Necessary and sufficient conditions for distinguishability of linear control systems

Distinguishability plays a crucial rule in studying observability of hybrid system such as switched system. Recently, for two linear systems, Lou and Si gave a condition not only necessary but also sufficient to the distinguishability of linear systems. However, the condition is not easy enough to verify. This paper will give a new equivalent condition which is relatively easy to verify.     

Necessary and sufficient conditions in constrained optimization

Additional conditions are attached to the Kuhn-Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications. Necessary and sufficient conditions are also given for optimality of the dual problem. Duality and converse duality are treated accordingly.     

多数满意偏好规则的充分必要条件

研究基于满意选择的群体决策的一个基本数学理论问题. 给出并证明了群体在方案集上的任一群体满意偏好映射是多数满意偏好规则的充分必要条件.     

Necessary and sufficient conditions for oscillation of second‐order dynamic equations on time scales

In this paper, we establish necessary and sufficient conditions for oscillation of second‐order strongly superlinear and strongly sublinear dynamic equations. Our results unify and improve many known results in the literature.     

抛物型时滞偏微分方程解振动的充要条件

讨论一类多滞量抛物型时滞偏微分方程解的振动性质，获得了其一切解振动的充要条件及一些充分条件；指出了其与普通抛物型偏微分方程解的质的差异．     

Necessary and sufficient conditions for discrete and differential inclusions of elliptic type

This paper deals for the first time with the Dirichlet problem for discrete (PD), discrete approximation problem on a uniform grid and differential (PC) inclusions of elliptic type. In the form of Euler-Lagrange inclusion necessary and sufficient conditions for optimality are derived for the problems under consideration on the basis of new concepts of locally adjoint mappings. The results obtained are generalized to the multidimensional case with a second order elliptic operator.     

零对称BZ-代数的充要条件

重新证明文[10]中几个重要结论并修正文[10]中的定理1(11)和定理2．在此基础上，利用这些重新证明过的结论及修正过的定理可以按照文[10]中引理3，定理4，定理6，定理7，定理10的证明过程原样证明文[10]中的相应结果．因而在文[10]中，除性质11是结合BZ一代数的等价性质(见文[15])，定理1(11)及定理2需要进行修正外，其余结论及证明过程均成立．     

Necessary and sufficient conditions for linear suboptimality in constrained optimization

This article is devoted to the study of some extremality and optimality notions that are different from conventional concepts of optimal solutions to optimization-related problems. These notions reflect certain amounts of linear subextremality for set systems and linear suboptimality for feasible solutions to multiobjective and scalar optimization problems. In contrast to standard notions of optimality, it is possible to derive necessary and sufficient conditions for linear subextremality and suboptimality in general nonconvex settings, which is done in this article via robust generalized differential constructions of variational analysis in finite-dimensional and infinite-dimensional spaces.      

On necessary and sufficient conditions in vector optimization

It is shown that some general multiplier rules are necessary conditions for vector optimization in infinite-dimensional spaces. Under additional convexity assumptions, these conditions are sufficient. As an application, the Pontryagin maximum principle for cooperative differential games is examined.The authors are grateful to Professor W. Stadler and the referees of the previous edition of this paper for their valuable remarks and suggestions, which have been very helpful in the preparation of this paper.     

Necessary conditions for stochastic optimal control problems in infinite dimensions

The purpose of this paper is to establish the first and second order necessary conditions for stochastic optimal controls in infinite dimensions. The control system is governed by a stochastic evolution equation, in which both drift and diffusion terms may contain the control variable and the set of controls is allowed to be nonconvex. Only one adjoint equation is introduced to derive the first order necessary optimality condition either by means of the classical variational analysis approach or, under an additional assumption, by using differential calculus of set-valued maps. More importantly, in order to avoid the essential difficulty with the well-posedness of higher order adjoint equations, using again the classical variational analysis approach, only the first and the second order adjoint equations are needed to formulate the second order necessary optimality condition, in which the solutions to the second order adjoint equation are understood in the sense of the relaxed transposition.     

Necessary and sufficient conditions for stabilization of discrete-time planar switched systems

This paper discusses the stabilization problem for single-input discrete-time planar switched systems. We establish necessary and sufficient conditions for the stabilization of planar switched systems. A series of linear inequalities are presented for describing the set of all common quadratic Lyapunov functions. Our results are not only easily testable, but also constructive.     

Necessary and sufficient conditions for bang-bang control

Necessary and sufficient conditions for the optimal control to be bang-bang are presented for a nonlinear system. The payoff, which is not necessarily quadratic, is assumed to be described by a Hilbert-space norm and to be differentiable and convex. The results are extensions of Ref. 1 to the case of nonlinear systems.     

非线性抛物型时滞微分方程解振动的充要条件

讨论了一类多滞量非线性抛物型时滞微分方程解的振动性质，获得了其一切解振动的充要条件；指出了其与普通抛物型偏微分方程解的质的差异。     

Second-order necessary conditions for domain optimization problems in elastic structures,part 1: Surface traction given as a field

In this paper, domain optimization problems for both linear and nonlinear elastic structures are studied. The first variation and the second variation of the objective function are calculated in terms of the solution, of the first variation of the solution for the primal elastic system, and of the adjoint variables introduced. The adjoint variables obey a (fictitious) linear elastic system in contrast with the nonlinear adjoint systems introduced by Dems and Mróz, and by Dems and Haftka. From these results, the first-order and the second-order necessary conditions that an optimal domain should satisfy are immediately derived.Portions of this paper were presented at the 5th IFAC Symposium on Control of Distributed Parameter Systems, Perpignan, France, 1989. The authors would like to express their sincere thanks to the referees for their critical readings.     

Near-optimal control of a stochastic vegetation-water system with reaction diffusion

In this article, we study the near-optimal control of a class of stochastic vegetation-water model. The near-optimal control is one problem in which the density of vegetation and water is higher at the lowest cost. We have provided a priori estimates of the vegetation and water densities and obtained the sufficient and necessary conditions for the system's near-optimal control problem by applying the maximum condition of the Hamiltonian function and the Ekeland principle. A numerical simulation is presented to verify our theoretical results.     

Necessary and sufficient conditions for the existence of stabilizing feedback for control systems

We prove that the existence of a non-smooth control Lyapunovfunction is a necessary and sufficient condition for the existenceof an ordinary smooth time-varying feedback that stabilizesan affine time-varying control system. Results concerning thenon-affine case are also provided.     

Optimal scheduling of reservoir releases during flood: Deterministic optimization problem,part 1, procedure

In this paper, we are concerned with the optimal scheduling of water releases from retention reservoirs during flood, with the objective of minimizing flood damages at the important damage centers downstream of the reservoirs. Unlike in most other papers devoted to this subject, the flood routing equations are nonlinear. The performance index of the problem leads to a minimax optimal control problem. For this problem, the necessary optimality conditions are provided and a version of the feasible directions method is proposed.The research reported here has been supported by the Central Basic Research Program CPBP-03.09, Metody Analizy i Uytkowania Zasobow Wodnych, Polish Academy of Sciences, Warsaw, Poland. This support is kindly acknowledged.     

Necessary and sufficient conditions for expansions of Gabor type

In this paper, we give necessary and sufficient conditions for two families of Gabor functions of a certain type to yield a reproducing identity on L^2（R^n）. As applications, we characterize when such families yield orthonormal or bi-orthogonal expansions. We also obtain a generalization of the Balian-Low theorem for general reprodueing identities （not necessary coming from a frame）.     

Necessary optimality conditions for singular controls

A definition of singular controls with respect to components is given that includes, in particular, the conventional definition. On the basis of this definition, new necessary optimiality conditions for singular controls with respect to components are derived for the processes governed by systems of ordinary differential equations.     

A sufficient condition for near-optimal stochastic controls and its application to manufacturing systems

This paper presents an asymptotic analysis of control models governed by stochastic ordinary differential equations. A sufficient condition of near-optimal controls is given based on Ekeland's principle. It is shown that, under some concavity assumptions, the-maximum condition in terms of the Hamiltonian implies the -optimality. By applying this result to a general manufacturing system, the common practice of hierarchical controls employed in order to reduce the overall complexity of the system is justified on a rigorous basis. A near-optimal control for the operational level is constructed from a near-optimal control at the corporate level, and an asymptotic error bound is obtained. A stochastic extension of the classical HMMS model is treated as a specific example. The approach of this paper is different from those in the literature, and it allows us to handle some previously unsolved problems with nonlinear state equations as well as nonseparable cost functions.This work was partly supported by NSERC Grant A4619, URIF, and the Manufacturing Research Corporation of Ontario.