Reliable solution of special event location problems for ODEs
ACM Transactions on Mathematical Software (TOMS)
Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods
ACM Transactions on Mathematical Software (TOMS)
State event location in differential-algebraic models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Studies in hybrid systems: modeling, analysis, and control
Studies in hybrid systems: modeling, analysis, and control
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Simulation with Visual Slam and Awesim
Simulation with Visual Slam and Awesim
Nonlinear Control Systems
Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Event Detection for ODEs and Nonrecursive Hierarchies
Proceedings of the Colloquium in Honor of Arto Salomaa on Results and Trends in Theoretical Computer Science
Simulation with Arena
Simulation and control of hybrid systems with applications to mobile robotics
Simulation and control of hybrid systems with applications to mobile robotics
An asynchronous integration and event detection algorithm for simulating multi-agent hybrid systems
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Thermal analysis of multiprocessor SoC applications by simulation and verification
ACM Transactions on Design Automation of Electronic Systems (TODAES)
A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side
Journal of Computational and Applied Mathematics
Original article: Rosenbrock-type methods applied to discontinuous differential systems
Mathematics and Computers in Simulation
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This article describes an algorithm for detecting the occurrence of events, which signify discontinuities in the first derivative of the state variables, while simulating a set of nonsmooth differential equations. Such combined-discrete continuous systems arise in many contexts and are often referred to as hybrid systems, switched systems, or nonsmooth systems. In all cases, the state events are triggered at simulated times which generate states corresponding to the zeros of some algebraic “event” function. It has been noted that all existing simulators are prone to failure when these events occur in the neighborhood of model singularities---regions of the state space where the right-hand side of the differential equation is undefined. Such model singularities are often the impetus for using nonsmooth models in the first place. This failure occurs because existing algorithms blindly attempt to interpolate across singular regions, checking for possible events after the fact. The event detection algorithm described here overcomes this limitation using an approach inspired by feedback control theory. A carefully constructed extrapolation polynomial is used to select the integration step size by checking for potential future events, avoiding the need to evaluate the differential equation in potentially singular regions. It is shown that this alternate approach gives added functionality with little impact on the simulation efficiency.