Solvability and Construction of a Solution to the Fredholm Integral Equation of the First Kind

The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.

Virtual Element Discretization of Optimal Control Problem Governed by Brinkman Equations

In this paper, we discuss virtual element method (VEM) approximation of optimal control problem governed by Brinkman equations with control constraints. Based on the polynomial projections and variational discretization of the control variable, we build up the virtual element discrete scheme of the optimal control problem and derive the discrete first order optimality system. A priori error estimates for the state, adjoint state and control variables in L2 and H1 norm are derived. The theoretical findings are illustrated by the numerical experiments.

Solution of the HJI equations for nonlinear H_∞ control design by state-dependent Riccati equations approach

The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix equations for partial derivates of the solution of the SDREs and introducing symmetry measure for some related matrices, a method is proposed for examining whether the SDRE method admits a global optimal control equiva- lent to that solved by the HJI equation method. Two examples with simulation are given to illustrate the method is effective.

EXACT EVALUATIONS OF FINITE TRIGONOMETRIC SUMS BY SAMPLING THEOREMS

We use the sampling representations associated with Sturm-Liouville difference operators to derive generalized integral-valued trigonometric sums. This extends the known results where zeros of Chebyshev polynomials of the first kind are involved to the use of the eigenvalues of difference operators, which leads to new identities. In these identities Bernoulli＇s numbers play a role similar to that of Euler＇s in the old ones. Our technique differs from that of Byrne-Smith （1997） and Berndt-Yeap （2002）.

SINGULARLY PERTURBED METHODS IN THE THEORY OF OPTIMAL CONTROL OF SYSTEMS GOVERNED BY PARTIAL DIFFERENTIAL EQUATIONS

In this paper, the various problems associaled with the optimal control of systemsgoverned by partial differential equations are introduced by using singularly perturbedmethods for analysis based on stale equations, or the cost funtction and also stateequations defined in perturbed domains.

CONTROLLABILITY OF NEUTRAL STOCHASTIC EVOLUTION EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION

In this paper,we investigate the controllability for neutral stochastic evolution equations driven by fractional Brownian motion with Hurst parameter H ∈（1/2,1） in a Hilbert space.We employ the α-norm in order to reflect the relationship between H and the fractional power α.Sufficient conditions are established by using stochastic analysis theory and operator theory.An example is provided to illustrate the effectiveness of the proposed result.

Numerical Simulation about the Characteristics of the Store Released from the Internal Bay in Supersonic Flow

To understand the influence of the initial release conditions on the separation characteristics of the store and improve it under high Mach number(Ma=4)flight conditions,the overset grid method and the Realizable k−εturbulence model coupled with an equation with six degrees of freedom are used to simulate the store released from the internal bay.The motion trajectory and the attitude angle of the store separation under the conditions of different centroid,velocity,height and control measures are given by the calculated result.Through analysis,the position of the centroid will affect the separation of the store,which needs to be considered in the design.Increasing the launching height is conducive to the separation of the store.If the store has an initial velocity,it can leave the internal bay more quickly and reduce the probability of collision with the wall.Cylindrical rod and slanted aft wall control measures can improve the attitude of the store and make the store fall more smoothly.

Robust Radiometric Normalization of the near Equatorial Satellite Images Using Feature Extraction and Remote Sensing Analysis

Relative radiometric normalization (RRN) minimizes radiometric differences among images caused by inconsistencies of acquisition conditions rather than changes in surface. Scale invariant feature transform (SIFT) has the ability to automatically extract control points (CPs) and is commonly used for remote sensing images. However, its results are mostly inaccurate and sometimes contain incorrect matching caused by generating a small number of false CP pairs. These CP pairs have high false alarm matching. This paper presents a modified method to improve the performance of SIFT CPs matching by applying sum of absolute difference (SAD) in a different manner for the new optical satellite generation called near-equatorial orbit satellite and multi-sensor images. The proposed method, which has a significantly high rate of correct matches, improves CP matching. The data in this study were obtained from the RazakSAT satellite a new near equatorial satellite system. The proposed method involves six steps: 1) data reduction, 2) applying the SIFT to automatically extract CPs, 3) refining CPs matching by using SAD algorithm with empirical threshold, and 4) calculation of true CPs intensity values over all image’ bands, 5) preforming a linear regression model between the intensity values of CPs locate in reverence and sensed image’ bands, 6) Relative radiometric normalization conducting using regression transformation functions. Different thresholds have experimentally tested and used in conducting this study (50 and 70), by followed the proposed method, and it removed the false extracted SIFT CPs to be from 775, 1125, 883, 804, 883 and 681 false pairs to 342, 424, 547, 706, 547, and 469 corrected and matched pairs, respectively.

Sustainable Ecosystem Management via H∞-Control Theory of Stochastic Systems

In this paper, aiming to provide accurate protocols for management of sustainable ecosystems, a design methodology of H∞-controller for hunter-prey model under exposure to exogenous disturbance and stochastic noise is presented. Along the development, solution procedure of the stochastic Hamilton-Jacobi-Isaacs equation via Successive Galerkin’s Approximation is described. Utilizing the proposed solution methodology of Hamilton-Jacobi-Isaacs equation, H∞-controller of hunter-prey model was successfully designed. Robustness and performance against exogenous disturbance of the designed H∞-controller is validated and confirmed by numerical simulations including Monte-Carlo simulation by Simulink software on MATLAB.

Finite-time consensus of multi-agent systems driven by hyperbolic partial differential equations via boundary control

The leaderless and leader-following finite-time consensus problems for multiagent systems(MASs)described by first-order linear hyperbolic partial differential equations(PDEs)are studied.The Lyapunov theorem and the unique solvability result for the first-order linear hyperbolic PDE are used to obtain some sufficient conditions for ensuring the finite-time consensus of the leaderless and leader-following MASs driven by first-order linear hyperbolic PDEs.Finally,two numerical examples are provided to verify the effectiveness of the proposed methods.

Robust Control Synthesis of Polynomial Nonlinear Systems Using Sum of Squares Technique

在这篇论文，广场(求救) 加技术被用来与多项式向量领域为不明确的仿射的非线性的系统的一个类分析柔韧的州的反馈合成问题。没有或与保证费用或 Hperformance 目的，足够的条件被给获得答案到上述控制问题。而且，如此的可解决的条件能以能被 SOS 技术直接处理的州的依赖线性矩阵不平等(LMI ) 作为求救编程问题被提出。而且，一个想法被提供由介绍一些额外的多项式描述多项式或甚至合理的矩阵的逆。一个数字例子被举说明途径的有效性。

Decentralized Optimal Control and Stabilization of Interconnected Systems With Asymmetric Information

The paper addresses the decentralized optimal control and stabilization problems for interconnected systems subject to asymmetric information.Compared with previous work,a closed-loop optimal solution to the control problem and sufficient and necessary conditions for the stabilization problem of the interconnected systems are given for the first time.The main challenge lies in three aspects:Firstly,the asymmetric information results in coupling between control and estimation and failure of the separation principle.Secondly,two extra unknown variables are generated by asymmetric information(different information filtration)when solving forward-backward stochastic difference equations.Thirdly,the existence of additive noise makes the study of mean-square boundedness an obstacle.The adopted technique is proving and assuming the linear form of controllers and establishing the equivalence between the two systems with and without additive noise.A dual-motor parallel drive system is presented to demonstrate the validity of the proposed algorithm.

Matrix Riccati Equations in Optimal Control

In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated. This article proposes a change of variable that allows to find explicit solution of the Matrix Riccati equation. We then apply this solution to Optimal Control.

Solving nonlinear master equation describing quantum damping by virtue of the entangled state representation

This paper solves the newly constructed nonlinear master equation dρ/dt = κ[2f （N） aρ （1/f （N - 1））a^＋ -a^＋aρ- ρa^＋a], where f（N） is an operator-valued function of N = a^＋a, for describing amplitude damping channel, and derives the infinite operator sum representation of quasi-Kraus operators for the density operator. It also shows that in this nonlinear process the initial pure number state density operator will evolve into the binomial field （a mixed state） when f （N） = 1√N ＋ 1.

On the Solutions of the Matrix Equations in Optimal Stochastic Control

In this paper, the matrix algebraic equations involved in the optimal control problem of time-invariant linear Ito stochastic systems, named Riccati- Ito equations in the paper, are investigated. The necessary and sufficient condition for the existence of positive definite solutions of the Riccati- Ito equations is obtained and an iterative solution to the Riccati- Ito equations is also given in the paper thus a complete solution to the basic problem of optimal control of time-invariant linear Ito stochastic systems is then obtained. An example is given at the end of the paper to illustrate the application of the result of the paper.

A FIELD METHOD FOR INTEGRATING THE EQUATIONS OF MOTION OF NONHOLONOMIC CONTROLLABLE SYSTEMS

This paper presents a field method for integrating the equations of motion of nonholonomic controllable systems. An example is given to illustrate the application of the method.

The cost of approximate controllability for semilinear heat equations

We consider the semilinear heat equation with globally Lipschitz non-linearity involving gradient terms in a bounded domain of R^n. In this paper, we obtain explicit bounds of the cost of approximate controllability, i.e., of the minimal norm of a control needed to control the system approximately. The methods we used combine global Carleman estimates, the variational approach to approximate controllability and Schauder＇s fixed point theorem.

Modified Modeling of the Heart by Applying Nonlinear Oscillators and Designing Proper Control Signal

Rhythmic phenomena are one of the most striking manifestations of dynamic behavior in biological systems. Understanding the mechanisms of biological rhythms, is crucial for understanding the dynamic of life. Each type of dynamic behaviors may be related to the performance of both normal physiology and pathological. Conductive system of the heart can be stimulated to action as a network of elements and these elements show the oscillatory behavior then can be modeled as nonlinear oscillators. This paper provides the mathematical model of the heart rhythm by considering different states of Vanderpol nonlinear oscillators. Proposed oscillator model is designed in order to reproduce time series of action potential of natural pacemakers cardiac, such as SA or AV nodes. So model of heart is presented by a system of differential equations and to be considered chaotic or nonchaotic for different parameters of the model by using of the 0-1 test. Finally, the model is synchronized by applying an appropriate control signal, if it is needed.

Solution and Analysis of the Fuzzy Volterra Integral Equations viaHomotopy Analysis Method

Homotopy Analysis Method(HAM)is semi-analytic method to solve the linear and nonlinear mathematical models which can be used to obtain the approximate solution.The HAM includes an auxiliary parameter,which is an efficient way to examine and analyze the accuracy of linear and nonlinear problems.The main aim of this work is to explore the approximate solutions of fuzzy Volterra integral equations(both linear and nonlinear)with a separable kernel via HAM.This method provides a reliable way to ensure the convergence of the approximation series.A new general form of HAM is presented and analyzed in the fuzzy domain.A qualitative convergence analysis based on the graphical method of a fuzzy HAM is discussed.The solutions sought by the proposed method show that the HAM is easy to implement and computationally quite attractive.Some solutions of fuzzy second kind Volterra integral equations are solved as numerical examples to show the potential of the method.The results also show that HAM provides an easy way to control and modify the convergence area in order to obtain accurate solutions.