共查询到20条相似文献,搜索用时 109 毫秒
1.
In this paper we consider the optimal control problem for a system of first-order hyperbolic equations. The right-hand side of this system is determined by a control system of ordinary differential equations. Admissible controls belong to the class of smooth functions. We obtain an optimality condition and propose a general scheme of improvement methods for the mentioned problem. 相似文献
2.
We study the existence of solutions of control problems relative to a nonlinear elliptic system with Dirichlet boundary conditions.
In this problem, the control variables are the coefficients of the equations and the open set where they are posed. It is
known that this class of problems has no solution in general, but using homogenization results about elliptic systems we show
the existence of solutions when the controls are searched in a bigger set. These results are related to the selection of optimal
materials and shapes. 相似文献
3.
We study the optimal input-output stabilization of discrete time-invariant linear systems in Hilbert spaces by state feedback.
We show that a necessary and sufficient condition for this problem to be solvable is that the transfer function has a right
factorization over H-infinity. A necessary and sufficient condition in terms of an (arbitrary) realization is that each state
which can be reached in a finite time from the zero initial state has a finite cost. Another equivalent condition is that
the control Riccati equation has a solution (in general unbounded and even non densely defined). The optimal state feedback
input-output stabilization problem can then be solved explicitly in terms of the smallest solution of this control Riccati
equation. We further show that after renorming the state space in terms of the solution of the control Riccati equation, the
closed-loop system is not only input-output stable, but also strongly internally stable.
Received: July 4, 2007. Revised: October 17, 2007. 相似文献
4.
This paper provides a unified framework to study monotone optimal control for a class of Markov decision processes through D-multimodularity. We demonstrate that each system in this class can be classified as either a substitution-type or a complement-type system according to the possible transition set, which can be used as a classification mechanism that integrates a variety of models in the literature. We develop a generic proof of the structural properties of both types of system. In particular, we show that D-multimodularity is a generally sufficient condition for monotone optimal control of different types of system in this class. With this unified theory, there is no need to pursue each problem ad hoc and the structural properties of this class of MDPs follow with ease. 相似文献
5.
S. Ya. Serovaiskii 《Russian Mathematics (Iz VUZ)》2009,53(1):64-70
We consider the optimal control problem for a system governed by a nonlinear hyperbolic equation without any constraints on the parameter of nonlinearity. No uniqueness theorem is established for a solution to this problem. The control-state mapping of this system is not Gateaux differentiable. We study an approximate solution of the optimal control problem by means of the penalty method. 相似文献
6.
Qinqin Chai Ryan Loxton Kok Lay Teo Chunhua Yang 《Nonlinear Analysis: Real World Applications》2013,14(3):1536-1550
We consider a general nonlinear time-delay system with state-delays as control variables. The problem of determining optimal values for the state-delays to minimize overall system cost is a non-standard optimal control problem–called an optimal state-delay control problem–that cannot be solved using existing optimal control techniques. We show that this optimal control problem can be formulated as a nonlinear programming problem in which the cost function is an implicit function of the decision variables. We then develop an efficient numerical method for determining the cost function’s gradient. This method, which involves integrating an auxiliary impulsive system backwards in time, can be combined with any standard gradient-based optimization method to solve the optimal state-delay control problem effectively. We conclude the paper by discussing applications of our approach to parameter identification and delayed feedback control. 相似文献
7.
In this paper we study the problem of personnel planning in care-at-home facilities. We model the system as a Markov decision process, which leads to a high-dimensional control problem. We study monotonicity properties of the system and derive structural results for the optimal policy. Based on these insights, we propose a trunk reservation heuristic to control the system. We provide numerical evidence that the heuristic yields close to optimal performance, and scales well for large problem instances. 相似文献
8.
In this paper, we consider a nonlinear dynamic system with uncertain parameters. Our goal is to choose a control function for this system that balances two competing objectives: (i) the system should operate efficiently; and (ii) the system’s performance should be robust with respect to changes in the uncertain parameters. With this in mind, we introduce an optimal control problem with a cost function penalizing both the system cost (a function of the final state reached by the system) and the system sensitivity (the derivative of the system cost with respect to the uncertain parameters). We then show that the system sensitivity can be computed by solving an auxiliary initial value problem. This result allows one to convert the optimal control problem into a standard Mayer problem, which can be solved directly using conventional techniques. We illustrate this approach by solving two example problems using the software MISER3. 相似文献
9.
In this paper, a nonlinear control-affine system that describes the dynamics of a continuous crystallizer with fines trap is considered. We study the approximate steering problem for this system, i. e. the problem of constructing an admissible open-loop control that steers the system from a given initial state to a neighborhood of the target state. This problem is reduced to solving a system of algebraic equations with respect to the control parameters. We show that the resulting algebraic system is locally solvable in a neighborhood of the equilibrium point. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
A. K. Demenchuk 《Differential Equations》2011,47(9):1253-1258
We consider a linear periodic control system such that the ranks of the matrix multiplying the control and the extended matrix
consisting of the averaged coefficient matrix and the matrix multiplying the control are the same. We assume that the control
has the form of feedback linear in the state variables and is periodic with the same period as the system itself. We pose
the problem of control of the frequency spectrum of strongly irregular periodic oscillations with an objective set, that is,
the problem of finding a feedback coefficient such that the closed system has a strongly irregular periodic solution with
the desired frequencies. We obtain necessary and sufficient conditions for the solvability of this problem. 相似文献
11.
This paper deal with optimal control problems for a non-stationary Stokes system. We study a simultaneous distributed-boundary optimal control problem with distributed observation. We prove the existence and uniqueness of a simultaneous optimal control and we give the first order optimality condition for this problem. We also consider a distributed optimal control problem and a boundary optimal control problem and we obtain estimations between the simultaneous optimal control and the optimal controls of these last ones. Finally, some regularity results are presented. 相似文献
12.
A. I. Kalinin 《Differential Equations》2012,48(3):419-429
For a transient process in a quasilinear system, we consider an optimization problem of finding a (multi-dimensional) control
with minimum intensity. We suggest an algorithm for constructing asymptotic approximations to the solution of this problem.
The main advantage of the algorithm is that an optimal control problem for a linear system is solved instead of the original
essentially nonlinear problem. 相似文献
13.
L. A. Manita 《Journal of Mathematical Sciences》2011,177(2):257-269
The problem on minimizing a quadratic functional on trajectories of the wave equation is considered. We assume that the density
of external forces is a control function. A control problem for a partial differential equation is reduced to a control problem
for a countable system of ordinary differential equations by use of the Fourier method. The controllability problem for this
countable system is considered. Conditions of the noncontrollability for some wave equations were obtained. 相似文献
14.
N. L. Grigorenko A. V. Anisimov L. N. Luk’yanova 《Proceedings of the Steklov Institute of Mathematics》2016,292(1):106-114
We consider a terminal control problem with state constraints and additional constraints on the qualitative behavior of the terminal trajectory for a second-order system in two-dimensional Euclidean space under geometric constraints on control parameters. A class of control functions solving this control problem is proposed. Numerical results for the control system with model parameters are presented. 相似文献
15.
In this paper, we outline an impulse stochastic control formulation for pricing variable annuities with a guaranteed minimum
withdrawal benefit (GMWB) assuming the policyholder is allowed to withdraw funds continuously. We develop a numerical scheme
for solving the Hamilton–Jacobi–Bellman (HJB) variational inequality corresponding to the impulse control problem. We prove
the convergence of our scheme to the viscosity solution of the continuous withdrawal problem, provided a strong comparison
result holds. The scheme can be easily generalized to price discrete withdrawal contracts. Numerical experiments are conducted,
which show a region where the optimal control appears to be non-unique. 相似文献
16.
《European Journal of Operational Research》2006,168(2):311-321
We examine an optimal impulse control problem of a stochastic system whose state follows a geometric Brownian motion. We suppose that, when an agent intervenes in the system, it requires costs consisting of a quadratic form of the system state. Besides the intervention costs, running costs are continuously incurred to the system, and they are also of a quadratic form. Our objective is to find an optimal impulse control of minimizing the expected total discounted sum of the intervention costs and running costs incurred over the infinite time horizon. In order to solve this problem, we formulate it as a stochastic impulse control problem, which is approached via quasi-variational inequalities (QVI). Under a suitable set of sufficient conditions on the given problem parameters, we prove the existence of an optimal impulse control such that, whenever the system state reaches a certain level, the agent intervenes in the system. Consequently it instantaneously reduces to another level. 相似文献
17.
A. K. Demenchuk 《Differential Equations》2010,46(10):1389-1394
We consider a linear periodic control system with zero mean of the coefficient matrix and with linear state feedback control
periodic with the same period. We obtain necessary and sufficient conditions for the solvability of the frequency spectrum
control problem with a given goal set for strongly irregular periodic vibrations. In this problem, one should find a feedback
coefficient such that the closed system has a strongly irregular periodic solution with the desired frequencies. 相似文献
18.
We consider an elliptic optimal control problem with control constraints and pointwise bounds on the gradient of the state.
We present a tailored finite element approximation to this optimal control problem, where the cost functional is approximated
by a sequence of functionals which are obtained by discretizing the state equation with the help of the lowest order Raviart–Thomas
mixed finite element. Pointwise bounds on the gradient variable are enforced in the elements of the triangulation. Controls
are not discretized. Error bounds for control and state are obtained in two and three space dimensions. A numerical example
confirms our analytical findings. 相似文献
19.
Nikolaos S. Papageorgiou Francesca Papalini Francesca Renzacci 《Rendiconti del Circolo Matematico di Palermo》1999,48(2):341-364
In this paper we consider nonlinear-dependent systems with multivalued perturbations in the framework of an evolution triple
of spaces. First we prove a surjectivity result for generalized pseudomonotone operators and then we establish two existence
theorems: the first for a periodic problem and the second for a Cauchy problem. As applications we work out in detail a periodic
nonlinear parabolic partial differential equation and an optimal control problem for a system driven by a nonlinear parabolic
equation. 相似文献
20.
The problem of minimization of an integral functional with an integrand that is nonconvex with respect to the control is considered. We minimize our functional over the solution set of a nonlinear evolution control system with a time-dependent subdifferential operator in a Hilbert space. The control constraint is given by a nonconvex closed bounded set. The integrand, the control constraint, the initial conditions and the operators in the equation describing the control system all depend on a parameter. We consider, along with the original problem, the problem of minimizing an integral functional with an integrand convexified with respect to the control over the solution set of the same system, but now subject to the convexified control constraint. By a solution of the control system we mean a “trajectory–control” pair. We prove that for each value of the parameter the convexified problem has a solution, which is the limit of a minimizing sequence of the original problem, and the minimum value of the functional of the convexified problem is a continuous function of the parameter. 相似文献