Exact null controllability of semilinear evolution systems

We study the exact null controllability for the abstract evolution equations in Hilbert spaces. Assuming the exact null controllability of the corresponding linearized equation we obtain sufficient conditions for the exact null controllability of the semilinear evolution equation. The results we obtained are generalization and continuation of the recent results on this issue. In the end, an example is given to show the application of our result.     

Approximate controllability of a class of semilinear degenerate systems with boundary control

This paper concerns a class of control systems governed by semilinear degenerate equations with boundary control in one-dimensional space. The control is proposed on the ‘degenerate’ part of the boundary. The control systems are shown to be approximately controllable by Kakutani's fixed point theorem.     

Exact null controllability of semilinear integrodifferential systems in Hilbert spaces

Sufficient conditions for exact null controllability of the semilinear integrodifferential systems in Hilbert spaces are obtained. It is shown that under some natural conditions exact null controllability of the semilinear integrodifferential system is implied by the exact null controllability of the corresponding linear system with additive term. An application to partial integrodifferential equations is given.     

Approximate controllability of a class of semilinear systems with boundary degeneracy

In this paper we consider the approximate controllability of a class of degenerate semilinear systems. The equations may be weakly degenerate and strongly degenerate on a portion of the lateral boundary. We prove that the control systems are approximately controllable and the controls can be taken to be of quasi bang-bang form.     

Exact controllability of the wave equation with Neumann boundary control

We consider the wave equation defined on a smooth bounded domainR ⁿ with boundary =₀₁, with ₀ possibly empty and ₁ nonempty and relatively open in . The control action is exercised in the Neumann boundary conditions only on ₁, while homogeneous boundary conditions of Dirichlet type are imposed on the complementary part ₀. We study by a direct method (i.e., without passing through uniform stabilization) the problem of exact controllability on some finite time interval [0,T] for initial data on some preassigned spaceZ=Z ₁ ×Z ₂ based on and with control functions in some preassigned space based on ₁ and [0,T]. We consider several choices of pairs [Z, ] of spaces, and others may be likewise studied by similar methods. Our main results are exact controllability results in the following cases: (i) and and , both under suitable geometrical conditions on the triplet {, ₀, ₁} expressed in terms of a general vector field; (iii)Z = L ² ()×[H ¹ ()] in the Neumann case ₀=Ø in the absence of geometrical conditions on , but with a special classV of controls, larger thanL ² (). The key technical issues are, in all cases, lower bounds on theL ² ( ₁)-norm of appropriate traces of the solution to the corresponding homogeneous problem. These are obtained by multiplier techniques.This paper was presented by the second named author at the IFIP WG 7.2 Conference on Boundary Control and Boundary Variations held at the Department de Mathématiques, Universite de Nice, France, June 10–13, 1986 (a preliminary version will appear as Lectures Notes in Control Sciences, edited by J. P. Zolezio [T4]); at the International Conference on Control of Distributed Parameter Systems, held at Vorau, Austria, July 6–12, 1986; at the Second Workshop on Control of Systems Governed by Partial Differential Equations, held at Val David, Quebec, Canada, October 5–9, 1986; and at the 26th IEEE Conference on Decision and Control, held at Los Angeles, CA, December 9–11, 1987 [LT6]. This research was partially supported by the National Science Foundation under Grant No. NSF 8301668 and by the Air Force Office of Scientific Research under Grant No. AFOSR-84-0365.     

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.     

Approximate controllability and regularity for semilinear retarded control systems

We deal with the approximate controllability for semilinear systems with time delay in a Hilbert space. First, we show the existence and uniqueness of solutions of the given systems with the more general Lipschitz continuity of nonlinear operator f fromR ×V toH. Thereafter, it is shown that the equivalence between the reachable set of the semilinear system and that of its corresponding linear system. Finally, we make a practical application of the conditions to the system with only discrete delay.     

Approximations of riccati equation for abstract boundary control problems applications to hyperbolic systems

Galerkin approximations of Differential Riccati equations arising in abstract hyperbolic boundary control problems are considered. Abstract results are then applied to the first order nondissipative hyperbolic system with L₂-boundary controls.     

Exact controllability of a semilinear thermoelastic system with control and nonlinearity in thermal component only

A result concerning the exact controllability of semilinear thermoelastic system, in which the control and nonlinear term occurs solely in the thermal equation, is derived under the influence of rotational inertia and Lipschitz nonlinearity, subject to the clamped/Dirichlet boundary conditions. In the proof we make use the result given by Avalos G. [Differential and Integral Equations, 13 (2000), 613-630] which states that the corresponding linear system is exact controllable. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Relative approximate controllability of abstract functional systems with infinite delay and delayed control

This paper is concerned with the relative approximate controllability of functional systems with infinite delay and delayed control in Hilbert spaces. In particular, we begin with studying some criteria of the controllability of linear systems. Based on those results, sufficient conditions are derived for the relative approximate controllability of nonlinear functional systems. Finally, an example is included to illustrate the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Approximate positive controllability of positive boundary control systems

This paper is devoted to the study of the approximate positive controllability for linear systems with positive boundary controls. The results are applied to an abstract transport equation and controlled flows in networks.     

Exact boundary controllability of an integrodifferential equation

An integrodifferential equation of the Volterra type is considered under the action of anL ₂(0, T, L₂())-boundary control. By harmonic analysis arguments it is shown that the controllability results obtained in [17] for the underlying reference model associated with a trivial convolution kernel, carry over to the model under consideration without any smallness assumption concerning the memory kernel.     

拟线性双曲型方程组具较少控制函数的双侧精确边界能控性

研究具有一般非线性边界条件的一阶拟线性双曲型方程组的具有较少控制函数的双侧精确边界能控性.在正负特征数不相等的情况下,以一阶拟线性双曲型方程组混合初边值问题的半整体C1解理论为基础,采用一个直接的构造方法,使用较少的边界控制函数实现了局部双侧精确边界能控性,并且对精确控制时间给出了最佳估计.     

Approximate controllability of semilinear measure driven systems

This paper investigates approximate controllability of semilinear measure driven equations in Hilbert spaces. By using the semigroup theory and Schauder fixed point theorem, sufficient conditions for approximate controllability of measure driven equations are established. The obtained results are a generalization and continuation of the recent results on this issue. Finally, an example is provided to illustrate the application of the obtained results.     

Robust controllability of linear systems: Analysis and application to pursuit problems

Robust controllability conditions for a linear uncertain system are derived. A class of transferring strategies is obtained. A robust controllability set, respecting a given control constraint, is constructed. An application example is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Approximate controllability of fractional order semilinear systems with bounded delay

In this paper, sufficient conditions are established for the approximate controllability of a class of semilinear delay control systems of fractional order. The existence and uniqueness of mild solution of the system is also proved. The results are obtained by using contraction principle and the Schauder fixed point theorem. Some examples are given to illustrate the theory.     

Optimal control problems with state constraints for semilinear distributed-parameter systems

We consider optimal control problems for distributed-parameter systems described by semilinear equations, with constraints on the control and on the state, and an exact pointwise target condition. As an application of a general theory of nonlinear programming problems in Banach spaces, a version of the Pontryagin maximum principle is obtained.This research was partly supported by the National Science Foundation under Grant DMS-92-21819.