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.     

Exact controllability of thermoelastic plate equation with memory

In this paper, we consider exact control problem for a coupled system of plate with Gurtin‐Pipkin equation. Using duality arguments, the problem is reduced to the obtention of suitable observability estimates for the dual system. Firstly, we obtain the observability inequality of the dual system by means of multiplier method. Then, we prove that the system is exactly controllable based on the Hilbert Unique Method.     

On a thermoelastic plate equation in an exterior domain

Obtained are the existence of solutions and the local energy decay of a linear thermoelastic plate equation in a 3 dim. exterior domain. The thermoplate equation is formulated as a Sobolev equation in the abstract framework. Our proof of the existence theorem is based on an argument due to Goldstein (Semigroups of Linear Operators and Applications. Oxford University Press: New York, 1985). To obtain the local energy decay, we use the commutation method in order to treat the high‐frequency part and a precise expansion of the resolvent operator obtained by constructing the parametrix in order to treat the low‐frequency. Copyright © 2002 John Wiley & Sons, Ltd.     

Controllability of a system of parabolic equations with non-diagonal diffusion matrix

In this paper we give a necessary and sufficient algebraic conditionfor the approximate controllability of the following systemof parabolic equations with Dirichlet boundary condition: {z_t = D z + b₁(x)u₁ + ··· + b_m(x)u_m, t 0, z ⁿ, z = 0, on where is a sufficiently smooth bounded domain in ^N, b_i L²(;ⁿ), the control functions u_i L²(0, t₁; ); i = 1, 2, ..., mand D is an n x n non-diagonal matrix whose eigenvalues aresemi-simple with positive real part. This algebraic conditionis checkable since it is given in terms of the n_j x m matricesDP_j and P_jB, i.e. Rank [P_jBDP_jBD²P_jB··· D^n_j–1 P_jB]= n_j, where P_jBu = P_jb₁u₁ + ··· + P_jb_mu_m. Finally,this result can be applied to those systems of partial differentialequations that can be rewritten as a diffusion system (see deOliveira, 1998).     

Approximate controllability of a parabolic integrodifferential equation

In this paper, we obtain the approximate controllability of a parabolic integrodifferential equation with interior controls. The proof relies on the linear operator semigroup theory and the controllability theory for abstract equations. Copyright © 2013 John Wiley & Sons, Ltd.     

A note on the necessary conditions for the algebraic Riccati equation

We derive some useful and easily computable necessary conditionsfor the existence of a positive semi-definite solution to thealgebraic Ricatti equation (ARE). A motivating example is givento highlight the usefulness of the conditions for controllerand observer designs for nonlinear systems. Further, an upperbound on the trace of the solution to the ARE is also derived.     

On the Lp–Lq maximal regularity for the linear thermoelastic plate equation in a bounded domain

This paper is concerned with the thermoelastic plate equations in a domain Ω: subject to the boundary condition: u|=D_νu|=θ|=0 and initial condition: (u, u_t, θ)|_t=0=(u₀, v₀, θ₀). Here, Ω is a bounded domain in ?ⁿ(n≧2). We assume that the boundary ?Ω of Ω is a C⁴ hypersurface. We obtain an L_p–L_q maximal regularity theorem. Copyright © 2008 John Wiley & Sons, Ltd.     

Krylov subspace methods of Hessenberg based for algebraic Riccati equation

In this paper, we propose a class of special Krylov subspace methods to solve continuous algebraic Riccati equation (CARE), i.e., the Hessenberg-based methods. The presented approaches can obtain efficiently the solution of algebraic Riccati equation to some extent. The main idea is to apply Kleinman-Newton"s method to transform the process of solving algebraic Riccati equation into Lyapunov equation at every inner iteration. Further, the Hessenberg process of pivoting strategy combined with Petrov-Galerkin condition and minimal norm condition is discussed for solving the Lyapunov equation in detail, then we get two methods, namely global generalized Hessenberg (GHESS) and changing minimal residual methods based on the Hessenberg process (CMRH) for solving CARE, respectively. Numerical experiments illustrate the efficiency of the provided methods.     

Exact controllability of the heat equation with bilinear control

This paper deals with exact controllability of bilinear heat equation. Namely, given the initial state, we would like to provide a class of target states that can be achieved through the heat equation at a finite time by applying multiplicative controls. For this end, an explicit control strategy is constructed. Simulations are provided. Copyright © 2015 John Wiley & Sons, Ltd.     

Boundary controllability for the time-fractional nonlinear Korteweg-de Vries (KdV) equation

In this paper, we study the time-fractional nonlinear Korteweg-de Vries (KdV) equation. By using the theory of semigroups, we prove the well-posedness of the time-fractional nonlinear KdV equation. Moreover, we present the boundary controllability result for the problem.     

Null controllability of a pseudo-parabolic equation with moving control

In this paper, we study the internal controllability of the pseudo-parabolic equation on the one-dimensional torus. Our control function is acting on a moving small interval with a constant velocity. With this moving distributed control, we obtain the system is null controllable for given data with certain regularity.     

A necessary and sufficient condition for singular nonlinear second-order boundary value problems to have positive solutions

In this paper the following result is obtained: Suppose f(g,u,v) is nonnegative, continuous in (a, 6) ×R⁺ ×R ⁺ ; f may be singular at κ = a(and/or κ = b) and υ = 0; f is nondecreasing on u for each κ,υ,nonincreasing on υ for each κ,u; there exists a constant q ε (0,1) such that

A nonlinear transmission problem for a compound plate with thermoelastic part

In this paper, we study a nonlinear transmission problem for a plate that consists of thermoelastic and isothermal parts. The problem generates a dynamical system in a suitable Hilbert space. The main result is the proof of the asymptotic smoothness of this dynamical system. We also prove the existence of a compact global attractor in special cases when the nonlinearity is of Berger type or scalar. Copyright © 2012 John Wiley & Sons, Ltd.     

A necessary and sufficient condition for Hardy's operator in

The equivalent conditions are proved for the Hardy inequality to be fulfilled in the norms of a Lebesgue space with variable exponent . It is assumed that the function is monotone and positive on (0, 1).     

Approximate controllability for trajectories of semilinear control systems

We treat an abstract semilinear control system and study the controllability problem for its trajectories. Assuming a range condition of the control action operator and an inequality condition on the system parameters, we can show that the reachable trajectory set of the semilinear system is equivalent to that of its corresponding linear system.The author wishes to express his deep appreciation to Prof. T. I. Seidman for his many helpful suggestions and to Prof. W. Takahashi for many stimulating conversations.     

Controllability of the Ornstein-Uhlenbeck equation

^** Email: Leiva{at}ula.ve In this paper we study the controllability of the followingcontrolled Ornstein–Uhlenbeck equation [graphic: see PDF] then the system is approximately controllable on [0, t₁]. Moreover,the system can never be exactly controllable.     

A necessary and sufficient condition for duality in multiobjective variational problems

In this paper we move forward in the study of duality and efficiency in multiobjective variational problems. We introduce new classes of pseudoinvex functions, and prove that not only it is a sufficient condition to establish duality results, but it is also necessary. Moreover, these functions are characterized in order that all Kuhn–Tucker or Fritz John points are efficient solutions. Recent papers are improved. We provide an example to show this improvement and illustrate these classes of functions and results.