Differential equations and dynamical systems
Differential equations and dynamical systems
Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
Asymptotic Optimization of a Nonlinear Hybrid System Governed by a Markov Decision Process
SIAM Journal on Control and Optimization
Optimal Controller Switching for Stochastic Systems
Hybrid Systems V
Probability: Theory and Examples
Probability: Theory and Examples
Decidable Model Checking of Probabilistic Hybrid Automata
FTRTFT '00 Proceedings of the 6th International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems
Mode Estimation of Probabilistic Hybrid Systems
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Optimotaxis: A Stochastic Multi-agent Optimization Procedure with Point Measurements
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Proceedings of the 1st ACM/IEEE International Conference on Cyber-Physical Systems
Verification of discrete time stochastic hybrid systems: A stochastic reach-avoid decision problem
Automatica (Journal of IFAC)
A stochastic reach-avoid problem with random obstacles
Proceedings of the 14th international conference on Hybrid systems: computation and control
Stochastic differential dynamic logic for stochastic hybrid programs
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Reachability analysis for controlled discrete time stochastic hybrid systems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Approximate abstraction of stochastic hybrid automata
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
Specification and analysis of distributed object-based stochastic hybrid systems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Safety verification for probabilistic hybrid systems
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Optimal control of discrete hybrid stochastic automata
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Polynomial stochastic hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Adjoint-based optimal control of the expected exit time for stochastic hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
A stochastic hybrid system model of collective transport in the desert ant aphaenogaster cockerelli
Proceedings of the 16th international conference on Hybrid systems: computation and control
Rewarding probabilistic hybrid automata
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)
Robust optimization for hybrid MDPs with state-dependent noise
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Optimal control of stochastic hybrid system with jumps: A numerical approximation
Journal of Computational and Applied Mathematics
A compositional modelling and analysis framework for stochastic hybrid systems
Formal Methods in System Design
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n this paper, we present a scheme of stochastic hybrid system which introduces randomness to the deterministic framework of the traditional hybrid systems by allowing the flow inside each invariant set of the discrete state variables to be governed by stochastic differential equation (SDE) rather than the deterministic ones. The notion of embedded Markov chains is proposed for such systems and some illustrative example from high way model is presented. As an important application, these ideas are then applied to the state space discretization of one dimensional SDE to obtain the natural discretized stochastic hybrid system together with its embedded MC. The invariant distribution and exit probability from interval of the MC are studied and it is shown that they converge to their counterparts for the solution process of the original SDE as the discretization step goes to zero. As a result, the discretized stochastic hybrid system provides a useful tool for studying various sample path properties of the SDE.