Existence Theorem For Optimal Control Research Articles

The Existence Theorem for Optimal Control with Non-Standard Cost Functional and Analysis

The Existence Theorem for Optimal Control with Non-Standard Cost Functional and Analysis

Existence theorems for optimal control in some problems of trajectories bundles control

Existence theorems for optimal control in some problems of trajectories bundles control

Existence of optimal controls for viscous flow problems

A class of optimal control problems in viscous flow is studied. Main result is the existence theorem for optimal control. Three typical flow control problems are formulated within this general class.

Optimization of the thickness of layers of sandwich conical shells

We deal with an optimal control problem for variational inequalities, where the linear operators as well as the convex sets of possible states depend on the control parameter. The existence theorem for optimal control is applied to optimal design problems for sandwich conical shells where a variable thickness of given layers appears as a control variable.

An existence theorem for optimal control with nonstandard cost functionals

An existence theorem for optimal control is obtained for a general nonstandard cost functional of fractional type in this work. As an application of our result we can derive an existence theorem for optimal control given by M. B. Subrahamanyam for a cost functional, which is a ratio of two given integral cost functionals.

Existence Theorems for Optimal Control and Calculus of Variations Problems Where the States Can Jump

We examine optimal control and calculus of variations problems where the states can be discontinuous. In the control theory setting this is caused by allowing impulse controls. Conditions under which optimal solutions will exist for these problems are determined after we derive suitable objective functionals that can handle the jump terms.

The controllability problem for nonlinear Volterra systems

We discuss the controllability of systems whose dynamics are governed by a large class of nonlinear Volterra integral equations. The property of controllability is shown to be equivalent to the existence of a fixed point of a certain set-valued map. We show that convexity and seminormality conditions intimately related to those assumed in proofs of existence theorems for optimal controls are sufficient to guarantee controllability. Approximate controllability results are obtained by first introducing generalized solutions and then showing, under only mild additional restrictions, that ordinary solutions are dense in this broader class of trajectories.

Some remarks on existence of optimal controls for Mayer problems with singular components

This paper proves an existence theorem for optimal controls for systems governed by ordinary differential equations and a large class of functional differential equations of neutral type. Extensions beyond earlier work are made as a result of employing a new closure theorem originally used by Cesari and Suryanarayana in their study of Pareto optima and which is, in turn, based on the Fatou lemma for vector-valued functions as proved by Schmeidler. The use of these techniques simplifies the standard arguments for existence in the presence of singular components and allows the use of very weak semi-normality conditions. It also permits the consideration of a significantly larger class of hereditary systems than has been treated in the existing literature.

Existence theorems for optimal control of quasilinear parabolic partial differential equations

AbstractThe question on existence of optimal controls for a system governed by quasilinear parabolic partial differential equations which is linear in the control variables is considered. It is shown that whenever the controls converge in the weak * topology of L∞, the corresponding solutions converge uniformly. Using this result and results on lower semi-continuity of integral functionals, existence theorems for optimal controls are proved.

Optimal control of systems governed by a class of nonlinear evolution equations in a reflexive Banach space

The paper presents a closure theorem for the attainable trajectories of a class of control systems governed by a large class of nonlinear evolution equations in reflexive Banach spaces. Several existence theorems for optimal controls are proven that include a terminal control problem, a time-optimal control problem, and a special Bolza problem. Some results of independent interest are also presented.

An existence theorem for optimal controls of non-linear vector delay-differential equations with time-lag controls

An existence theorem for optimal controls which transfer a fixed given function to a moving target set is shown for a class of non-linear systems containing time delays in both the state and control variables.

Geometric and analytic views in existence theorems for optimal control. III. Weak solutions

Existence theorems are proved for weak optimal solutions of problems of optimization with distributed and boundary control. Many examples are given. Application is made of recent remarks on closure properties of linear and nonlinear operators. Recent geometric, topological, and analytical views are brought to bear on the underlying seminormality conditions.

Geometric and analytic views in existence theorems for optimal control. II. Distributed and boundary controls

Existence theorems are proved for Lagrange problems of optimization in a given domainG with possibly unbounded distributed controls inG and on the boundary ofG, and with functional relations onG and on the boundary represented by closed operators, not necessarily linear. The case where the functional relations are partial differential equations is emphasized. Recent work concerning the reduction or elimination of seminormality requirements is taken into account. Many examples are given.

Geometric and analytic views in existence theorems for optimal control in Banach spaces. Part 1. Distributed parameters

Existence theorems for optimal control problems in Banach spaces are stated and proved.

Optimal feedback control of stochastic McShane differential systems

In this paper, the optimal control problem of system described by stochastic McShane differential equations is considered. It is shown that this problem can be reduced to an equivalent optimal control problem of distributed parameter systems of parabolic type with controls appearing in the coefficients of the differential operator. Further, to this reduced problem, necessary conditions for optimality and an existence theorem for optimal controls are given.

Optimal feedback control of stochastic McShane differential systems

In this paper, the optimal control problem of system described by stochastic McShane differential equations is considered. It is shown that this problem can be reduced to an equivalent optimal control problem of distributed parameter systems of parabolic type with controls appearing in the coefficients of the differential operator. Further, to this reduced problem, necessary conditions for optimality and an existence theorem for optimal controls are given.

An existence theorem for optimal controls

An existence theorem is given based on a criterion ensuring compactness of the controls in the metric corresponding to convergence in measure.

Remarks on some existence theorems for optimal control

First, a remark is made that a growth condition contained in previous papers by Cesari concerning existence theorems for optimal controls can be replaced by a slightly more general condition. In this more general condition, a constantMźź0 is replaced by any functionMź(t)ź0 which is assumed to beL-integrable in every finite interval. Then, the remark is made that the same condition, which is usually required to be satisfied by the functionsf0(t, x, u),f(t, x, u) characterizing the control, can be required to be satisfied only by the admissible pairsx(t),u(t) of the class Ω in which the optimum is being sought. This generalization requires a subtle argument. The new condition parallels now the usual conditions of the type ź|xź|pdtźM, which are required to be satisfied by the admissible pairs of the class Ω.

Existence Theorems for Optimal Controls of the Mayer Type

Existence Theorems for Optimal Controls of the Mayer Type

An existence theorem for optimal control in the Boltz problem, some of its applications and the necessary conditions for the optimality of moving and singular systems

A THEOREM is proved below which gives sufficient conditions for the existence of an optimal control in the Boltz problem. Theorems on the existence of an optimal control in a high-speed problem (see [1]) and in Mayer's problem (see [2]) follow from it as particular cases. If we reduce the Boltz problem to the Mayer problem and then use the theorem of [1], stronger conditions are required than those used by the author. Some questions on the theory of optimal control, in which the theorem is directly used, are also considered. In particular the results of paper [3] are refined. An example is given for which V.F. krotov's principle of optimality (see [4]) does not hold. In conclusion some optimality conditions for moving and singular systems are formulated.