切换自治系统的动态输出反馈镇定

本文研究离散时间切换线性自治系统的输出反馈镇定问题. 在切换系统可观测的假设下, 设计具有多线性 时变增益的动态观测器, 实现有限时间状态估计. 在此基础上, 设计多路径动态输出反馈切换策略, 实现闭环系统指 数收敛.     

Stabilization of linear, autonomous differential-delay systems

Sufficient conditions for a linear, autonomous differential delay system to be stabilizable are established. The proof is constructive in that a readily computable stabilizing feedback control law is generated.     

A pole-assignment algorithm for linear state feedback

A new algorithm for the pole-assignment problem of a controllable time-invariant linear multivariable system with linear state feedback is presented. The resulting feedback matrix is a least-squares solution and is robust in a loose sense. The method is based on the controllability canonical (staircase) form and amounts to a new proof for the existence of a solution of the pole-assignment problem. Illustrative examples are given.     

Stability of two-dimensional feedback systems

Stability conditions for discrete-time linear dynamical systems in two independent variables are considered. A new proof of a known condition is given, enabling a more transparent interpretation. It is shown that closed-loop stability of a feedback system can be determined from open-loop information by using an infinite family of Nyquist plots. On the basis of these results, the extension of classical design methods, using root loci and frequency response, is advocated.     

A sufficient condition for output feedback stabilization ofuncertain dynamical systems

A different proof than the one given by E. Zeheb (ibid., vol.AC-31, p.1055-7, Nov. 1986) is given for the existence of an output feedback controller which stabilizes an uncertain single-input/single-output dynamical system with a linear nominal part and matched uncertainties. However, there is no need to assume that the nominal system is stable. A simple expression is obtained for the feedback gain which is necessary for the closed-loop nominal system to become strictly positive real     

Existence of SDRE stabilizing feedback

The state-dependent Riccati equation (SDRE) approach to nonlinear system stabilization relies on representing a nonlinear system's dynamics in a manner to resemble linear dynamics, but with state-dependent coefficient matrices that can then be inserted into state-dependent Riccati equations to generate a feedback law. Although stability of the resulting closed-loop system need not be guaranteed a priori, simulation studies have shown that the method can often lead to suitable control laws. In this note, we consider the nonuniqueness of state-dependent representations. In particular, we show that if there exists any stabilizing feedback leading to a Lyapunov function with star-convex level sets, then there always exists a representation of the dynamics such that the SDRE approach is stabilizing. The main tool in the proof is a novel application of the S-procedure for quadratic forms.     

Symplectic feedback using Hamiltonian Lie algebra and its applications to an inverted pendulum

From the symplectic representation of an autonomous nonlinear dynamical system with holonomic constraints, i.e., those that can be represented through a symplectic form derived from a Hamiltonian, we present a new proof on the realization of the symplectic feedback action, which has several theoretical advantages in demonstrating the uniqueness and existence of this type of solution. Also, we propose a technique based on the interpretation, construction and characterization of the pull-back differential on the symplectic manifold as a member of a one-parameter Lie group. This allows one to synthesize the control law that governs a certain system to achieve a desired behavior; and the method developed from this is applied to a classical system such as the inverted pendulum.     

Algebraic separation in realizing a linear state feedback control law by means of an adaptive observer

Based on a novel adaptive observer, which does not require signal boundedness in its stability proof, an algebraic separation property of linear state feedback control and adaptive state observation is established. This means, whenever a linear, stabilizing state feedback control law is realized with the state replaced by the state estimate of the given stable adaptive observer, then the resulting nonlinear control system is also globally asymptotically Lyapunov stable with respect to the initial state and parameter observation error of the adaptive observer. In particular, no assumptions on the system dynamics nor on the speed of the adaptation are made.     

Control of neutral delay linear systems using feedback with dynamic structure

To solve the problem of modal controllability of linear autonomous systems of neutral type, a new class of linear difference-differential controllers with feedback of dynamic structure is proposed. The construction principle of these controllers is based on the use of aftereffect in the control action. The domain of application of such controllers includes systems that do not possess the modal controllability property in the class of conventional classes of feedback controllers of constant structure.     

On interconnections, control, and feedback

The purpose of this paper is to study interconnections and control of dynamical systems in a behavioral context. We start with an extensive physical example which serves to illustrate that the familiar input-output feedback loop structure is not as universal as we have been taught to believe. This leads to a formulation of control problems in terms of interconnections. Subsequently, we study interconnections of linear time-invariant systems from this vantage point. Let us mention two of the results obtained. The first one states that any polynomial can be achieved as the characteristic polynomial of the interconnection with a given plant, provided the plant is not autonomous. The second result states that any subsystem of a controllable system can be implemented by means of a singular feedback control law. These results yield pole placement and stabilization of controllable plants as a special case. These ideas are finally applied to the stabilization of a nonlinear system around an operating point     

微机械陀螺仪检测反馈控制系统研究

以单自由度硅微振动轮式陀螺仪的检测动极板为控制对象,系统的结构特性决定了只能选择反馈控制方式对其进行控制。为实现这种控制对控制系统进行建模以及设计合适的校正环节。反馈方式控制的应用可以有效地改善系统的动态特性和稳态特性。加入校正环节后的系统幅值和相角裕度分别达到了17.5dB和57.3°,这为实际的应用提供了指导。     

Global stabilization of linear discrete-time systems with bounded feedback

This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time case by the authors, and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less than or equal to one. The proof provides in principle an algorithm for the construction of such feedback laws, which can be implemented either as cascades or as parallel connections (“single hidden layer neural networks”) of simple saturation functions.     

利用多级线性预测改善有限反馈系统反馈量

以先进的长期演进技术(LTE-Advanced)为背景,针对多输入多输出（MIMO）系统中基于码本的有限反馈技术进行了研究,提出了一种基于多级线性预测的有限反馈新方法。利用信道的时间相关性,对信道值进行多级线性预测,以预测误差为基础,通过最小化均方误差来设计量化码本,将码本中对应的码字序号用于系统反馈。仿真结果表明：采用多级线性预测能有效地降低系统预测误差,等效地,减小了系统的反馈开销,最大降低幅度能达到15%。     

A theorem on global stabilization of nonlinear systems by linear feedback

In this paper we investigate the global stabilizability problem for a wide class of single-input nonlinear systems whose the linearization at the equilirrium is controllable. We show that under general assumptions there exists a linear feedback law which globally exponentially stabilizes the system at its equilibrium. The proof of our main theorem is based on some ideas from a previous paper. We use the theorem to recover a recent result of Gauthier et al. concerning the observer design problem.     

Persistent disturbance rejection via static-state feedback

In contrast with ℋ_∞ and ℋ₂ control theories, the problem of persistent disturbance rejection (l¹ optimal control) leads to dynamic controllers, even when the states of the plant are available for feedback. Using viability theory, Shamma showed (1993), in a nonconstructive way, that in the state-feedback case the same performance achieved by any dynamic linear time-invariant controller can be achieved using memoryless nonlinear state feedback. In this paper we give an alternative, constructive proof of these results for discrete- and continuous-time systems. The main result of the paper shows that in both cases, the l¹ norm achieved by any stabilizing state-feedback linear dynamic controller can be also achieved using a memoryless variable structure controller     

On receding horizon feedback control

Receding horizon feedback control (RHFC) was originally introduced as an easy method for designing stable state-feedback controllers for linear systems. Here those results are generalized to the control of nonlinear autonomous systems, and we develop a performance index which is minimized by the RHFC (inverse optimal control problem). Previous results for linear systems have shown that desirable nonlinear controllers can be developed by making the RHFC horizon distance a function of the state. That functional dependence was implicit and difficult to implement on-line. Here we develop similar controllers for which the horizon distance is an easily computed explicit function of the state.     

Improving stability margins via dynamic-state feedback for systemswith constant uncertainty

It is well known that if a linear system with time-varying uncertainty in the system matrix and/or the input connection matrix is quadratically stabilizable by linear dynamic state feedback, then it is also quadratically stabilizable by linear static state feedback. In this paper, we provide an example of a system with unknown constant real uncertainty which is stabilizable by a linear, dynamic-state feedback controller but not by a static-state feedback controller     

Nonquadratic cost and nonlinear feedback control

Nonlinear controllers offer significant advantages over linear controllers in a variety of circumstances. Hence there has been significant interest in extending linear-quadratic synthesis to nonlinear-nonquadratic problems. The purpose of this paper is to review the current status of such efforts and to present, in a simplified and tutorial manner, some of the basic ideas underlying these results. Our approach focuses on the role of the Lyapunov function in guaranteeing stability for autonomous systems on an infinite horizon. Sufficient conditions for optimality are given in a form that corresponds to a steady-state version of the Hamilton-Jacobi-Bellman equation. These results are used to provide a simplified derivation of the nonlinear feedback controller obtained by Bass and Webber (1966)³⁸ and to obtain a deterministic variation of the stochastic nonlinear feedback controller developed by Speyer (1976).⁴⁵.     

Stabilization of persistently excited linear systems by delayed feedback laws

This paper considers the stabilization to the origin of a persistently excited linear system by means of a linear state feedback, where we suppose that the feedback law is not applied instantaneously, but after a certain positive delay (not necessarily constant). The main result is that, under certain spectral hypotheses on the linear system, stabilization by means of a linear delayed feedback is indeed possible, generalizing a previous result already known for non-delayed feedback laws.