Approximate Controllability for a Class of Linear Neutral Evolution Systems with Infinite Delay

This paper deals with the approximate controllability problem for a class of linear neutral evolution systems with infinite delay in Banach spaces. Since the concerned system involves additional linear terms, the fundamental solution theory is used to describe the mild solutions. Based on the spectral analysis and the adjoint system, sufficient conditions for the approximate controllability of the concerned system are established. The rank condition is also shown when the control space is finite-dimensional. A practical example is given to show the application of the obtained results.

     

Uniqueness of Local Control Sets

The local controllability behavior near an equilibrium is discussed. If the Jacobian of the linearized system is hyperbolic, uniqueness of local control sets is established.     

Approximate Controllability of Impulsive Neutral Stochastic Differential Equations Driven by Poisson Jumps

This work studies the approximate controllability of a class of impulsive neutral stochastic differential equations with infinite delay and Poisson jumps involving generalized Caputo fractional derivative under the condition that the corresponding linear system is approximately controllable. Utilizing the fixed point theory and sectorial operator theory, the existence of the mild solution of the impulsive neutral stochastic equation is established imposing weaker regularity on nonlinear terms. A set of sufficient conditions establishing controllability results is derived with the help of stochastic analysis and fractional calculus. Finally, an example is provided to illustrate the obtained abstract result.     

Existence of Solutions and Approximate Controllability of Fractional Nonlocal Neutral Impulsive Stochastic Differential Equations of Order 1 &lt; <Emphasis Type="Italic">q</Emphasis> &lt; 2 with Infinite Delay and Poisson Jumps

In this paper, we study the existence of mild solutions and the approximate controllability of nonlinear fractional nonlocal neutral impulsive stochastic differential equations of order 1 < q < 2 with infinite delay and Poisson jumps in which the initial value belong to the abstract phase space C _h . The existence of mild solutions is derived with the help of Sadovskii’s fixed point theorem. The approximate controllability of the nonlinear fractional nonlocal neutral impulsive stochastic differential systems of order 1 < q < 2 with infinite delay and Poisson jumps is discussed under the assumption that the corresponding linear system is approximately controllable. Moreover, the approximate controllability of the above control system is established by using Lebesgue dominated convergence theorem. An example is provided to illustrate the theory.     

A Necessary Condition for Small Time Local Controllability

A necessary condition for small time local controllability of an analytic control system is proved. This condition is expressed in terms of Lie brackets of the vector fields (generating this control system) evaluated at the initial point and depends on the set where the control function takes its values. For a particular choice of a three-dimensional polynomial control system, a necessary and sufficient controllability condition is obtained.     

Controllability of the Impulsive Semilinear Heat Equation with Memory and Delay

For many control systems in real life, impulses and delays are intrinsic properties that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system do not modify certain properties such as controllability. In other words, the controllability is robust by looking the impulses and delays as perturbations. In this regard, in this paper, we prove the interior approximate controllability of the Impulsive Semilinear Heat Equation with Memory and Delay. This is done by employing A.E. Bashirov and at. technique which avoids fixed point theorems. In this case, the delay helps us to prove the approximate controllability by pulling back the control solution to a fixed curve in a short time interval.     

Exact controllability for semilinear parabolic equations with Neumann boundary conditions

This paper studies the problem of exact boundary controllability of second-order semilinear parabolic equations when the control is under Neumann's boundary conditions. For a nonlinear term with a sublinear growth we prove the global null-controllability and for the superlinear growth case we prove the local exact controllability of the equations.     

用模拟退火算法改进管壳式换热器的优化设计

介绍了一种由两级管壳式换热器组成的换热器系统的优化设计数学模型，数学模型属于典型的有约束非线性规划问题。目前对有约束非线性规划问题还没有通用的求全局最优解的算法。转轴直径搜索可行方向法(DSFD方法)是一种比较有效的求解有约束非线性规划问题的算法。但它只能得到局部最优解。将模拟退火(Simulated Annealing)算法结合DSFD算法，构成了一种DSFD—SA—DSFD算法。在应用模拟退火算法的同时引入了罚函数法．将有约束非线性问题转化为无约束非线性问题。计算结果表明，DSFD—SA—DSFD算法能较快得到换热器优化问题的最优解，克服了单纯用DSFD算法只能得到局部最优解和单纯用SA算法效率不高的缺点。图3表11参8     

Hermes-Sussmann and ad-rank Conditions for Local Controllability

In this paper, we consider linear control systems on Lie groups and compare three different approaches to local controllability for these systems: Hermes-Sussmann conditions, Hermes condition, and ad-rank condition. We prove that the ad-rank condition can be deduced from the Hermes-Sussmann conditions. We also prove that the Hermes condition and the ad-rank condition are equivalent in case of systems with scalar control. As application, we provide a criterion for global controllability for restricted linear systems on the Heisenberg group.     

Controllability of Generic Inequalities Near Singular Points

In this paper the authors obtained some sufficient conditions under which one has the small local controllability property for a general nonlinear control system described by a system of nonlinear inequalities.     

Approximate Controllability of Nonlocal Neutral Fractional Integro-Differential Equations with Finite Delay

In this paper, we obtain a set of sufficient conditions to prove the approximate controllability for a class of nonlocal neutral fractional integro-differential equations, with time varying delays, considered in a Hilbert space. We also establish the existence of a mild solution of the system. The main tools used in our analysis are the theory of analytic semigroups, the theory of fractional powers of operators, α-norm, fractional calculus, and Krasnoselskii’s fixed point theorem. An example is provided to illustrate the applicability of the main results.     

应用遗传算法优化设计管壳式换热器

两级管壳式换热器优化设计是一个有约束非线性规划问题,目前还没有方法能够保证寻找到该问题的全局最优解.传统的转动坐标轴直接搜索可行方向法(DSFD方法)可以获得该问题的局部最优解,但该最优解对初始点的依赖性很大,需要多次尝试寻找"全局"最优解.应用遗传算法对两级管壳式换热器进行优化设计,优化结果与DSFD方法优化结果对比表明,遗传算法更易于寻找"全局"最优解,提高优化过程的效率.     

The General Solution for Affine Control Systems on Lie Groups

The purpose of this paper is to present explicitly the solution curve for commutative affine control systems on Lie groups under the assumption that the automorphisms associated with the linear vector fields commutes. If we assume that the derivations associated with the linear vector fields of the system are inner, we obtain a simpler solution and we show some results of controllability. To finish, we work with conjugation by homomorphism of Lie groups between affine systems.

     

Controllability of cross-flow two-phase heat exchangers

The analysis of controllability of a heat exchanger operating under two-phase conditions is performed. An evaporator operating in a vapor compression system is chosen for the analysis. A moving-boundary model is used to simulate the dynamic behavior of the evaporator. First, the controllability of the linearized model is verified. Then, it is shown that the nonlinear model can be classified as a control-affine system with drift. Short-term local controllability of the nonlinear model is shown using Lie algebras. A linear quadratic (LQ) controller is developed for the linearized system and numerical simulations are provided that show a strong coupling between the variables of the model.     

Local Controllability for Linear Control Systems on Lie Groups

Abtract  In this work, we study controllability properties of linear control systems on Lie groups. Using Lie theory of semigroups, we obtain local controllability results for this type of systems. In addition, properties for the flow of the drift vector field X and for the reachable set of the system are presented. Finally, an example on the Heisenberg Lie group is considered, and its properties are proved using the theory developed. 2000 Mathematics Subject Classification. Primary 93B05; Secondary 93C25, 93B27. The authors want to thank the Fachbereich Mathematik of the Technische Universit?t Darmstadt for warm hospitality during the production of this work. The first author is pleased to thank Professor Guillermo Ferreyra and the department of mathematics at LSU for their support.     

Null Controllability of a Coupled Degenerate System with the First Order Terms

This paper deals with the null controllability of the system governed by coupled degenerate equations with the first order terms. The null controllability of the system with two controls is proved firstly, then the system with one control is shown to be null controllable by constructing the control function. To investigate the null controllability, we establish the Carleman estimate and the observability inequality for the adjoin system by using the Carleman estimate for the single degenerate equation.     

Existence and Controllability for Impulsive Evolution Inclusions without Compactness

In this paper, we investigate the existence and controllability for impulsive evolution inclusions in Banach spaces. By using weak topology technique and Glicksberg-Ky Fan fixed point theorem, we obtain the existence of mild solutions and controllability outcomes, avoiding hypotheses of compactness on the semigroup generated by the linear part and any conditions on the multivalued nonlinearity expressed in terms of measures of noncompactness. Finally, we show an illustration to outline the plausibility of the theoretical results.     

电厂循环水系统的建模与优化

循环水系统作为火电厂的重要组成部分,其优化问题已引起人们的高度重视.针对火电厂循环水系统高能耗问题,根据某火电厂提供的数据,建立了其循环水系统发电量与耗电量差额的数学模型,用有约束非线性规划的方法解出其最优解.仿真结果表明,该优化模型和求解算法能够找到最优循环水量和最佳真空,使水泵高效运行,以节约电厂耗电.     

Controllability,Observability, and Stability of a Volterra Integro-Dynamic System on Time Scales

This paper deals with the controllability, observability, and stability of the solution of time-varying Volterra integro-dynamic system on time scales. We obtain new results about controllability and observability and generalize to a time scale some known properties about stability from the continuous case.     

Control Systems on Three-Dimensional Lie Groups: Equivalence and Controllability

We consider left-invariant control affine systems, evolving on three-dimensional matrix Lie groups. Equivalence and controllability are investigated. All full-rank systems are classified, under detached feedback equivalence. A representative is identified for each equivalence class. The controllability nature of these representatives is determined.