Viability theory
Inverse Optimality in Robust Stabilization
SIAM Journal on Control and Optimization
Lyapunov Characterizations of Input to Output Stability
SIAM Journal on Control and Optimization
Metrics for labelled Markov processes
Theoretical Computer Science - Logic, semantics and theory of programming
Bisimulation relations for dynamical, control, and hybrid systems
Theoretical Computer Science
Reachability analysis of large-scale affine systems using low-dimensional polytopes
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Reachability of uncertain linear systems using zonotopes
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Automatica (Journal of IFAC)
Approximate Simulation Relations for Hybrid Systems
Discrete Event Dynamic Systems
Brief paper: Hierarchical control system design using approximate simulation
Automatica (Journal of IFAC)
Discrete Semantics for Hybrid Automata
Discrete Event Dynamic Systems
MTL robust testing and verification for LPV systems
ACC'09 Proceedings of the 2009 conference on American Control Conference
Bisimulation conversion and verification procedure for goal-based control systems
Formal Methods in System Design
Pre-orders for reasoning about stability
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Approximate bisimulations for sodium channel dynamics
CMSB'12 Proceedings of the 10th international conference on Computational Methods in Systems Biology
| Hi-index | 22.15 |
In this paper, we define the notion of approximate bisimulation relation between two continuous systems. While exact bisimulation requires that the observations of two systems are and remain identical, approximate bisimulation allows the observations to be different provided the distance between them remains bounded by some parameter called precision. Approximate bisimulation relations are conveniently defined as level sets of a so-called bisimulation function which can be characterized using Lyapunov-like differential inequalities. For a class of constrained linear systems, we develop computationally effective characterizations of bisimulation functions that can be interpreted in terms of linear matrix inequalities and optimal values of static games. We derive a method to evaluate the precision of the approximate bisimulation relation between a constrained linear system and its projection. This method has been implemented in a Matlab toolbox: MATISSE. An example of use of the toolbox in the context of safety verification is shown.