Polynomial-time probabilistic observability analysis of sampled-data piecewise affine systems

This paper proposes a polynomial-time probabilistic approach to solve the observability problem of sampled-data piecewise affine systems. First, an algebraic characterization for the system to be observable is derived. Next, based on the characterization, we propose a randomized algorithm that can determine if the system is observable in a probabilistic sense or the system is not observable in a deterministic sense. Finally, it is shown with some examples, for which it is hopeless to check the observability in a deterministic way, that the proposed algorithm is very useful.     

Feedback control of linear systems by multirate pulse-widthmodulation

In this note, sampled-data methods for modeling and control design of pulse-width modulated systems are examined. Both single-rate and multirate approaches are considered. Local controllability and observability analyses of the sampled-data models are performed, and feedback linearizability conditions for the sampled-data models are derived. Multirate nonlinear state and output feedback designs are presented that permit asymptotic regulation or tracking     

Controllability indices of sampled-data systems

The controllability of the sampled-data system derived from a controllable continuous-time system is considered. In particular, some relations between the controllability indices of the original continuous-time system and those of the sampled-data system are studied. Examples are given to illustrate the results, and similar results for observability are also indicated.     

Observability Under Sampling for Nonlinear Systems

A previous article has investigated the problem of the preservation of the observability under sampling in the framework of compact manifolds. A natural generalization of the cited result would be to extend it to the systems globally Lipschitzian defined on non compact manifolds. A simple representative of this class of systems is constituted by the set of bilinear systems, for this particular class of systems the preservation of the property of observability has been shown in a previous work. In this paper, we deal with the preservation of the observability under sampling for globally Lipschitzian systems defined on R ⁿ.     

Preservation of reachability and observability under sampling witha first-order hold

This paper gives the necessary and sufficient condition for the reachability of the sampled-data system S₁ obtained by the discretization of a linear time-invariant continuous-time system with a first-order hold. Equivalence of the reachability and controllability of S₁ is also shown. Similar results are given also for observability and reconstructibility. It turns out that S₁ is reachable only if S₀ is reachable, while S₁ is observable if and only if S₄l0 is observable, where S₀ is the sampled-data system obtained by the discretization with a zero-order hold of the same sampling period     

Hankel norm of sampled-data systems

Generalizes the concept of Hankel norm for purely continuous-time systems to sampled-data systems. The Hankel norm of a sampled-data system is defined by taking into account intersample behaviors. The formula of the Hankel norm of a sampled-data system is given by a hybrid state-space model approach. The authors show that the Hankel norm is equal to that of an equivalent discrete-time system. Two simple examples including sampled-data controller reduction are demonstrated     

Multirate sampled-data systems: computing fast-rate models

This paper studies identification of a general multirate sampled-data system. Using the lifting technique, we associate the multirate system with an equivalent linear time-invariant system, from which a fast-rate discrete-time system is extracted. Uniqueness of the fast-rate system, controllability and observability of the lifted system, and other related issues are discussed. The effectiveness is demonstrated through simulation and real-time implementation.     

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

In practice, the system is often modeled as a continuous-time fuzzy system, while the control input is applied only at discrete instants. This system is called a sampled-data control system. In this paper, robust guaranteed cost control for uncertain sampled-data fuzzy systems is discussed. A guaranteed cost control where a quadratic cost function is bounded by a certain scalar, not only stabilizes a system but also considers a control performance. A typical sampled-data control is the zero-order input, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the sampled-data guaranteed cost control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, guaranteed cost control performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using Leibniz–Newton formula and free weighting matrix method for fuzzy systems under the assumption that sampling time is not greater than some prescribed scalar. Then, a design method of robust guaranteed cost state feedback controller for uncertain sampled-data fuzzy systems is proposed. Examples are given to illustrate our robust sampled-data guaranteed cost control design.     

非线性时变时延系统的模糊采样最优控制

针对非线性时变时延系统,采用输入时延和自由权重矩阵方法研究模糊采样最优控制问题.应用T-S模糊系统表征非线性系统,控制器是零阶保持采样信号.由线性矩阵不等式给出最优控制准则,所设计的模糊采样控制器在闭环系统渐近稳定意义下可保证期望最优控制性能.最后,通过卡车拖车系统实验验证模糊采样控制设计方案的可行性.     

Design of H 2 Controllers for Sampled-Data Systems with Input Time Delays

This paper presents a general framework based on lifting technique for sampled-data systems with input time delays. By analyzing the properties of operator-valued matrices of lifted systems with input time delays, an extended lifting technique is obtained. It is then shown that, with the proposed lifting technique, the complex behavior of the system can be illustrated by two simple lifted systems, which construct the extended lifted system. The extended lifted system has the same induced norm as that of the original system with an input time delay, since the proposed lifting technique is an isometric isomorphism. Through applying the proposed lifting technique to sampled-data systems with input time delays, the time-invariant discrete-time system with infinite-dimensional input and output spaces is obtained. The equivalent discrete-time system, which is derived from the extended lifted system, can satisfy the problem of H ₂ sampled-data control systems with input time delays. Simulation results are given to show that the proposed method can guarantee a more stable system response than the conventional H ₂ sampled-data controller for the sampled-data systems with the various input time delays.     

A Sampled-Data Singularly Perturbed Boundary Control for a Heat Conduction System With Noncollocated Observation

This note presents a sampled-data strategy for a boundary control problem of a heat conduction system modeled by a parabolic partial differential equation (PDE). Using the zero-order-hold, the control law becomes a piecewise constant signal, in which a step change of value occurs at each sampling instant. Through the ‘lifting’ technique, the PDE is converted into a sequence of constant input problems, to be solved individually for a sampled-data formulation. The eigenspectrum of the parabolic system can be partitioned into two groups: a finite number of slow modes and an infinite number of fast modes, which is studied via the theory of singular perturbations. Controllability and observability of the sampled-data system are preserved, irrelevant to the sampling period. A noncollocated output-feedback design based upon the state observer is employed for set-point regulation. The state observer serves as an output-feedback compensator with no static feedback directly from the output, satisfying the so-called ‘low-pass property’. The feedback controller is thus robust against the observation error due to the neglected fast modes.      

Discrete-time model reference adaptive control for continuous-timesystems using generalized sampled-data hold functions

The generalized sampled-data hold functions approach of P.T. Kabamba (1987) is extended to the control of linear time-invariant systems with unknown parameters. The idea of Kabamba's approach is to periodically sample the plant output and define the control as the sampled output plus a discrete-time reference, each multiplied by an individual modulating function. Such a control makes it possible to assign an arbitrary discrete-time transfer function for the sampled closed-loop system and does not make assumptions on the plant other than controllability and observability. The authors propose an indirect adaptive controller which is based on this approach and estimates the modulating functions online. In particular, the control is modified so that persistent excitation of the continuous-time plant is ensured without making an assumption on the reference signal, and discrete-time asymptotic model-following is nevertheless obtained. The only assumptions on the plant are minimality, for the continuous and sampled plant, and known order     

切换非线性系统采样控制的研究现状与进展

切换非线性系统由于其广泛的工程应用背景以及重要的理论研究价值引起各行业学者的广泛关注.近年来,随着计算机技术的快速发展,切换非线性系统采样控制问题成为研究热点.对目前切换非线性系统采样控制领域的研究现状进行综述.首先介绍了切换非线性系统的基本问题,并梳理了切换非线性系统几个常用控制方法的基本思想.然后从时间触发采样控制和事件触发采样控制两个方面对切换非线性系统采样控制的国内外研究现状进行了论述.最后进行了总结并提出切换非线性系统采样控制领域未来值得关注的研究方向.     

2 optimal control for sampled-data systems

This paper considers an ₂ optimal control problem for sampled-data systems. After defining a new ₂ norm for sampled-data systems, we give a state space solution to the optimal controller synthesis problem. We show that the ₂ optimal control problem for a sampled-data system is equivalent to a standard ₂ optimal control problem for a related discrete-time system.     

时滞不确定采样控制系统的鲁棒稳定性

本文给出了一种可定量分析采样控制系统的时滞鲁棒稳定性的方法.因为采样系统的对象是连续时间的,所以对象中的时滞也应该是按连续时间来处理.文中指出,一个整数倍时滞是稳定的采样系统,可能会因为有并不很大的连续时间时滞而失稳.定义了一个新的变量w(t),用来描述这个不确定连续时间时滞带来的动特性.将w(t)的反馈回路分成与时滞无关和有关的两个部分,并提出了一种用频率响应来确定是否存在由不确定时滞引起的周期解的方法.用修正z-变换法和仿真验证了这个由图解解析所求得的解.本方法既可用于采样系统,也可用于一般的连续时间系统.     

Sampled-data consensus of general linear multi-agent systems under switching topologies: averaging method

This paper investigates sampled-data consensus problems of general linear multi-agent systems under switching topologies. To perform the consensus analysis by the averaging method, the multi-agent system in the sampled-data setting is first converted into the continuous-time system with the input delay. Then, the approximate relationship between the states of this input delay system and the states of its averaged system is established by using the tool from non-standard analysis. Subsequently, a sufficient condition ensuring the sampled-data consensus is obtained by linear matrix inequalities. It is shown that the sampled-data consensus of general linear multi-agent systems, including exponential unstable agents, can be achieved, if the speed of topology switching is fast enough and the sampled-data consensus under the averaging topology can be achieved. Finally, numerical simulations are provided to demonstrate the effectiveness of theoretical analyses.     

高阶系统方法—Ⅲ.能观性与观测器设计

平行于第Ⅰ部分中提出的非线性系统的全驱性概念, 本文提出了非线性系统的全量测性概念.首先给出了非线性系统的一种能观规范型, 并证明了任何与该类非线性系统能观规范型等价的系统, 以及任何能观的线性系统, 都等价于一个高阶全量测系统.然后据此提出了一般动态系统的完全能观性定义, 同时指出线性系统的完全能观性等同于其通常意义下的能观性.最后提出了非线性全量测系统观测器设计的一种简洁方法.基于这种设计, 可以使观测误差系统为线性定常系统, 并且可以任意配置其特征多项式的系数矩阵.     

Observability and observateur under sampling

This work is a continuation of (S. Ammar and J.-C. Vivalda, “On the preservation of observability under sampling”, Systems and Control Letters, 52, pp. 7–15, 2004) in which the authors showed the preservation of the observability under sampling. In the first step of this paper, by removing the assumption of infinitesimal observability and by adding the analyticity of the continuous system, we show the conservation of the observability under sampling almost everywhere. In the second step, we discuss the problem of the observateur under sampling.     

Takagi-Sugeno模糊连续系统的模糊采样控制

研究了T-S模糊连续系统的模糊采样控制问题．利用广义系统的描述方法、Lyapunov-Krasovikii泛函以及线性矩阵不等式(LMI)方法,建立了LMIs形式的依赖于采样时间间隔的模糊采样镇定条件,同时给出了模糊采样控制律的设计方法．所设计的模糊采样控制律可以镇定T-S模糊系统．而且,当连续时间模糊控制律可以镇定T-S模糊系统时,对于足够小的采样时间间隔,带有同样增益矩阵的模糊采样控制律也可以镇定T-S模糊系统．最后,通过两个仿真实例说明了所给方法的有效性．     

FR-operator approach to the H2 analysis and synthesis ofsampled-data systems

Recently, a frequency-domain operator called frequency response (FR) operator was defined and shown to represent the transfer characteristics of a stable sampled-data system. Using this novel frequency-domain notion and introducing its extended notion called hybrid FR-operator, we define an H₂-norm for sampled-data systems in this paper. Then, sampled-data H₂ control problems are formulated and solved, whereby the usefulness of these frequency-domain notions is demonstrated both in the analysis and synthesis aspects of sampled-data systems. For the case of sampled-data systems with hybrid (i.e., both continuous-time and discrete-time) input and output signals, the H₂-norm defined by a hybrid FR-operator turns out to be slightly different from that defined in previous studies. The source of the discrepancy is also identified