广义时变脉冲系统的输入输出时域稳定

研究了广义时变脉冲系统的输入输出时域稳定问题.基于矩阵微分不等式(Differential matrix inequalities,DMI),给出了两个上述系统输入输出时域稳定的充分条件分别对应 L2干扰输入和 L∞干扰输入.这样的条件要求矩阵微分不等式解的存在性.接下来根据给出的充分条件设计了控制器,使得闭环系统输入输出时域稳定.本文的结果对于一般情况下的广义时变系统同样适用.最后,给出了两个算例来验证结果的有效性.     

Input–output finite-time stability of discrete-time systems under finite-time boundedness

This paper deals with the input–output finite-time stability of discrete time-varying linear systems in the presence of finite-time boundedness. The state boundedness and output stability of this system are concerned simultaneously to avoid the large unacceptable values during certain transients. For two different classes of norm-bounded input signals, the sufficient conditions for the system satisfying both the state finite-time boundedness (FTB) and input–output finite-time stability (IO-FTS) are developed. Based on a set of linear matrix inequalities (LMIs), the controller design method via state feedback for the discrete-time system satisfying both FTB and IO-FTS is presented for the two classes of external norm-bounded input. The conditions proposed can simultaneously guarantee the state and output of closed-loop system do not exceed the boundary during the specified finite-time interval. Two examples are employed to verify the effectiveness of the proposed method.     

Finite-time control of linear parameter-varying systems with norm-bounded exogenous disturbance

In this paper, a new approach is presented for finite-time control problems for linear systems subject to time-varying parametric uncertainties and exogenous disturbance. The disturbance is assumed to be time varying and bounded. Sufficient conditions are obtained for the existence of a linear parameter-dependent state feedback gain, which can ensure that the closed-loop system is finite-time bounded (FTB). The conditions can be reduced to feasibility problems involving LMIs. Numerical examples show the validity of the proposed methodology.     

Finite-time control of linear parameter-varying systems with norm-bounded exogenous disturbance

In this paper, a new approach is presented for finite-time control problems for linear systems subject to time-varying parametric uncertainties and exogenous disturbance. The disturbance is assumed to be time varying and bounded. Sufficient conditions are obtained for the existence of a linear parameter-dependent state feedback gain, which can ensure that the closed-loop system is finite-time bounded （FTB）. The conditions can be reduced to feasibility problems involving LMIs. Numerical examples show the validity of the proposed methodology.     

线性连续时间时滞系统的有限时间有界跟踪控制

研究一类线性连续时间时滞系统的有限时间有界跟踪控制问题.首先,采用预见控制理论中求导的方法构造带有时滞的误差系统,把误差信号的信息包含在误差系统的状态向量中,再将其作为误差系统的输出向量;其次,通过为误差系统设计一个有记忆的状态反馈控制器,把问题转化为研究带有时滞的误差系统的闭环系统输入-输出有限时间稳定问题;再次,借鉴输入-输出有限时间稳定的研究方法和线性矩阵不等式的方法, 通过构造Lyapunov-Krasovskii函数,给出由一组线性矩阵不等式表征的控制器增益矩阵的设计方法,由此得到原系统的一个有限时间有界跟踪控制器;最后,通过一个数值实例验证所设计的控制器的有效性和优越性.     

Input–output finite-time mean square stabilisation of stochastic systems with Markovian jump

The notion of input–output finite-time mean square (IO-FTMS) stability is introduced for Itô-type stochastic systems with Markovian jump parameters. Concerning a class of random input signals W, sufficient conditions are presented for the IO-FTMS stability and stabilisation of stochastic nonlinear Markov jump systems in terms of coupled Hamilton–Jacobi inequalities. When specialising to the linear case, these criteria are turned into coupled linear matrix inequalities. Moreover, the quadratic IO-FTMS stabilisation is addressed when polytopic uncertainty appears in the transition rate. Finally, a numerical example with simulations is exploited to illustrate the proposed techniques.     

Linearization by generalized input-output injection

The problem under interest is the linearization of nonlinear MIMO systems by generalized input-output injection in order to design observers with linear error dynamics. The method is based on the study of the structure of the input-output differential equations; thus, the problem is solved as a realization problem. In this note, one considers the linearization under two kinds of inout-output injection. In the first case, the transformation depends on the output and time derivatives of the input, whereas in the second case, derivatives of both the input and the output are considered. Necessary and sufficient conditions are obtained which generalize the ones on standard input-output injection linearization.     

Finite-time consensus protocols for networks of dynamic agents by terminal iterative learning

This paper aims to address finite-time consensus problems for multi-agent systems under the iterative learning control framework. Distributed iterative learning protocols are presented, which adopt the terminal laws to update the control input and are offline feedforward design approaches. It is shown that iterative learning protocols can guarantee all agents in a directed graph to reach the finite-time consensus. Furthermore, the multi-agent systems can be enabled to achieve a finite-time consensus at any desired terminal state/output if iterative learning protocols can be improved by introducing the desired terminal state/output to a portion of agents. Simulation results show that iterative learning protocols can effectively accomplish finite-time consensus objectives for both first-order and higher order multi-agent systems.     

Finite-time control of discrete-time linear systems

In this note, we consider the finite-time stabilization of discrete-time linear systems subject to disturbances generated by an exosystem. Finite-time stability can be used in all those applications where large values of the state should not be attained, for instance in the presence of saturations. The main result provided in the note is a sufficient condition for finite-time stabilization via state feedback. This result is then used to find some sufficient conditions for the existence of an output feedback controller guaranteeing finite-time stability. All the conditions are then reduced to feasibility problems involving linear matrix inequalities (LMIs). Some numerical examples are presented to illustrate the proposed methodology.     

Identifiability of linear stochastic systems operating under linear feedback

The identifiability of multiple input-multiple output stochastic systems operating in closed loop is considered for the case where the plant and the regulator are both linear and time-invariant. Two basic identification methods have been proposed for such systems: the joint input-output method, in which the input and output processes are modelled jointly as the output of a white noise driven system; and the direct method, in which a prediction error method is used on the input-output data as if the system were in open loop. Previously obtained identifiability results for the joint input-output method are extended to a number of new situations, including but extending beyond the identifiability results obtained with the direct method.     

Design of decoupled non-linear multivariable stochastic control systems

A technique is presented for decoupling a non-linear system with input disturbance, The class of matrices which decouple the nominal system is first obtained. Then, the free parameters in the feedback matrix are selected to minimize the effect of disturbances on the output by minimizing a performance index which involves the input-output error magnitude. An example is presented to illustrate the approach.     

Robust control for a nonlinear servomechanism problem

This paper deals with the design of output feedback control to achieve asymptotic tracking and disturbance rejection for a class of nonlinear systems when the exogenous signals are generated by a known linear exosystem. The system under consideration is single-input single-output, input-output linearizable, minimum phase, and modelled by an input-output model of the form of an nth-order differential equation. We assume that, at steady state, the nonlinearities of the system can only introduce a finite number of harmonics of the original exosystem modes. This assumption enables us to identify a linear servo-compensator which is augmented with the original system. Moreover, we augment a series of m integrators at the input side, where m is the highest derivative of the input, and then represent the augmented system by a state model. The augmented system is stabilized via a separation approach in which a robust state feedback controller is designed first to ensure boundedness of all state variables and tracking error convergence; then, a high gain observer and control saturation are used to recover the asymptotic properties achieved under state feedback.     

Input-output linearizing control of constrained nonlinear processes

An input-output linearization strategy for constrained nonlinear processes is proposed. The system may have constraints on both the manipulated input and the controlled output. The nonlinear control system is comprised of: (i) an input-output linearizing controller that compensates for processes nonlinearities; (ii) a constraint mapping algorithm that transforms the original input constraints into constraints on the manipulated input of the feedback linearized system; (iii) a linear model predictive controller that regulates the resulting constrained linear system; and (iv) a disturbance model that ensures offset-free setpoint tracking. As a result of these features, the approach combines the computational simplicity of input output linearization and the constraint handling capability of model predictive control. Simulation results for a continuous stirred tank reactor demonstrate the superior performance of the proposed strategy as compared to conventional input-output linearizing control and model predictive control techniques.     

Adaptive output rejection of unmatched input disturbances

To adaptively reject the effect of certain unmatched input disturbances on the output of a linear time-invariant system, a transfer function matching condition is needed. A lemma which presents a novel basic property of linear systems is derived to characterize system conditions for such transfer function matching. An adaptive disturbance rejection control scheme is developed for such systems with uncertain dynamics parameters and disturbance parameters. This adaptive control technique is applicable to control of systems with actuator failures whose failure values, failure time instants, and failure patterns are unknown. A solution is presented to this adaptive actuator failure compensation problem, which ensures closed-loop stability and asymptotic output tracking, in the presence of any up to m−1 uncertain failures of the total m actuators. Desired adaptive system performance is verified by simulation results.     

Robust input-output energy decoupling for uncertain singular systems

1 Introduction During recent years, singular systems have at- tracted the interest of a number of researchers due to the fact that they appear more naturally in the study of naturally occurring systems than regular systems (state-space systems), e.g. in economic, circuit, and boundary control systems, and chemical processes[1～3]. Many contributions have been made to the study of these systems, and a great number of results on the theory of regular systems have been generalized to the area of …     

Barrier function based finite-time tracking control for a class of uncertain nonlinear systems with input saturation

In this article, a novel robust finite-time tracking control scheme is proposed for a class of uncertain nonlinear systems subject to the model uncertainty, external disturbance, and input saturation. A barrier function based disturbance observer (BFDO) with finite-time convergence performance is developed to estimate the non-smooth nonlinear compound disturbance, which includes the uncertainty, disturbance of system and input saturation. In addition, an adaptive continuous nonsingular terminal sliding mode controller, based on the barrier function and the estimate of the BFDO is developed. The Lyapunov stability and finite-time convergence of the proposed control scheme are proved. The effectiveness and performance advantage of the proposed control scheme is demonstrated by numerical simulations and comparison with existing works.     

Realization theory in Hilbert space

A representation theorem for infinite-dimensional, linear control systems is proved in the context of strongly continuous semigroups in Hilbert spaces. The result allows for unbounded input and output operators and is used to derive necessary and sufficient conditions for the realizability in a Hilbert space of a time-invariant, causal input-output operator ℐ. The relation between input-output stability and stability of the realization is discussed. In the case of finite-dimensional input and output spaces the boundedness of the output operator is related to the existence of a convolution kernel representing the operator ℐ. This research has been supported by the Nuffields Foundation.     

一类非线性随机不确定系统有限时间H∞无穷滤波

研究一类具有时变、有界干扰的非线性随机不确定系统有限时间H∞滤波问题.首先,给出了非线性随机不确定系统有限时间H∞滤波问题的定义;其次,通过构造Lyapunov-Krasoviskii函数,并结合线性矩阵不等式（LMI）方法,给出了非线性随机不确定系统有限时间∞滤波器存在的充分条件;再次,将该问题简化为具有LMI约束的优化问题,并给出了相应的求解算法;最后,通过数值算例表明了所提出设计方法的有效性.     

Bounding the Parameters of Linear Systems With Input Backlash

In this note we present a two-stage procedure for deriving parameters bounds of linear systems with input backlash when the output measurement errors are bounded. First, using steady-state input-output data, parameters of the nonlinear dynamic block are tightly bounded. Then, given a suitable PRBS input sequence we evaluate tight bounds on the unmeasurable inner signal which, together with noisy output measurements are employed for bounding the parameters of the linear dynamic system     

一类非线性时滞系统的解耦控制

利用微分几何方法研究了一类非线性多输入多输出时滞系统的解耦问题．讨论了此类系统可解耦的充分条件，并给出了此类系统实现输入/输出间精确线性化的条件以及其标准形．文中给出了非线性时滞系统得以解耦的非线性状态反馈控制律；此状态控制律不但可以实现输出与时滞状态变量的解耦，还可以实现输出与输入间的精确线性化．而其闭环标准形的给出为此类系统实现各种控制目标带来了方便．