Search

The stabilization problem for a cable with tip mass subject to boundary input disturbance is concerned in this paper. First, a nonlinear feedback controller is designed using sliding mode control method to reject the disturbance. Second, observation blind point which leads to zero output is found in this system. Third, the existence of the solution is obtained based on the solvability of a class of variational equations. Finally, by the LaSalle's Invariance Principle-like together with the observation blind point theory, we show the closed loop system converges asymptotically to zero. [ABSTRACT FROM AUTHOR]

This work deals with the problem of partial asymptotic null controllability for constrained systems governed by semi-linear evolution equations, where the linear part generates a strongly continuous compact semigroup on Hilbert spaces. This consists of driven only a desired part of the system's state to the origin, taking into account mixed state-input constraints. We give sufficient conditions for the existence of appropriate control laws to ensure partial asymptotic null controllability. The explicit expression of such controls is given as strongly-weakly continuous selections of a set-valued map which is defined through a certain practical tangential condition. Application to semilinear parabolic partial differential equations is treated in order to illustrate the results established. [ABSTRACT FROM AUTHOR]

This paper aims to study the stabilization problem for a Euler–Bernoulli beam equation with boundary observation subject to a general external disturbance. A new infinite dimensional estimator is designed to estimate the disturbance in the corrupted boundary angular velocity signal in real time. Furthermore, a boundary output feedback control is constructed to stabilize the related system. By using the Riesz basis approach, it is proven that, in case the initial conditions satisfy certain smoothness, the closed-loop system is exponentially stable and all internal signals are bounded. Finally, a numerical example is given to show the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the energy decay for solutions of the weakly coupled dissipative Schrödinger system. Among the m-coupled equations, only one equation is directly damped. Under some assumptions about the damping and the coupling terms, it is shown that sufficiently smooth solutions of the system decay logarithmically with mixed boundary conditions, including the coupling of the Schrödinger system subject to Dirichlet and Robin type boundary conditions, respectively. The proof is based on some frequency estimates with an exponential loss on the resolvent operators, which will be solved by establishing an interpolation inequality for a suitable weakly coupled elliptic system. [ABSTRACT FROM AUTHOR]

In this paper, we prove exact observability, boundary and internal exact controllability results for a nonsimple elastic rod. By the spectral analysis method, it is shown that the considered problem has a sequence of eigenfunctions, which forms a Riesz basis for the state space. The exact observability is proved by application of a modified version of Ingham's Theorem. Then, via the Hilbert Uniqueness method, we prove a boundary controllability result with only one controller and an internal controllability result. [ABSTRACT FROM AUTHOR]

This paper is addressed to showing the existence of-insensitizing controls for the linear stochastic Korteweg–de Vries equation. We solve this problem by reducing the original problem to a controllability problem. [ABSTRACT FROM PUBLISHER]

The stabilization problem of a 1D Schrödinger equation subject to boundary control is concerned in this paper. The control input is suffered from time delay. A “partial state” predictor is designed for the system and undelayed system is deduced. Based on the undelayed system, a feedback control strategy is designed to stabilize the original system. The exact observability of the dual one of the undelayed system is checked. Then it is shown that the system can be stabilized exponentially under the feedback control. [ABSTRACT FROM AUTHOR]

In this article, we prove uniqueness results for coefficient inverse problems regarding wave, heat or Schrödinger equation on a tree-shaped network, as well as the corresponding stability result of the inverse problem for the wave equation. The objective is the determination of the potential on each edge of the network from the additional measurement of the solution at all but one external end points. Several results have already been obtained in this precise setting or in similar cases, and our main goal is to propose a unified and simpler method of proof of some of these results. The idea which we will develop for proving the uniqueness is to use a more traditional approach in coefficient inverse problems by Carleman estimates. Afterwards, using an observability estimate on the whole network, we apply a compactness–uniqueness argument and prove the stability for the wave inverse problem. [ABSTRACT FROM AUTHOR]

In our preceding paper [Sun B, Wu MX. Appl. Anal. 2013;92:901–921], we investigated an optimal control problem of age-structured population dynamics for spread of universally fatal diseases and derived the necessary optimality condition for the problem in fixed final horizon case. As a follow-up, in this paper, under weaker additional conditions, we address ourselves to the investigation of the foregoing system in free final horizon case and present further new results of current interests. [ABSTRACT FROM PUBLISHER]

We consider the Bolza problem associated with boundary/point control systems governed by strongly continuous semigroups. In continuation of our work in Lasiecka and Tuffaha [I. Lasiecka and A. Tuffaha,Riccati equations for the Bolza problem arising in boundary/point control problems governed by C 0–semigroups satisfying a singular estimate, J. Optim. Theory Appl. 136 (2008), pp. 229–246; I. Lasiecka and A. Tuffaha,A Bolza optimal synthesis problem for singular estimate control systems, Control Cybernet 38(4B) (2009), pp. 1429–1460], we yet extend the theory to a more general class of control problems that are notanalyticproviding sharp blow-up rates for the regularity. Solvability of the associated Riccati equations and an optimal feedback synthesis are established. The presence of unbounded control actions, such as boundary/point controls, naturally lead to a singularity at the terminal pointt = Tof the optimal control and of the corresponding feedback operator as before. The class of control systems considered in this article is a generalization to the class usually referred to in the literature as ‘Singular Estimate Control Systems’. The prototype is still that of a PDE system consisting of coupled hyperbolic parabolic dynamics interacting on an interface with point/boundary control. The distinct feature of the class considered in this article is that the degree of unboundedness in the control is stronger than that allowed in the usual singular estimate control system configuration, giving rise to less regular optimal state trajectories. [ABSTRACT FROM AUTHOR]

This article is concerned with the optimal control problem of age-structured population dynamics for the spread of universally fatal diseases. The existence and uniqueness of solution of the system, which consists of a group of partial differential equations with nonlocal boundary conditions, is proved. The Dubovitskii and Milyutin functional analytical approach is adopted in the investigation of the Pontryagin maximum principle of the system. The necessary condition is presented for the optimal control problem in fixed final horizon case. Finally, a remark on how to utilize the obtained results is also made. [ABSTRACT FROM PUBLISHER]