共查询到20条相似文献,搜索用时 36 毫秒
1.
V. I. Maksimov 《Differential Equations》2018,54(11):1449-1455
For a distributed second-order differential equation, we consider the problem of constructing a control law ensuring that the solution of this equation tracks the solution of a standard equation subjected to an unknown disturbance. A control design algorithm based on constructions of feedback control theory is proposed. The algorithm is stable under information noise and computational errors. 相似文献
2.
V. I. Maksimov 《Russian Mathematics (Iz VUZ)》2012,56(1):35-42
We consider a control problem for a parabolic equation. It consists in constructing an algorithm for finding a feedback control
such that a solution of a given equation should track a solution of another equation generated by an unknown right-hand side.
We propose two noise-resistant solution algorithms for the indicated problem. They are based on the method of extremal shift
well-known in the guaranteed control theory. The first algorithm is applicable in the case of “continuous” measurements of
phase states, whereas the second one implies discrete measurements. 相似文献
3.
V. I. Maksimov 《Proceedings of the Steklov Institute of Mathematics》2016,293(1):137-147
A problem of tracking a solution of a second-order differential equation in a Hilbert space by a solution of another equation is considered. It is assumed that the first (reference) equation is subject to the action of an unknown control, which is unbounded in time. In the case when the current states of both equations are observed with small errors, a solution algorithm stable with respect to informational noises and computational inaccuracies is designed. The algorithm is based on N.N. Krasovskii’s extremal shift method known in the theory of guaranteed control. 相似文献
4.
P. G. Surkov 《Russian Mathematics (Iz VUZ)》2016,60(10):44-54
We consider a control problem for a parabolic equation with memory. It consists in constructing an algorithm for finding a feedback control which enables one to track a solution of the given equation with an unknown right-hand side. For this problem we propose two noise-resistant solution algorithms based on the method of extremal shift. The first algorithm is applicable in the case of continuous measurements of phase states, whereas the second one presumes discrete measurements. 相似文献
5.
6.
V. I. Maksimov 《Proceedings of the Steklov Institute of Mathematics》2015,291(1):143-156
We consider the problem of recovering the input of a linear differential equation with delay and propose a solution algorithm that is stable to perturbations. The algorithm is based on the extremal shift principle known in the theory of guaranteed control. 相似文献
7.
In this paper, the problem of the numerical computation of the stabilizing solution of the game theoretic algebraic Riccati
equation is investigated. The Riccati equation under consideration occurs in connection with the solution of the H
∞ control problem for a class of stochastic systems affected by state dependent and control dependent white noise. The stabilizing
solution of the considered game theoretic Riccati equation is obtained as a limit of a sequence of approximations constructed
based on stabilizing solutions of a sequence of algebraic Riccati equations of stochastic control with definite sign of the
quadratic part. The efficiency of the proposed algorithm is demonstrated by several numerical experiments. 相似文献
8.
We consider the general continuous time finite-dimensional deterministic system under a finite horizon cost functional. Our
aim is to calculate approximate solutions to the optimal feedback control. First we apply the dynamic programming principle
to obtain the evolutive Hamilton–Jacobi–Bellman (HJB) equation satisfied by the value function of the optimal control problem.
We then propose two schemes to solve the equation numerically. One is in terms of the time difference approximation and the
other the time-space approximation. For each scheme, we prove that (a) the algorithm is convergent, that is, the solution
of the discrete scheme converges to the viscosity solution of the HJB equation, and (b) the optimal control of the discrete
system determined by the corresponding dynamic programming is a minimizing sequence of the optimal feedback control of the
continuous counterpart. An example is presented for the time-space algorithm; the results illustrate that the scheme is effective. 相似文献
9.
10.
In this paper, a nonlinear distributed second order equation is considered. An algorithm for tracking a prescribed solution based on constructions of feedback control theory is designed. The algorithm is stable with respect to information noise and computation errors. It is designed for solutions in a sufficiently large time interval. 相似文献
11.
We are concerned with mathematical analysis related to the bi-pointwise control for a mixed type of wave equation. In particular, we are interested in the systematic build-up of the bi-pointwise control actuators; one at the boundary and the other at the interior point simultaneously. The main purpose is to examine Hilbert Uniqueness Method for the setting of bi-pointwise control actuators and to establish relevant algorithm based on our analysis. After discussing the weak solution for the state equation, we investigate bi-pointwise control mechanism and relevant mathematical analysis based on HUM. We then proceed to set up an algorithm based on the conjugate gradient method to establish bi-pointwise control actuators to halt the system. 相似文献
12.
A game control problem for a parabolic differential equation with memory is considered. An algorithm for its solution based on Krasovskii’s method of extreme shift and the method of stable paths is proposed. 相似文献
13.
The main goal of this paper is to apply the so-called policy iteration algorithm (PIA) for the long run average continuous
control problem of piecewise deterministic Markov processes (PDMP’s) taking values in a general Borel space and with compact
action space depending on the state variable. In order to do that we first derive some important properties for a pseudo-Poisson
equation associated to the problem. In the sequence it is shown that the convergence of the PIA to a solution satisfying the
optimality equation holds under some classical hypotheses and that this optimal solution yields to an optimal control strategy
for the average control problem for the continuous-time PDMP in a feedback form. 相似文献
14.
The problem of identification in fuzzy systems described by the use of fuzzy equation is considered. The identification method and its performance index is also presented. The formal procedure of the identification algorithm is illustrated by means of a numerical example. The possibility of using the proposed algorithm for the solution of a control problem is given as well. 相似文献
15.
V. I. Maksimov 《Proceedings of the Steklov Institute of Mathematics》2008,262(1):170-178
The problem of dynamic reconstruction of boundary controls in a nonlinear parabolic equation is considered. In the case of a control concentrated in the Neumann boundary conditions, a solution algorithm is described, which is stable with respect to the information noise and calculation errors. The algorithm is based on the construction of feedback-controlled auxiliary models. 相似文献
16.
Songtao Guo Hongying Zheng Qun Liu 《Nonlinear Analysis: Real World Applications》2010,11(4):3077-3090
In this paper, a congestion control algorithm with heterogeneous delays is considered. Local stability of the equilibrium solution of this algorithm is investigated based on analyzing the corresponding transcendental characteristic equation. Especially, using one of the system parameters of congestion control algorithm as the bifurcation parameter, when the system parameter exceeds a critical value, the congestion control algorithm undergoes a supercritical Hopf bifurcation, and the explicit formulae determining the stability and the direction of periodic solutions bifurcating from the equilibrium are obtained by applying Hassard et al.’s approaches. Finally, some numerical simulations are performed to verify the theoretical results. 相似文献
17.
A discrete time optimal forestry model is built and a shooting method solution algorithm identified. The applicability of the model and algorithm to public policies that affect forestry resources is demonstrated in an application of the model to examine the development of wood processing capacity in Southeast Asia. The necessary conditions of the optimal control model are manipulated to identify a difference equation problem with initial and terminal conditions. The solution to this boundary value problem is identified using a search routine that repetitively, numerically evaluates (shoots) the difference equations. The solution is the trajectory that satisfies the initial and terminal conditions. 相似文献
18.
A. A. Dryazhenkov M. M. Potapov 《Computational Mathematics and Mathematical Physics》2016,56(2):206-220
An algorithm for solving a quadratic minimization problem on an ellipsoidal set in a Hilbert space is proposed. The algorithm is stable to nonuniform perturbations of the operators. A key condition for its application is that we know an estimate for the norm of the exact solution. Applications to boundary control problems for the one-dimensional wave equation are considered. Numerical results are presented. 相似文献
19.
Zu-guang Ying Yin-miao LuoWei-qiu Zhu Yi-qing NiJan-ming Ko 《Communications in Nonlinear Science & Numerical Simulation》2012,17(4):1956-1964
A semi-analytical direct optimal control solution for strongly excited and dissipative Hamiltonian systems is proposed based on the extended Hamiltonian principle, the Hamilton-Jacobi-Bellman (HJB) equation and its variational integral equation, and the finite time element approximation. The differential extended Hamiltonian equations for structural vibration systems are replaced by the variational integral equation, which can preserve intrinsic system structure. The optimal control law dependent on the value function is determined by the HJB equation so as to satisfy the overall optimality principle. The partial differential equation for the value function is converted into the integral equation with variational weighting. Then the successive solution of optimal control with system state is designed. The two variational integral equations are applied to sequential time elements and transformed into the algebraic equations by using the finite time element approximation. The direct optimal control on each time element is obtained respectively by solving the algebraic equations, which is unconstrained by the system state observed. The proposed control algorithm is applicable to linear and nonlinear systems with the quadratic performance index, and takes into account the effects of external excitations measured on control. Numerical examples are given to illustrate the optimal control effectiveness. 相似文献
20.
We propose a generalization of the structured doubling algorithm to compute invariant subspaces of structured matrix pencils that arise in the context of solving linear quadratic optimal control problems. The new algorithm is designed to attain better accuracy when the classical Riccati equation approach for the solution of the optimal control problem is not well suited because the stable and unstable invariant subspaces are not well separated (because of eigenvalues near or on the imaginary axis) or in the case when the Riccati solution does not exist at all. We analyze the convergence of the method and compare the new method with the classical structured doubling algorithm as well as some structured QR methods. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献