共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
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
3.
A. K. Demenchuk 《Differential Equations》2014,50(4):434-440
We consider a linear periodic control system with a two-sided dependence of blocks of complete column rank in the nonstationary component of the coefficient matrix in the critical case. In this case, the nontrivial intersection of vector subspaces formed by linear spans of the columns in the blocks can be arbitrary. We assume that the control is given in the form of feedback linear in the state variables and is periodic with the period of the system. We derive necessary and sufficient conditions for the solvability of the control problem for the asynchronous spectrum, that is, the problem of finding a feedback coefficient such that the closed system has a strongly irregular periodic solution with the desired frequencies. 相似文献
4.
A. K. Demenchuk 《Differential Equations》2013,49(1):1-6
We consider a linear periodic control system with linearly independent column bases of the blocks of the coefficient matrix, which has zero mean value and admits a block triangular representation. For the case of a linear state feedback control periodic with the same period as the system itself, we obtain necessary and sufficient conditions for the solvability of the asynchronous pole assignment problem, i.e., the problem of finding a feedback coefficient such that the closed-loop system has a strongly irregular periodic solution with the desired frequencies. 相似文献
5.
Differential Equations - We consider a linear control system with an almost periodic coefficient matrix whose mean is a diagonal matrix and with a linear state feedback control. The control matrix... 相似文献
6.
The present paper deals with the exposition of methods for solving the Brockett problem on the stabilization of linear control
systems by a nonstationary feedback. The paper consists of two parts. We consider continuous linear control systems in the
first part and discrete systems in the second part. In the first part, we consider two approaches to the solution of the Brockett
problem. The first approach permits one to obtain low-frequency stabilization, and the second part deals with high-frequency
stabilization. Both approaches permit one to derive necessary and sufficient stabilization conditions for two-dimensional
(and three-dimensional, for the first approach) linear systems with scalar inputs and outputs. In the second part, we consider
an analog of the Brockett problem for discrete linear control systems. Sufficient conditions for low-frequency stabilization
of linear discrete systems are obtained with the use of a piecewise constant periodic feedback with sufficiently large period.
We obtain necessary and sufficient conditions for the stabilization of two-dimensional discrete systems. In the second part,
we also consider the control problem for the spectrum (the pole assignment problem) of the monodromy matrix for discrete systems
with a periodic feedback. 相似文献
7.
Sergei Gusev Stefan Johansson Bo Kågström Anton Shiriaev Andras Varga 《BIT Numerical Mathematics》2010,50(2):301-329
Efficient and accurate structure exploiting numerical methods for solving the periodic Riccati differential equation (PRDE)
are addressed. Such methods are essential, for example, to design periodic feedback controllers for periodic control systems.
Three recently proposed methods for solving the PRDE are presented and evaluated on challenging periodic linear artificial
systems with known solutions and applied to the stabilization of periodic motions of mechanical systems. The first two methods
are of the type multiple shooting and rely on computing the stable invariant subspace of an associated Hamiltonian system.
The stable subspace is determined using either algorithms for computing an ordered periodic real Schur form of a cyclic matrix
sequence, or a recently proposed method which implicitly constructs a stable deflating subspace from an associated lifted
pencil. The third method reformulates the PRDE as a convex optimization problem where the stabilizing solution is approximated
by its truncated Fourier series. As known, this reformulation leads to a semidefinite programming problem with linear matrix
inequality constraints admitting an effective numerical realization. The numerical evaluation of the PRDE methods, with focus
on the number of states (n) and the length of the period (T) of the periodic systems considered, includes both quantitative and qualitative results. 相似文献
8.
We propose a new quadratic control problem for linear periodic systems which can be finite or infinite dimensional. We consider both deterministic and stochastic cases. It is a generalization of average cost criterion, which is usually considered for time-invariant systems. We give sufficient conditions for the existence of periodic solutions.Under stabilizability and detectability conditions we show that the optimal control is given by a periodic feedback which involves the periodic solution of a Riccati equation. The optimal closed-loop system has a unique periodic solution which is globally exponentially asymptotically stable. In the stochastic case we also consider the quadratic problem under partial observation. Under two sets of stabilizability and detectability conditions we obtain the separation principle. The filter equation is not periodic, but we show that it can be effectively replaced by a periodic filter. The theory is illustrated by simple examples.This work was done while this author was a visiting professor at the Scuola Normale Superiore, Pisa. 相似文献
9.
《Communications in Nonlinear Science & Numerical Simulation》2010,15(12):4100-4113
In this paper, we consider the problem of synchronizing a master–slave chaotic system in the sampled-data setting. We consider both the intermittent coupling and continuous coupling cases. We use an Euler approximation technique to discretize a continuous-time chaotic oscillator containing a continuous nonlinear function. Next, we formulate the problem of global asymptotic synchronization of the sampled-data master–slave chaotic system as equivalent to the states of a corresponding error system asymptotically converging to zero for arbitrary initial conditions. We begin by developing a pulse-based intermittent control strategy for chaos synchronization. Using the discrete-time Lyapunov stability theory and the linear matrix inequality (LMI) framework, we construct a state feedback periodic pulse control law which yields global asymptotic synchronization of the sampled-data master–slave chaotic system for arbitrary initial conditions. We obtain a continuously coupled sampled-data feedback control law as a special case of the pulse-based feedback control. Finally, we provide experimental validation of our results by implementing, on a set of microcontrollers endowed with RF communication capability, a sampled-data master–slave chaotic system based on Chua’s circuit. 相似文献
10.
V. B. Larin 《Journal of Applied Mathematics and Mechanics》1980,44(6):727-732
The problem of designing a regulator, optimal by a quadratic performance criterion, on an infinite time interval is examined for a linear periodic system. It is assumed that the control plant's motion is described by a system of linear periodic finite-difference equations. Controllable plants whose motion is described by differential and by finite-difference equations on different parts of the period are analyzed as well. The optimal regulator design problem is reduced to the determination of a periodic solution of an appropriate Riccati equation. An algorithm for constructing such a solution is derived. It is noted that this result can be used in periodic optimization problems /1/ and in the design of a stabilization system for a pacing apparatus. 相似文献
11.
研究状态矩阵和控制输入矩阵均具不确定性广义周期时变系统的鲁棒H_∞控制问题.提出参数不确定性广义周期时变系统广义可镇定和广义二次可镇定且具有H_∞性能指标的概念,利用线性矩阵不等式(LMI)方法,得到了参数不确定性广义周期时变系统广义二次可镇定且具有H_∞性能指标γ的充要条件,给出了相应的鲁棒H_∞状态反馈控制律的设计方法.最后,通过数值算例说明了设计方法的有效性. 相似文献
12.
We consider the problem on periodic solutions for linear systems of functionaldifferential equations of neutral type with
periodic coefficients and periodic deviations of the argument. By reduction to associated functional equations, we derive
necessary and sufficient conditions under which the problem on periodic solutions for such a system is Fredholm or semi-Fredholm. 相似文献
13.
研究了状态矩阵具有不确定性的广义周期时变系统的鲁棒非脆弱控制问题.利用线性矩阵不等式(LMI)方法,分别对控制器增益具有加法式摄动和乘法式摄动两种情形加以讨论,而非脆弱控制器的设计可以通过求解一组线性矩阵不等式得到.最后,数值例子说明了所给方法的有效性. 相似文献
14.
V. P. Yakovets 《Ukrainian Mathematical Journal》1997,49(9):1442-1463
For a linear system of ordinary differential equations with degenerate matrix of derivatives, we find conditions of reducibility
to the central canonical form. We also establish the structure of the general solution and conditions of solvability of the
Cauchy problem, and study the problem of periodic solutions.
Nezhin Pedagogic Institute, Nezhin. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 9, pp. 1278–1296, September,
1997. 相似文献
15.
16.
T. Morozan 《随机分析与应用》2013,31(1):87-110
We discuss the problem of the existence of periodic and stationary solutions of affine stochastic differential equations. We prove that under a controllability condition the system has a periodic solution if and only if the linear part is eyponentially stable in mean square. It is also shown that the controllability assumption is necessary for the existence of a “unique” weakly periodic solution with nondegenerate covariance. 相似文献
17.
In this paper we concern with the nonlinear third order quasi‐linear system of ordinary differential equations as: X′′′ + Λ X′ = ϵ F(X, X′, X″) where X ∈ ℝn and Λ is a diagonal matrix. We obtain some simple sufficient conditions for the existence of periodic solution using theorem of Brouer's degree. As we showed earlier [1], the scalar form the (1) can be treated by the Implicit Function Theorem instead of Brouer degree. Also because of the possibility of rewriting a 2n + 1 order equation into a third order system by a simple transformation [2], we can obtain useful results for such equations too. The main problem for this kind of equations is the validity of the results for the parameter free problem, i.e. when ϵ = 1. We consider it by study of dynamic of curves formed by the initial conditions that force the system be periodic when ϵ starts to increase. 相似文献
18.
Controllability and stabilizability of linear time‐varying distributed hereditary control systems
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Hernán R. Henríquez Andréa Prokopczyk 《Mathematical Methods in the Applied Sciences》2015,38(11):2250-2271
This paper is concerned with the controllability and stabilizability problem for control systems described by a time‐varying linear abstract differential equation with distributed delay in the state variables. An approximate controllability property is established, and for periodic systems, the stabilization problem is studied. Assuming that the semigroup of operators associated with the uncontrolled and non delayed equation is compact, and using the characterization of the asymptotic stability in terms of the spectrum of the monodromy operator of the uncontrolled system, it is shown that the approximate controllability property is a sufficient condition for the existence of a periodic feedback control law that stabilizes the system. The result is extended to include some systems which are asymptotically periodic. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
19.
I. I. Korol' 《Ukrainian Mathematical Journal》2005,57(4):583-599
We study the problem of the existence of periodic solutions of two-dimensional linear inhomogeneous periodic systems of differential
equations for which the corresponding homogeneous system is Hamiltonian. We propose a new numerical-analytic algorithm for
the investigation of the problem of the existence of periodic solutions of two-dimensional nonlinear differential systems
with Hamiltonian linear part and their construction. The results obtained are generalized to systems of higher orders.
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 4, pp. 483–495, April, 2005. 相似文献
20.
In this article, a new canonical function has been established to deal with Riemann boundary‐value problem of periodic analytic functions discussed in 16 . In comparison with the corresponding result in 16 , the expression of solution obtained here is much simpler. Then, we demonstrate the equivalence of solutions for the homogeneous Riemann problem. What's more, we obtain the precise rank of matrix of coefficients for the system of linear algebraic equations (4.35) in 16 . Those results can simplify the discussion of Riemann problem of single‐periodic polyanalytic functions in 16 . 相似文献