共查询到20条相似文献,搜索用时 0 毫秒
1.
Irena Lasiecka 《Applied Mathematics and Optimization》1977,4(1):301-327
Boundary control problems for the linear, parabolic equations and a quadratic performance index are considered. The controls are allowed to be in the spaceL
2[OT;L2()], where is a boundary. Exploiting the semigroup approach, it is shown that optimal control belongs toL
2[OT;H1/2()] and, as a consequence, optimal trajectory belongs toL
1[OT;H1()]. This result is obtained for two kinds of domains. The first are the domains withC
-boundary and the second are the domains being the parallelepipeds. 相似文献
2.
V. E. Kapustyan 《Ukrainian Mathematical Journal》1996,48(1):56-64
We construct and justify asymptotic solutions of optimal parabolic problems with locally constrained control which depends only on time. 相似文献
3.
K. Malanowski 《Journal of Optimization Theory and Applications》1987,53(3):429-449
A family of optimal control problems for discrete systems that depend on a real parameter is considered. The problems are strongly convex and subject to state and control constraints. Some regularity conditions are imposed on the constraints.The control problems are reformulated as mathematical programming problems. It is shown that both the primal and dual optimal variables for these problems are right-differentiable functions of a parameter. The right-derivatives are characterized as solutions to auxiliary quadratic control problems. Conditions of continuous differentiability are discussed, and some estimates of the rate of convergence of the difference quotients to the respective derivatives are given. 相似文献
4.
5.
V. E. Kapustyan 《Ukrainian Mathematical Journal》1993,45(10):1506-1519
A complete asymptotic solution is constructed and justified for the optimal singular parabolic problems with constrained control and a completely degenerate differential part of an operator.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1345–1355, October, 1993. 相似文献
6.
R.B. Vinter 《Journal of Mathematical Analysis and Applications》2018,457(2):1696-1712
In a recent, related, paper, necessary conditions in the form of a Maximum Principle were derived for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions covered fixed end-time problems and, under additional hypotheses, free end-time problems. These conditions improved on previous conditions in the following respects. They provided the first fully non-smooth Pontryagin Maximum Principle for problems involving delays in both state and control variables, only special cases of which were previously available. They provide a strong version of the Weierstrass condition for general problems with possibly non-commensurate control delays, whereas the earlier literature does so only under structural assumptions about the dynamic constraint. They also provided a new ‘two-sided’ generalized transversality condition, associated with the optimal end-time. This paper provides an extension of the Pontryagin Maximum Principle of the earlier paper for time delay systems, to allow for the presence of a unilateral state constraint. The new results fully recover the necessary conditions of the earlier paper when the state constraint is absent, and therefore retain all their advantages but in a setting of greater generality. 相似文献
7.
Walter Alt 《Applied Mathematics and Optimization》1990,21(1):53-68
We consider a family of nonlinear optimal control problems depending on a parameter. Under the assumption of a second-order sufficient optimality condition it is shown that the solutions of the problems as well as the associated Lagrange multipliers are Lipschitz continuous functions of the parameter. 相似文献
8.
In this paper the application of the Multiplier Method (also known as Augmented Lagrangian Method or Penalty Shifting Method) to quadratic optimal control problems for linear parabolic distributed systems is studied and the convergence of the method on appropriate Hilbert spaces is proved. Numerical examples are reported.This work was partially supported by the Consiglio Nazionale delle Ricerche. 相似文献
9.
L. Steven Hou 《Journal of Mathematical Analysis and Applications》2006,313(1):284-310
Terminal-state tracking optimal control problems for linear parabolic equations are studied in this paper. The control objectives are to track a desired terminal state and the control is of the distributed type. Explicit solution formulae for the optimal control problems are derived in the form of eigen series. Pointwise-in-time L2 norm estimates for the optimal solutions are obtained and approximate controllability results are established. Exact controllability is shown when the target state vanishes on the boundary of the spatial domain. One-dimensional computational results are presented which illustrate the terminal-state tracking properties for the solutions expressed by the series formulae. 相似文献
10.
This paper considers the optimal control of a system governed by a parabolic partial differential equation with first boundary conditions. For this system, a condition of extremality is defined, which is proven to be a necessary condition for optimality. For non-extremal controls, a method of constructing a new control that has an improved criterion value is discussed. It is shown that if a sequence of controls, each constructed from the previous control in the manner discussed, converges, then the limit is extremal. 相似文献
11.
Kazimierz Malanowski 《Applied Mathematics and Optimization》1984,12(1):1-14
A family of convex, control constrained optimal control problems that depend on a real parameter is considered. It is shown that under some regularity conditions on data the solutions of these problems, as well as the associated Lagrange multipliers are directionally differentiable with respect to parameter. The respective right-derivatives are given as the solution and the associated Lagrange multipliers for some quadratic optimal control problem. If a condition of strict complementarity type hold, then directional derivatives become continuous ones. 相似文献
12.
13.
An optimal Robin boundary control problem associated with semilinear parabolic partial differential equations is considered. Existence of an optimal solution is proved and an optimality system of equations is derived. Semidiscrete finite element approximations of the optimality system are defined and error estimates are obtained. 相似文献
14.
In this paper, we derive a posteriori error estimators for the constrained optimal control problems governed by semi-linear parabolic equations under some assumptions. Then we use them to construct reliable and efficient multi-mesh adaptive finite element algorithms for the optimal control problems. Some numerical experiments are presented to illustrate the theoretical results. 相似文献
15.
Franco Tomarelli 《Numerische Mathematik》1984,45(1):23-50
Summary We prove some regularity results for the solution of a linear abstract Cauchy problem of parabolic type. As an application, we study the approximation of the solution by means of an implicit-Euler discretization in time, which is stable with respect to a wide class of Galerkin approximation methods in space. The error is evaluated in norms of typeL
2(0, ,L
2) andL
2(0, ,V)(H
00
1/2
(0, ,H)+H
1(0, ,V)), whereVHV are Hilbert spaces (the embeddings are supposed to be dense and continuous). We prove error estimates which are optimal with respect to the regularity assumptions on the right-hand side of the equation.The author was supported by G.N.A.F.A. and I.A.N. of C.N.R. and by M.P.I. 相似文献
16.
In this paper, we consider an optimal control problem of switched systems with continuous-time inequality constraints. Because of the complexity of such constraints and switching laws, it is difficult to solve this problem by standard optimization techniques. To overcome the difficulty, we adopt a bi-level algorithm to divide the problem into two nonlinear constrained optimization problems: one continuous and the other discrete. To solve the problem, we transform the inequality constraints into equality constraints which is smoothed using a twice continuously differentiable function and treated as a penalty function. On this basis, the smoothed problem can be solved by any second-order gradient algorithm, e.g., Newton’s Method. Finally, numerical examples show that our method is effective compared to existing algorithms. 相似文献
17.
A computational algorithm for solving a class of optimal control problems involving terminal and continuous state constraints of inequality type was developed in Ref. 1. In this paper, we extend the results of Ref. 1 to a more general class of constrained time-delayed optimal control problems, which involves terminal state equality constraints as well as terminal state inequality constraints and continuous state constraints. Two examples have been solved to illustrate the efficiency of the method. 相似文献
18.
We consider the fast and efficient numerical solution of linear-quadratic optimal control problems with additional constraints on the control. Discretization of the first-order conditions leads to an indefinite linear system of saddle point type with additional complementarity conditions due to the control constraints. The complementarity conditions are treated by a primal-dual active set strategy that serves as outer iteration. At each iteration step, a KKT system has to be solved. Here, we develop a multigrid method for its fast solution. To this end, we use a smoother which is based on an inexact constraint preconditioner.We present numerical results which show that the proposed multigrid method possesses convergence rates of the same order as for the underlying (elliptic) PDE problem. Furthermore, when combined with a nested iteration, the solver is of optimal complexity and achieves the solution of the optimization problem at only a small multiple of the cost for the PDE solution. 相似文献
19.
A linear elliptic control problem with pointwise state constraints is considered. These constraints are given in the domain.
In contrast to this, the control acts only at the boundary. We propose a general concept using virtual control in this paper.
The virtual control is introduced in objective, state equation, and constraints. Moreover, additional control constraints
for the virtual control are investigated. An error estimate for the regularization error is derived as main result of the
paper. The theory is illustrated by numerical tests. 相似文献
20.
This paper presents a numerical method for solving nonlinear optimal control problems including state and control inequality constraints. The method is based upon rationalized Haar functions. The differential and integral expressions which arise in the system dynamics, the performance index and the boundary conditions are converted into some algebraic equations which can be solved for the unknown coefficients. Illustrative examples are included to demonstrate the validity and applicability of the technique. 相似文献