and tubes for continuous systems with nonlinear dynamics and can treat inputs in either worst-case or best-case fashion; however, it can rarely be determined analytically and its numerical approximation typically requires computational resources that grow exponentially with the state space dimension. In this paper we describe a new formulation - also based on HJ PDEs - for reach sets and tubes of systems where some states are terminal integrators: states whose evolution can be written as an integration over time of the other states. The key contribution of this new mixed implicit explicit (MIE) scheme is that its computational cost is linear in the number of terminal integrators, although still exponential in the dimension of the rest of the state space. Application of the new scheme to four examples of varying dimension provides empirical evidence of its considerable improvement in computational speed.