Output controllability and optimal output control of positive fractional order linear discrete system with multiple delays in state, input and output

The article concerns output controllability and optimal output control of positive fractional order discrete linear systems with multiple delays in state, input and output. Necessary and sufficient conditions for output reachability (output controllability from zero initial conditions) and null output controllability (output controllability to zero final output) are given and proven. We also prove that the positive system is output controllable if it is output reachable and null output controllable with the output reachability index is equal or less than the null output controllability index. Sufficient conditions for the solvability of the optimal output control problem are given. Numerical examples are presented to illustrate the theoretical results.     

Insensitizing controls for a class of quasilinear parabolic equations

This paper is addressed to showing the existence of insensitizing controls for a class of quasilinear parabolic equations with homogeneous Dirichlet boundary conditions. As usual, this insensitizing problem is reduced to a nonstandard null controllability problem of some nonlinear cascade system governed by a quasilinear parabolic equation and a linear parabolic equation. Nevertheless, in order to solve the later quasilinear controllability problem by the fixed point technique, we need to establish the null controllability of the linearized cascade parabolic system in the framework of classical solutions. The key point is to find the desired control function in a Hölder space for given data with certain regularities.     

Boundary scalar controllability in projections for the Navier-Stokes system

We consider the following controllability problem for the Navier-Stokes equations: ensure, by dynamically varying the boundary values of the total fluid head, that the solution at a given time has a given projection onto some finite-dimensional subspace. We suggest a feedback control construction and obtain a priori estimates for the solution of the closed-loop system, which are then used to prove the boundary scalar controllability.     

不变流形方法与非线性控制系统的能控制性

在Kovalev方法基础上运用不变流形研究非线性系统的能控制性问题,得出了一类仿射非线性系统能控的必要条件,讨论了必要条件的实现问题,研究了带有两个陀螺的刚体运动,证明了它满足能控性的必要条件.     

广义系统能控性的两个充要条件

能控性判定问题是现代控制论研究的重要课题,它是系统分析和设计的理论基础.本文给出了广义系统能控性的两个充要条件,该些结果也为判定广义系统的能控性提供了一些实用方法,最后给出了一个例子.     

Spectral properties of non-homogeneous Timoshenko beam and its rest to rest controllability

The controllability of a slowly rotating non-homogeneous beam clamped to a disc is considered. It is assumed that at the beginning the beam remains at the position of rest and it is supposed to rotate by the given angle and stop. The movement is governed by the system of two differential equations with non-constant coefficients: mass density, flexural rigidity and shear stiffness. To solve the problem of controllability, the spectrum of the operator generating the dynamics of the model is studied. Then the problem of controllability is reduced to the moment problem that is, in turn, solved with the use of the asymptotics of the spectrum.     

线性脉冲控制系统的能控性与最优控制

首先讨论了一类线性随机脉冲控制系统的精确能控性质,给出了该类控制系统的脉冲精确能控的等价的代数判据.然后提出了一个确定性的二维线性脉冲控制系统的时间-脉冲强度最优控制问题;利用动态规划原理,给出了脉冲最优控制的反馈形式和值函数的显式表达式;说明了值函数在整个平面上是连续的,在左右两个半平面的内部还是连续可微的.     

On the Approximate Controllability of Stackelberg–Nash Strategies for Linearized Micropolar Fluids

We study a Stackelberg strategy subject to the evolutionary linearized micropolar fluids equations, considering a Nash multi-objective equilibrium (non necessarily cooperative) for the “follower players” (as is called in the economy field) and an optimal problem for the leader player with approximate controllability objective. We will obtain the following three main results: the existence and uniqueness of Nash equilibrium and its characterization, the approximate controllability of the linearized micropolar system with respect to the leader control, and the existence and uniqueness of the Stackelberg–Nash problem, where the optimality system for the leader is given.     

Global reachability results for systems with constrained controllers

The global reachability problem is to determine if, given a specified initial state, the state of a system can be steered via an admissible control to every point in the state space. This paper addresses the problem of global reachability when there are magnitude constraints on the controls. Necessary conditions and sufficient conditions for a system to be globally reachable are presented. The results are compared with those available for the global controllability problem.Dedicated to G. LeitmannThe research of the first author was supported by the National Science Foundation under Grant No. ECS-82-10284.     

Relative controllability of stochastic nonlinear systems with delay in control

The existence of solutions to systems is a natural premise to carry our study about controllability. Under the basic and readily verified conditions to guarantee the existence of the solutions to a system, in this paper, we prove the relative controllability (approximate controllability ) of the stochastic differential systems with delay in control. Sufficient conditions are given firstly for the relative controllability and relative approximate controllability in finite dimensional spaces, and these results are then generalized to infinite-dimensional Hilbert spaces. Finally, examples are given to illustrate the effectiveness of the proposed methods.     

Controllability for some integrodifferential equations driven by vector measures

In this work, we consider the question of controllability of a class of integrodifferential equations on Hilbert space with measures as controls. We assume that the linear part has a resolvent operator in the sense given by R. Grimmer. We generalize the original work of N. Ahmed on vector measures, and we use it to develop necessary and sufficient conditions for weak and the exact controllability of the integrodifferential equation. Using the latter, we prove that exact controllability of the integrodifferential equation implies exact controllability of a perturbed integrodifferential equation. Controllability problem for the perturbed system is formulated fixed point problem in the space of vector measures. Our results cover impulsive controls as well as regular controls. Copyright © 2016 John Wiley & Sons, Ltd.     

Control of interconnected nonlinear delay differential equations inW 2 (1)

Our main interest in this paper is the resolution of the problem of controllability of interconnected nonlinear delay systems in function space, from which hopefully the existence of an optimal control law can be deduced later. We insist that each subsystem be controlled by its own variables while taking into account the interacting effects. This is the recent basic insight of [13] on ordinary differential systems. Controllability is deduced for the composite system from the assumption of controllability of each free subsystem and a growth condition of the interconnecting structure. Conditions for a free system’s controllability are given. One application is presented. The insight it provides for the growth of global economy has important policy implications.     

Finite-dimensional controllability for systems of Navier-Stokes type

We consider the problem of partial controllability for an evolution equation with a quadratic nonlinearity, in which one should provide, at a given time, a given projection of the solution onto some finite-dimensional subspace by using the action of external forces that belong to one and the same subspace at each time. On the basis of estimates for the solution of a subdifferential Cauchy problem for a system of Navier-Stokes type, we prove the controllability and the existence of a control with minimum norm. We consider applications to the Navier-Stokes equations of a viscous incompressible fluid and a heat convection model.     

APPROXIMATE CONTROLLABILITY OF INFINITE DIMENSIONAL BILINEAR SYSTEMS

1.IntroductionRecentlymanyresultshavebeenobtainedfordistributedbilinearsystemsl3'7'8].In[3]thecontrollabilityofabilinearsystem%=Aw(t) p(t)Bw(t)wasstudied,whereAistheindnitesimalgeneratorofaCosemigroupofboundedlinearoperatorsT(t)onaBanachspaceX.B:X-- 5isaboundedlinearoperator,andpELI([0,T];R)isacontrol.TheconditionsforelementsofEtobeaccessiblefromagiveninitialstatecoweregiven.Itisclearthattheystudiedthebilinearsysteminaspecialcase.In[8]theystudiedthesysteminamorespecialcasebecausetheyass…     

一类混杂动态系统的能控性(Ⅰ)——基本结果

首次将时滞现象引入到线性切换系统的模型中,研究含有时滞线性切换系统的能控性及其判定条件。全部工作由三部分组成,第Ⅰ部分首先,提出含时滞的线性切换系统的数学模型,并介绍切换系统的基本概念—切换序列。其次,引入列空间、循环不变子空间和广义循环不变子空间等基本几何概念,给出一些有关概念的基本性质,特别是分离引理。然后以一个基本引理的形式揭式某一积分方程的解集与广义循环不变子空间之间的联系,这个引理将在能控性的判定中起关键作用。这些概念和引理都将作为以后展开能控性分析所必需的研究工具。     

Criteria for Modal Controllability of Completely Regular Differential-Algebraic Systems with Aftereffect

The problem of control of the coefficients of the characteristic quasipolynomial is studied for linear autonomous completely regular differential-algebraic systems with commensurate delays. Several criteria for modal controllability and weak modal controllability are obtained, schemes for synthesis of the corresponding controllers are proposed, and illustrative examples are given.     

Bounded controlling sequences,lower stability and certain penalty procedures

We present a unified approach to certain controllability and optimization questions such as approximate controllability with bounded sequences, necessary and sufficient conditions for lower stability, a problem of moments, penalty techniques. The control processes concerned are given by strongly continuous semigroups in Banach spaces, but the argument is led in the generality of continuous operators.     

Exact null controllability of the Lobesia botrana model with diffusion

This paper is devoted to analyze the exact null controllability of the diffusive Lobesia botrana model with nonlocal boundary condition. We study the null controllability of butterfly population by acting on eggs, larvas and female moths in a small age interval. We assume that the control of female moths is in a certain given region of the vineyard. The main result is established by combining some estimations and the Carleman inequality for the backward system related to an optimal control problem. A fixed point theorem is then used to draw the conclusion.     

Observability of hybrid discrete-continuous systems

We study the statement and solvability of observability problems in linear stationary hybrid discrete-continuous dynamical systems. Necessary and sufficient observability conditions expressed directly via the system parameters are derived. We consider linear observability problems and the dual controllability and reachability problems. The problem of computing the minimum number of inputs for which the system has a given observability is discussed. An example illustrating the results is presented.