共查询到20条相似文献,搜索用时 46 毫秒
1.
In this paper, we cast the design ofDelta-modulated control of a high-order system into the study of control Lyapunov functions. We classify the complex dynamics of the closed-loop system in three cases. In the first case, we show how Delta-modulated feedback introduces a finite set of globally attracting periodic points. We find the numbers and periods of all possible such periodic orbits. In addition, we characterize the attracting region for each of such periodic points. In the second case, we show that there is a maximal "stabilizable" region, and inside this region, there is a local attractor. In the last case, we show that all the states stabilizable by the Delta-modulated feedback constitute a Cantor set. This Cantor set is a repeller, and the closed-loop system is chaotic on the Cantor set 相似文献
2.
The saturation of linear controllers produces the undesirable existence of equilibrium points or periodic orbits of the closed-loop system. This typical nonlinear behavior has been observed in real systems or by means of simulation of certain examples. However, there are only a few studies in which the properties of saturated systems have been examined rigorously and, a proof of the existence of periodic orbits created by the saturation of the controller is lacking. In this paper we choose an example of an open-loop stable linear control system with an stabilizing saturated linear feedback to prove rigorously the existence of a periodic orbit. 相似文献
3.
Stabilization of uncertain nonholonomic systems via time-varying sliding mode control 总被引:4,自引:0,他引:4
This note addresses the robust stabilization problem for a general class of nonholonomic systems in the presence of drift uncertainties. The control approach developed is based on the combined applications of the sliding mode control technique and nonlinear time-varying systems theory. First, some properties of nonlinear time-varying systems are introduced for the purpose of designing sliding mode controller. An explicit time-varying feedback form is provided to guarantee the existence and uniqueness of periodic time-varying solution for the corresponding linear periodic partial differential equation. Second, an explicit discontinuous feedback control law is presented to guarantee the existence of sliding mode. The first integrals obtained by the previous periodic partial differential equation are then directly used to determine the switching function. The uniform asymptotic stability of the closed loop system is proved via the invariance principle of nonlinear time-varying systems. Finally, an example is given to illustrate the proposed approach. 相似文献
4.
YANG Qiu MA Jun College of Mathematics Physics Department of Mathematics Physics China University of Geosciences Wuhan university of Science engineering Wuhan Hubei China Wuhan Hubei China 《International Journal of Industrial Ergonomics》2006,(1)
Controlled object for a class of m × n flow show with infinite buffers, is a linear state space model in the sense of ordinary max-algebra R , ⊕, ? . S open[1~3]: ( ) ( ) ( )( ) ( ) X k A X k B u kY k C X k??? == ?? ⊕ ? , k = 1,2,L (1) where A ∈ R p × p , B ∈ R p × q ,C ∈ Rq ×p, p = mn, q = m + n. k denotes the processing batch of jobs J 1, J 2, …, J n; X = [ x1 1 , L , x1 n , x2 1 , L , xm 1 , L , xmn]T denotes the state vector; xi j is the time when job J j was processed… 相似文献
5.
Cyclomonotonicity and stabilizability properties of solutions ofthe difference periodic Riccati equation 总被引:1,自引:0,他引:1
The Kalman filter associated with a discrete-time linear T -periodic system is tested. The problem considered is that of selecting an initial covariance matrix such that the periodic filter based on the first T values of the Kalman filter gain is stabilizing. Sufficient conditions are given that hinge on the cyclomonotonicity of the solution of the periodic Riccati equation. Potential applications are found in filter design, quasi-linearization techniques for the periodic Riccati equation, and the design of receding-horizon control strategies for periodic and multirate systems. When specialized to time-invariant systems, the results give rise to new sufficient conditions for the cyclomonotonicity of the solutions of the time-invariant Riccati equation and the existence of periodic stabilizing feedback 相似文献
6.
Chaohong CaiAuthor Vitae Zhenyuan XuAuthor VitaeWenbo XuAuthor Vitae 《Automatica》2002,38(11):1927-1933
A simple control method is presented to convert chaos into periodic motion by using linear state feedback of an available system variable. The low-periodic orbits can be derived from the chaotic attractor with slight change of the dynamical structure in the original dynamics. Melnikov's perturbation method in generalized Hamiltonian systems is introduced to explain the control mechanism of directing chaotic motion towards low-periodic motion in the Lorenz equations. Moreover, the existence of periodic orbits is examined in the perturbed Lorenz system. Simulation results verify the effectiveness of Melnikov's analysis. 相似文献
7.
Relaxation oscillators can usually be represented as a feedback system with hysteresis. The relay relaxation oscillator consists of relay hysteresis and a linear system in feedback. The objective of this work is to study the existence of periodic orbits and the dynamics of coupled relay oscillators. In particular, we give a complete analysis for the case of unimodal periodic orbits, and illustrate the presence of degenerate and asymmetric orbits. We also discuss how complex orbits can arise from bifurcation of unimodal orbits. Finally, we focus on oscillators with an integrator as the linear component, and study the entrainment under external forcing, and phase locking when such oscillators are coupled in a ring 相似文献
8.
设计了状态变量的线性反馈控制器对Lorenz系统的平衡点和周期轨道进行控制.首先,利用Routh-Hurwitz准则对受控系统进行了稳定性分析,证明了达到控制目标反馈系数的选择原则.然后,通过数值计算证明了该方法能够有效地控制混沌系统达到稳定的平衡点同时也能使系统控制到1p周期轨道,并且得到了相应的稳定的1p周期轨道的控制参数和系统幅值的关系曲线.最后给出了控制到1p周期轨道的控制参数的选取范围. 相似文献
9.
The /spl Delta/-modulated control of a single input, discrete time, linear stable system is investigated. The modulation direction is given by c/sup T/x where c /spl isin/R/sup n//spl bsol/{0} is a given, otherwise arbitrary, vector. We obtain necessary and sufficient conditions for the existence of periodic points of a finite order. Some concrete results about the existence of a certain order of periodic points are also derived. We also study the relationship between certain polyhedra and the periodicity of the /spl Delta/-modulated orbit. 相似文献
10.
V. A. Zaitsev 《International journal of systems science》2017,48(16):3403-3410
We study the problem of uniform global asymptotic stabilisation of the origin for bilinear non-homogeneous control systems with periodic coefficients by means of state feedback. We assume that the free dynamic system is Lyapunov stable. We obtain new controllability-like rank conditions, which are sufficient for uniform global asymptotic stabilisation of the periodic bilinear systems. The proof is based on the use of the Krasovsky–La Salle invariance principle for periodic systems. A stabilising feedback control law is quadratic in the state variable and periodic in the time variable. Consequences derived for linear and homogeneous bilinear systems. Under some assumptions, the controllability-like rank condition for linear and homogeneous bilinear systems coincides correspondingly with the property of complete controllability and consistency. 相似文献
11.
Periodic stabilizability of switched linear control systems 总被引:1,自引:0,他引:1
Stabilizability via direct/observer-based state feedback control for discrete-time switched linear control systems (SLCSs) is investigated in this paper. For an SLCS, the control factors are not only the control input but also the switching signal, and they need to be designed in order to stabilize the system. As a result, stabilization design for SLCSs is more complicated than that for non-switched ones. Differently from the existing approaches, a periodic switching signal and piecewise constant linear state feedback control are adopted to achieve periodic stabilizability for such systems. It is highlighted that multiple feedback controllers need to be designed for one subsystem. For discrete-time SLCSs, it is proved that reachability implies periodic stabilizability via state feedback. A necessary and sufficient criterion for periodic stabilizability is also established. Two stabilization design algorithms are presented for real application. Moreover, it is proved that reachability and observability imply periodic stabilizability via observer-based feedback for discrete-time SLCSs. Periodic detectability, as the dual concept of periodic stabilizability, is discussed and the stabilization design algorithms via observer-based feedback are presented as well. 相似文献
12.
The authors present methods for pole assignment by feedback with constrained structure in linear periodic systems using generalized sampled-data hold functions (GSHF). Constrained structure is taken to mean that the input of each channel is restricted to depend only on the measurements of some specific output channels. The basic idea of GSHF control is to use sample and hold, but to consider the hold function as a design parameter. Four strategies are proposed for closing a control loop using GSHF. The key to the results obtained is that, when GSHF control with constrained structure is applied to a periodic system, a discrete-time time-invariant, decentralized system is obtained for which control design methods are available 相似文献
13.
14.
This note discusses the stabilization and spectrum assignment problems in linear periodically time-varying (LPTV) continuous-time systems with sampled state or output feedback. The hybrid nature of the overall feedback system in this case imposes some carefulness in handling classical concepts related to purely LPTV continuous-time systems, In particular, this note points out the fact that the stabilization of such systems by periodic feedback gains with sampled state or output does not imply the relocation of the original characteristic exponents of the LPTV systems. It is also shown that the concept of monodromy matrix as extended to LPTV hybrid systems has not all the features of a true monodromy matrix 相似文献
15.
J. -B. Pomet J. -M. Coron L. Praly 《Mathematics of Control, Signals, and Systems (MCSS)》1990,3(4):373-399
We consider a discrete-time system consisting of a linear plant and a periodically forced feedback controller whose parameters
are slowly adapted. Using degree theory, we give sufficient conditions for the existence of periodic solutions. Using linearization
methods, we give sufficient conditions for their (in)stability provided the adaptation is slow enough. We then study when
the degree theoretic conditions for the existence are satisfied byd-steps-ahead adaptive controllers in the presence of unmodeled dynamics and a persistently exciting periodic reference output. 相似文献
16.
17.
This paper considers the problem of stabilizing a linear time-invariant multivariable system by using several local feedback control laws. Each local feedback control law depends only on partial system outputs. A necessary and sufficient condition for the existence of local control laws with dynamic compensation to stabilize a given system is derived. This condition is stated in terms of a new notion, called "fixed modes," which is a natural generalization of the well-known concept of uncontrollable modes and unobservable modes that occur in centralized control system problems. A procedure that constructs a set of stabilizing feedback control laws is given. 相似文献
18.
This paper investigates the control and state observation problem for periodic linear controllable and observable multimodal systems. For a controllable periodic linear multimodal system, this paper proposes an alternative minimum-norm dynamic state feedback control scheme for state transition matrix assignment. Also presented is a new design of state observers for an observable periodic linear multimodal system. Finally, an analysis of closed-loop behaviour of controlled periodic linear multimodal systems using a state-estimate is given 相似文献
19.
Zhouchao Wei 《Computers & Mathematics with Applications》2012,63(3):728-738
In this paper, we investigate the effect of delayed feedbacks on the 3-D chaotic system only with two stable node-foci by Yang et al. The stability of equilibria and the existence of Hopf bifurcations are considered. The explicit formulas determining the direction, stability and period of the bifurcating periodic solutions are obtained by employing the normal form theory and the center manifold theorem. Numerical simulations and experimental results are given to verify the theoretical analysis. Hopf bifurcation analysis can explain and predict the periodic orbit in the chaotic system with direct time delay feedback. We also find that the control law can be applied to the chaotic system only with two stable node-foci for the purpose of control and anti-control of chaos. Finally, some numerical simulations are given to illustrate the effectiveness of the results found. 相似文献