On the Time-Discretization of Control Systems
SIAM Journal on Control and Optimization
Nonsmooth analysis and control theory
Nonsmooth analysis and control theory
Ordinary Differential Equations
Ordinary Differential Equations
Oriented Distance Function and Its Evolution Equation for Initial Sets with Thin Boundary
SIAM Journal on Control and Optimization
Global Optimization with Nonlinear Ordinary Differential Equations
Journal of Global Optimization
Diagnosis and Fault-Tolerant Control
Diagnosis and Fault-Tolerant Control
Computation of Discrete Abstractions of Arbitrary Memory Span for Nonlinear Sampled Systems
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
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A necessary and sufficient condition for the reachable set, i.e., the set of states reachable from a ball of initial states at some time, of an ordinary differential equation to be convex is presented. In particular, convexity is guaranteed if the ball of initial states is sufficiently small, an upper bound on the radius of that ball being obtained directly from the right hand side of the differential equation. In finite dimensions, the results cover the case of ellipsoids of initial states. A potential application of the results is inner and outer polyhedral approximation of reachable sets, which becomes extremely simple and almost universally applicable if these sets are known to be convex. An example demonstrates that the balls of initial states for which the latter property follows from the results are large enough to be used in actual computations.