Probabilistic control of Markov jump systems by scenario optimization approach
Yanqing Liu Yanyan Yin Kok Lay Teo Song Wang Fei Liu
Journal of Industrial & Management Optimization 2018, 13(5): 1-7 doi: 10.3934/jimo.2018103

This paper addresses the new problem of probabilistic robust stabilization for uncertain stochastic systems by using scenario optimization approach, where the uncertainties are not assumed to be norm-bounded. State feedback controllers are designed to guarantee that the closed-loop system is robust probabilistic stable. The problem of designing the controller gains is formulated and solved as linear matrix inequality (LMI) constraints. Simulation results are presented to illustrate the correctness and usefulness of the controllers designed.

keywords: Probabilistic robust stabilization stochastic systems scenario optimization uncertainties
Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds
Fei Liu Jaume Llibre Xiang Zhang
Discrete & Continuous Dynamical Systems - A 2011, 29(3): 1097-1111 doi: 10.3934/dcds.2011.29.1097
Let $\mathcal M$ be a smooth Riemannian manifold with the metric $(g_{ij})$ of dimension $n$, and let $H= 1/2 g^{ij}(q)p_ip_j+V(t,q)$ be a smooth Hamiltonian on $\mathcal M$, where $(g^{ij})$ is the inverse matrix of $(g_{ij})$. Under suitable assumptions we prove the existence of heteroclinic orbits of the induced Hamiltonian systems.
keywords: Heteroclinic orbit variational method Hamiltonian system Riemannian manifold.

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