TY - GEN
T1 - Guaranteed Simulation of Dynamical Systems with Integral Constraints and Application on Delayed Dynamical Systems
AU - Rousse, Paul
AU - Alexandre dit Sandretto, Julien
AU - Chapoutot, Alexandre
AU - Garoche, Pierre Loïc
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - A reachable set computation method for dynamical systems with an integral constraint over the input set is proposed. These models are typical in robustness analysis when studying the impact of bounded energy noises over a system response and can also model a large family of complex systems. The reachable set is over-approximated using a guaranteed set-based integration method within the interval arithmetic framework. A Runge-Kutta guaranteed integration scheme with pessimistic bounds over the input provides a first conservative bound over the reachable tube. Then, the integral constraint is used to define a contractor over the reachable tube. This contractor and a propagation step are successively applied on the over-approximation until a fixed point is reached. We evaluated our algorithm with DynIbex library to simulate a delayed system, i.e., an infinite dimensional system that can be modeled as a linear time-invariant system subject to an integral quadratic constraint. Our approach is shown to be tractable and enables the use of interval arithmetic and guaranteed integration for a richer set of dynamical systems.
AB - A reachable set computation method for dynamical systems with an integral constraint over the input set is proposed. These models are typical in robustness analysis when studying the impact of bounded energy noises over a system response and can also model a large family of complex systems. The reachable set is over-approximated using a guaranteed set-based integration method within the interval arithmetic framework. A Runge-Kutta guaranteed integration scheme with pessimistic bounds over the input provides a first conservative bound over the reachable tube. Then, the integral constraint is used to define a contractor over the reachable tube. This contractor and a propagation step are successively applied on the over-approximation until a fixed point is reached. We evaluated our algorithm with DynIbex library to simulate a delayed system, i.e., an infinite dimensional system that can be modeled as a linear time-invariant system subject to an integral quadratic constraint. Our approach is shown to be tractable and enables the use of interval arithmetic and guaranteed integration for a richer set of dynamical systems.
KW - Dynamical systems with integral constraint
KW - Interval arithmetic
KW - Numerical integration
U2 - 10.1007/978-3-030-41131-2_5
DO - 10.1007/978-3-030-41131-2_5
M3 - Conference contribution
AN - SCOPUS:85081173632
SN - 9783030411305
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 89
EP - 107
BT - Cyber Physical Systems. Model-Based Design - 9th International Workshop, CyPhy 2019, and 15th International Workshop, WESE 2019, Revised Selected Papers
A2 - Chamberlain, Roger
A2 - Edin Grimheden, Martin
A2 - Taha, Walid
PB - Springer
T2 - 9th International Workshop on Model-Based Design of Cyber Physical Systems, CyPhy 2019 and 15th International Workshop on Embedded and Cyber-Physical Systems Education, WESE 2019, held in conjunction with ESWeek 2019
Y2 - 17 October 2019 through 18 October 2019
ER -