Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Ergodic Control of Switching Diffusions
SIAM Journal on Control and Optimization
Towars a Theory of Stochastic Hybrid 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
DISCRETE TIME RISK MODELS UNDER RATES OF INTEREST
Probability in the Engineering and Informational Sciences
The Flexible, Extensible and Efficient Toolbox of Level Set Methods
Journal of Scientific Computing
Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems
Automatica (Journal of IFAC)
Stochastic Optimal Control: The Discrete-Time Case
Stochastic Optimal Control: The Discrete-Time Case
Computational approaches to reachability analysis of stochastic hybrid systems
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Reachability questions in piecewise deterministic Markov processes
HSCC'03 Proceedings of the 6th 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
Aircraft conflict prediction in the presence of a spatially correlated wind field
IEEE Transactions on Intelligent Transportation Systems
Computational Methods for Verification of Stochastic Hybrid Systems
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
On reachability and minimum cost optimal control
Automatica (Journal of IFAC)
Quantitative automata model checking of autonomous stochastic hybrid systems
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
Regularization of bellman equations for infinite-horizon probabilistic properties
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Higher-Order approximations for verification of stochastic hybrid systems
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
Formula-free finite abstractions for linear temporal verification of stochastic hybrid systems
Proceedings of the 16th international conference on Hybrid systems: computation and control
Quantitative automata-based controller synthesis for non-autonomous stochastic hybrid systems
Proceedings of the 16th international conference on Hybrid systems: computation and control
Control design for specifications on stochastic hybrid systems
Proceedings of the 16th international conference on Hybrid systems: computation and control
A stochastic games framework for verification and control of discrete time stochastic hybrid systems
Automatica (Journal of IFAC)
Stochastic system controller synthesis for reachability specifications encoded by random sets
Automatica (Journal of IFAC)
Characterization and computation of infinite-horizon specifications over Markov processes
Theoretical Computer Science
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We present a dynamic programming based solution to a probabilistic reach-avoid problem for a controlled discrete time stochastic hybrid system. We address two distinct interpretations of the reach-avoid problem via stochastic optimal control. In the first case, a sum-multiplicative cost function is introduced along with a corresponding dynamic recursion which quantifies the probability of hitting a target set at some point during a finite time horizon, while avoiding an unsafe set during each time step preceding the target hitting time. In the second case, we introduce a multiplicative cost function and a dynamic recursion which quantifies the probability of hitting a target set at the terminal time, while avoiding an unsafe set during the preceding time steps. In each case, optimal reach while avoid control policies are derived as the solution to an optimal control problem via dynamic programming. Computational examples motivated by two practical problems in the management of fisheries and finance are provided.