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A nonlinear control system is said to be weakly contractive in the control if the flow that it generates is non-expanding (in the sense that the distance between two trajectories is a non-increasing function of time) for some fixed Riemannian metric independent of the control. We prove in this paper that for such systems, local asymptotic stabilizability implies global asymptotic stabilizability by means of a dynamic state feedback. We link this result and the so-called Jurdjevic and Quinn approach.
The aim of this paper is to prove the superexponential stabilizability to the ground state solution of a degenerate parabolic equation of the form begin{equation*} u_t(t,x)+(x^{alpha}u_x(t,x))_x+p(t)x^{2-alpha}u(t,x)=0,qquad tgeq0,xin(0,1) end{equati
We provide out-of-sample certificates on the controlled invariance property of a given set with respect to a class of black-box linear systems. Specifically, we consider linear time-invariant models whose state space matrices are known only to belong
We consider a general multi-armed bandit problem with correlated (and simple contextual and restless) elements, as a relaxed control problem. By introducing an entropy premium, we obtain a smooth asymptotic approximation to the value function. This y
The long-time average behaviour of the value function in the calculus of variations, where both the Lagrangian and Hamiltonian are Tonelli, is known to be connected to the existence of the limit of the corresponding Abel means as the discount factor
We prove rapid stabilizability to the ground state solution for a class of abstract parabolic equations of the form begin{equation*} u(t)+Au(t)+p(t)Bu(t)=0,qquad tgeq0 end{equation*} where the operator $-A$ is a self-adjoint accretive operator on a H