اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدConditions to the density of accessible sets
41
0
0.0
(
0
)
تأليف
Diego S. Ledesma
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Given a control system $dot{p} = X_0(p) + sum_i u_i (t)X_i(p)$ on a compact manifold M we study conditions for the foliation defined by the accessible sets be dense in M . To do this we relate the control system to a stochastic differential equation and, using the support theorem, we give a characterization of the density in terms of the infinitesimal generator of the diffusion and its invariant measures. Also we give a different proof of Kreners theorem.
قيم البحث
اقرأ أيضاً
This paper concerns optimal control problems for a class of sweeping processes governed by discontinuous unbounded differential inclusions that are described via normal cone mappings to controlled moving sets. Largely motivated by applications to hys
teresis, we consider a general setting where moving sets are given as inverse images of closed subsets of finite-dimensional spaces under nonlinear differentiable mappings dependent on both state and control variables. Developing the method of discrete approximations and employing generalized differential tools of first-order and second-order variational analysis allow us to derive nondegenerated necessary optimality conditions for such problems in extended Euler-Lagrange and Hamiltonian forms involving the Hamiltonian maximization. The latter conditions of the Pontryagin Maximum Principle type are the first in the literature for optimal control of sweeping processes with control-dependent moving sets.
In this paper, we consider the dynamical modeling of a class of quantum network systems consisting of qubits. Qubit probes are employed to measure a set of selected nodes of the quantum network systems. For a variety of applications, a state space mo
del is a useful way to model the system dynamics. To construct a state space model for a quantum network system, the major task is to find an accessible set containing all of the operators coupled to the measurement operators. This paper focuses on the generation of a proper accessible set for a given system and measurement scheme. We provide analytic results on simplifying the process of generating accessible sets for systems with a time-independent Hamiltonian. Since the order of elements in the accessible set determines the form of state space matrices, guidance is provided to effectively arrange the ordering of elements in the state vector. Defining a system state according to the accessible set, one can develop a state space model with a special pattern inherited from the system structure. As a demonstration, we specifically consider a typical 1D-chain system with several common measurements, and employ the proposed method to determine its accessible set.
Compared to ordinary function minimization problems, min-max optimization algorithms encounter far greater challenges because of the existence of periodic cycles and similar phenomena. Even though some of these behaviors can be overcome in the convex
-concave regime, the general case is considerably more difficult. On that account, we take an in-depth look at a comprehensive class of state-of-the art algorithms and prevalent heuristics in non-convex / non-concave problems, and we establish the following general results: a) generically, the algorithms limit points are contained in the ICT sets of a common, mean-field system; b) the attractors of this system also attract the algorithms in question with arbitrarily high probability; and c) all algorithms avoid the systems unstable sets with probability 1. On the surface, this provides a highly optimistic outlook for min-max algorithms; however, we show that there exist spurious attractors that do not contain any stationary points of the problem under study. In this regard, our work suggests that existing min-max algorithms may be subject to inescapable convergence failures. We complement our theoretical analysis by illustrating such attractors in simple, two-dimensional, almost bilinear problems.
We propose an extension of the theory of control sets to the case of inputs satisfying a dwell-time constraint. Although the class of such inputs is not closed under concatenation, we propose a suitably modified definition of control sets that allows
to recover some important properties known in the concatenable case. In particular we apply the control set construction to dwell-time linear switched systems, characterizing their maximal Lyapunov exponent looking only at trajectories whose angular component is periodic. We also use such a construction to characterize supports of invariant measures for random switched systems with dwell-time constraints.
Estimating the regular normal cone to constraint systems plays an important role for the derivation of sharp necessary optimality conditions. We present two novel approaches and introduce a new stationarity concept which is stronger than M-stationari
ty. We apply our theory to three classes of mathematical programs frequently arising in the literature.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
