Sliding Dynamic in a 3-dimensional epidemiological system

Piecewise-affine (PWA) systems are widely used for modeling and control of robotics problems including modeling contact dynamics. A common approach is to encode the control problem of the PWA system as a Mixed-Integer Convex Program (MICP), which can be solved by general-purpose offthe-shelf MICP solvers. To mitigate the scalability challenge of solving these MICP problems, existing work focuses on devising efficient and strong formulations of the problems, while less effort has been spent on exploiting their specific structure to develop specialized solvers. The latter is the theme of our work. We focus on efficiently handling onehot constraints, which are particularly relevant when encoding PWA dynamics. We have implemented our techniques in a tool, Soy, which organically integrates logical reasoning, arithmetic reasoning, and stochastic local search. For a set of PWA control benchmarks, Soy solves more problems, faster, than two stateof-the-art MICP solvers.

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Sliding homoclinic orbits and bifurcations of three-dimensional piecewise affine systems

Huan

Liu

2023

Nonlinear Dyn

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Sliding Homoclinic Bifurcations in a Class of Three-Dimensional Piecewise Affine Systems

Wu,

Zhao,

Huan

2024

Int. J. Bifurcation Chaos

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This paper studies sliding homoclinic bifurcations in a class of symmetric three-zone three-dimensional piecewise affine systems. The systems have one parameter and the unperturbed systems have a pair of sliding homoclinic orbits to a saddle. Based on the analysis of the one-dimensional Poincaré maps, two types of sliding cycles are obtained from the sliding homoclinic bifurcations of the systems. In addition, two examples of sliding homoclinic orbits and sliding cycles are provided with simulations to illustrate the effectiveness of the theorems.

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Sliding Dynamic in a 3-dimensional epidemiological system

Cited by 2 publications

References 17 publications

Sliding homoclinic orbits and bifurcations of three-dimensional piecewise affine systems

Sliding homoclinic orbits and bifurcations of three-dimensional piecewise affine systems

Sliding Homoclinic Bifurcations in a Class of Three-Dimensional Piecewise Affine Systems

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