Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
The Bellman equation for minimizing the maximum cost
Non-Linear Analysis
Differential games maximum cost
Non-Linear Analysis
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
UPPAAL—a tool suite for automatic verification of real-time systems
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Pursuit Differential Games with State Constraints
SIAM Journal on Control and Optimization
TACAS '95 Proceedings of the First International Workshop on Tools and Algorithms for Construction and Analysis of Systems
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Formal Verification of Safety-Critical Hybrid Systems
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Verification of Polyhedral-Invariant Hybrid Automata Using Polygonal Flow Pipe Approximations
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Ellipsoidal Techniques for Reachability Analysis
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
Verification of Hybrid Systems with Linear Differential Inclusions Using Ellipsoidal Approximations
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Addressing Multiobjective Control: Safety and Performance through Constrained Optimization
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Safety verification of conflict resolution manoeuvres
IEEE Transactions on Intelligent Transportation Systems
Controllers for reachability specifications for hybrid systems
Automatica (Journal of IFAC)
Viability analysis of an aircraft flight domain for take-off in a windshear
Mathematical and Computer Modelling: An International Journal
Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems
Automatica (Journal of IFAC)
Monte-carlo techniques for falsification of temporal properties of non-linear hybrid systems
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
On the connections between PCTL and dynamic programming
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Verification of discrete time stochastic hybrid systems: A stochastic reach-avoid decision problem
Automatica (Journal of IFAC)
SIAM Journal on Control and Optimization
Proceedings of the 14th international conference on Hybrid systems: computation and control
A stochastic reach-avoid problem with random obstacles
Proceedings of the 14th international conference on Hybrid systems: computation and control
The reachability problem for uncertain hybrid systems revisited: a viability theory perspective
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Computational methods for reachability analysis of stochastic hybrid systems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
HJB approach for motion planning and reachabilty analysis
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
Computing the viability kernel using maximal reachable sets
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Falsification of temporal properties of hybrid systems using the cross-entropy method
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Stochastic system controller synthesis for reachability specifications encoded by random sets
Automatica (Journal of IFAC)
Structural and Multidisciplinary Optimization
| Hi-index | 22.15 |
Questions of reachability for continuous and hybrid systems can be formulated as optimal control or game theory problems, whose solution can be characterized using variants of the Hamilton-Jacobi-Bellman or Isaacs partial differential equations. The formal link between the solution to the partial differential equation and the reachability problem is usually established in the framework of viscosity solutions. This paper establishes such a link between reachability, viability and invariance problems and viscosity solutions of a special form of the Hamilton-Jacobi equation. This equation is developed to address optimal control problems where the cost function is the minimum of a function of the state over a specified horizon. The main advantage of the proposed approach is that the properties of the value function (uniform continuity) and the form of the partial differential equation (standard Hamilton-Jacobi form, continuity of the Hamiltonian and simple boundary conditions) make the numerical solution of the problem much simpler than other approaches proposed in the literature. This fact is demonstrated by applying our approach to a reachability problem that arises in flight control and using numerical tools to compute the solution.