共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper is the continuation of the paper ``Dirichlet boundary control of semilinear parabolic equations. Part 1: Problems
with no state constraints.' It is concerned with an optimal control problem with distributed and Dirichlet boundary controls
for semilinear parabolic equations, in the presence of pointwise state constraints. We first obtain approximate optimality
conditions for problems in which state constraints are penalized on subdomains. Next by using a decomposition theorem for
some additive measures (based on the Stone—Cech compactification), we pass to the limit and recover Pontryagin's principles
for the original problem.
Accepted 21 July 2001. Online publication 21 December 2001. 相似文献
2.
In this paper we formulate and study a minimax control problem for a class of parabolic systems with controlled Dirichlet
boundary conditions and uncertain distributed perturbations under pointwise control and state constraints. We prove an existence
theorem for minimax solutions and develop effective penalized procedures to approximate state constraints. Based on a careful
variational analysis, we establish convergence results and optimality conditions for approximating problems that allow us
to characterize suboptimal solutions to the original minimax problem with hard constraints. Then passing to the limit in approximations,
we prove necessary optimality conditions for the minimax problem considered under proper constraint qualification conditions.
Accepted 7 June 1996 相似文献
3.
We prove the approximate controllability of several nonlinear parabolic boundary-value problems by means of two different
methods: the first one can be called a Cancellation method and the second one uses the Kakutani fixed-point theorem.
Accepted 10 June 1996 相似文献
4.
Hamiltonian Pontryagin's Principles for Control Problems Governed by Semilinear Parabolic Equations 总被引:2,自引:0,他引:2
In this paper we study optimal control problems governed by semilinear parabolic equations. We obtain necessary optimality
conditions in the form of an exact Pontryagin's minimum principle for distributed and boundary controls (which can be unbounded)
and bounded initial controls. These optimality conditions are obtained thanks to new regularity results for linear and nonlinear
parabolic equations.
Accepted 17 March 1997 相似文献
5.
Lou 《Applied Mathematics and Optimization》2008,47(2):121-142
Abstract. Optimal control problems governed by semilinear parabolic partial differential equations are considered. No Cesari-type conditions
are assumed. By proving the existence theorem and the Pontryagin maximum principle of optimal ``state-control" pairs for the
corresponding relaxed problems, an existence theorem of optimal pairs for the original problem is established. 相似文献
6.
Lou 《Applied Mathematics and Optimization》2003,47(2):121-142
Abstract. Optimal control problems governed by semilinear parabolic partial differential equations are considered. No Cesari-type conditions
are assumed. By proving the existence theorem and the Pontryagin maximum principle of optimal ``state-control" pairs for the
corresponding relaxed problems, an existence theorem of optimal pairs for the original problem is established. 相似文献
7.
An abstract linear-quadratic regulator problem over finite time horizon is considered; it covers a large class of linear
nonautonomous parabolic systems in bounded domains, with boundary control of Dirichlet or Neumann type. The associated differential
Riccati equation is studied from the point of view of semigroup theory; it is shown to have a classical, explicitly represented
solution for very general final data; weighted H?lder regularity results for the optimal pair are deduced.
Accepted 10 December 1997 相似文献
8.
An abstract linear-quadratic regulator problem over finite time horizon is considered; it covers a large class of linear nonautonomous parabolic systems in bounded domains, with boundary control of Dirichlet or Neumann type. We give the proof of some result stated in [AT5], and in addition we prove uniqueness of the Riccati operator, provided its final datum is suitably regular. Accepted 14 October 1998 相似文献
9.
In this paper we are concerned with some optimal control problems governed by semilinear elliptic equations. The case of
a boundary control is studied. We consider pointwise constraints on the control and a finite number of equality and inequality
constraints on the state. The goal is to derive first- and second-order optimality conditions satisfied by locally optimal
solutions of the problem.
Accepted 6 May 1997 相似文献
10.
We study optimal control problems for hyperbolic equations
(focusing on the multidimensional wave equation) with control functions in the Dirichlet
boundary conditions under hard/pointwise control and state constraints. Imposing
appropriate convexity assumptions on the cost integral functional, we establish the
existence of optimal control and derive new necessary optimality conditions in the
integral form of the Pontryagin Maximum Principle for hyperbolic state-constrained systems. 相似文献
11.
We consider the Bellman equation related to the quadratic ergodic control problem for stochastic differential systems with
controller constraints. We solve this equation rigidly in C
2
-class, and give the minimal value and the optimal control.
Accepted 9 January 1997 相似文献
12.
Using nonlinear programming theory in Banach spaces we derive a version of Pontryagin's maximum principle that can be applied
to distributed parameter systems under control and state constrains. The results are applied to fluid mechanics and combustion
problems.
Accepted 3 December 1996 相似文献
13.
丁俊堂 《数学物理学报(A辑)》2004,24(1):63-70
文中构造了一类具有Dirichlet或Neumann边界条件的半线性抛物方程u_t=Δu+f(x,u,q,t) (q=|u|^2)的解的一个辅助函数,对其使用Hopf最大值原理和黎曼几何理论,从而获得了该函数的最大值原理,据此原理获得了梯度q和解u的估计. 相似文献
14.
Second-Order Analysis for Control Constrained Optimal Control Problems of Semilinear Elliptic Systems 总被引:2,自引:0,他引:2
J. F. Bonnans 《Applied Mathematics and Optimization》1998,38(3):303-325
This paper presents a second-order analysis for a simple model optimal control problem of a partial differential equation,
namely, a well-posed semilinear elliptic system with constraints on the control variable only. The cost to be minimized is
a standard quadratic functional. Assuming the feasible set to be polyhedric, we state necessary and sufficient second-order
optimality conditions, including a characterization of the quadratic growth condition. Assuming that the second-order sufficient
condition holds, we give a formula for the second-order expansion of the value of the problem as well as the directional derivative
of the optimal control, when the cost function is perturbed. Then we extend the theory of second-order optimality conditions
to the case of vector-valued controls when the feasible set is defined by local and smooth convex constraints. When the space
dimension n is greater than 3, the results are based on a two norms approach, involving spaces L
2
and L
s
, with s>n/2 .
Accepted 27 January 1997 相似文献
15.
Y. Fujita 《Applied Mathematics and Optimization》2001,43(2):169-186
In this paper we consider the Bellman equation in a one-dimensional ergodic control. Our aim is to show the existence and
the uniqueness of its solution under general assumptions. For this purpose we introduce an auxiliary equation whose solution
gives the invariant measure of the diffusion corresponding to an optimal control. Using this solution, we construct a solution
to the Bellman equation. Our method of using this auxiliary equation has two advantages in the one-dimensional case. First,
we can solve the Bellman equation under general assumptions. Second, this auxiliary equation gives an optimal Markov control
explicitly in many examples. \keywords{Bellman equation, Auxiliary equation, Ergodic control.}
\amsclass{49L20, 35G20, 93E20.}
Accepted 11 September 2000. Online publication 16 January 2001. 相似文献
16.
The Bellman equation of the risk-sensitive control problem with full observation is considered. It appears as an example
of a quasi-linear parabolic equation in the whole space, and fairly general growth assumptions with respect to the space variable
x are permitted. The stochastic control problem is then solved, making use of the analytic results. The case of large deviation
with small noises is then treated, and the limit corresponds to a differential game.
Accepted 25 March 1996 相似文献
17.
Nabih N. Abdelmalek 《Numerical Functional Analysis & Optimization》2013,34(3-4):399-418
Two algorithms are here presented. The first one is for obtaining a Chebyshev solution of an overdetermined system of linear equations subject to bounds on the elements of the solution vector. The second algorithm is for obtaining an L1 solution of an overdetermined system of linear equations subject to the same constraints. Efficient solutions are obtained using linear programming techniques. Numerical results and comments are given. 相似文献
18.
19.
Stochastic Linear Quadratic Optimal Control Problems 总被引:2,自引:0,他引:2
This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the
coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control
variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward—backward
stochastic differential equations are established. Some results involving Riccati equation are discussed as well.
Accepted 15 May 2000. Online publication 1 December 2000 相似文献
20.
Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints
Pham 《Applied Mathematics and Optimization》2008,46(1):55-78
Abstract. This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility
and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as
a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value
function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a
stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear
equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation.
This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate
our results with several examples of stochastic volatility models popular in the financial literature. 相似文献