Subgradient algorithm for computing contraction metrics for equilibria. (English) Zbl 1525.37087
Summary: We propose a subgradient algorithm for the computation of contraction metrics for systems with an exponentially stable equilibrium. We show that for sufficiently smooth systems our method is always able to compute a contraction metric on any forward-invariant compact neighbourhood of the equilibrium, which is a subset its basin of attraction. We demonstrate the applicability of our method by constructing contraction metrics for three planar and one three-dimensional systems.
MSC:
| 37M22 | Computational methods for attractors of dynamical systems |
| 65P40 | Numerical nonlinear stabilities in dynamical systems |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 37C75 | Stability theory for smooth dynamical systems |
| 39A30 | Stability theory for difference equations |
| 34D20 | Stability of solutions to ordinary differential equations |
Software:
ResEntSGReferences:
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