Input-to-state stabilization for nonlinear dual-rate sampled-data systems via approximate discrete-time model

The problem of state feedback stabilization of nonlinear sampled-data systems is considered under the “low measurement rate” constraint. A dual-rate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the current state. Given an approximate discrete-time model of a sampled nonlinear plant and given a family of controllers that stabilizes the plant model in input-to-state sense, we show that under some standard assumptions the closed loop dual-rate sampled data system is input-to-state stable in the semiglobal practical sense.     

Global sampled-data output feedback stabilisation for a class of nonlinear systems with unknown output function

This paper discusses the problem of global sampled-data output feedback stabilisation for a class of nonlinear systems whose output function is unknown. A systematic design scheme is developed to construct a linear output feedback control law in sampled-data form. An explicit formula for the maximum allowable sampling period is computed to guarantee global stability of the uncertain nonlinear systems under the proposed controller with appropriate gains. Two examples are given to demonstrate the effectiveness of the proposed design procedure.     

产品质量与生产过程的集成控制: 双率采样数据方法

本文在集成控制的框架下研究了工业过程中产品质量和生产过程的实时一体控制问题.首先,基于双速率采样数据提出了产品质量和生产过程的集成控制方案.然后,把控制器设计问题归结为求解一组非线性矩阵不定式,进而提出基于同伦算法的控制器设计方法.最后,通过数值仿真说明所提方法的有效.     

Combined parameter and output estimation of dual-rate systems using an auxiliary model

For a dual-rate sampled-data system, an auxiliary model based identification algorithm for combined parameter and output estimation is proposed. The basic idea is to use an auxiliary model to estimate the unknown noise-free output (true output) of the system, and directly to identify the parameters of the underlying fast single-rate model from the dual-rate input-output data. It is shown that the parameter estimation error consistently converges to zero under generalized or weak persistent excitation conditions and unbounded noise variance, and that the output estimates uniformly converge to the true outputs. An example is included.     

A modified stochastic gradient based parameter estimation algorithm for dual-rate sampled-data systems

In this paper, we propose a novel identification algorithm for a class of dual-rate sampled-data systems whose input–output data are measured by two different sampling rates. A polynomial transformation technique is employed to derive a mathematical model for such dual-rate systems. The proposed modified stochastic gradient algorithm has faster convergence rate than stochastic gradient algorithms for parameter identification using the dual-rate input–output data. Convergence properties of the algorithm are analyzed. Finally, illustrative and comparison examples are provided to verify the effectiveness and performance improvement of the proposed method.     

Multirate versions of sampled-data stabilization of nonlinear systems

The problem of state feedback sampled-data stabilization of nonlinear systems is considered under the “low measurement rate” constraint and in the presence of (not necessarily small) time delay in the measurement channel. A multirate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the current state from the delayed measurements. For both the controller emulation approach and the approach based on approximate discrete-time model of the system, we show that under standard assumptions the closed-loop multirate sampled data system is asymptotically stable in the semiglobal practical sense. An illustrative example of sampled-data control of vertical take off and landing aircraft is discussed.     

Global sampled-data output feedback control for a class of feedforward nonlinear systems

This paper investigates the problem of global output feedback stabilization for a class of feedforward nonlinear systems via linear sampled-data control. To solve the problem, we first construct a linear sampled-data observer and controller. Then, a scaling gain is introduced into the proposed observer and controller. Finally, we use the sampled-data output feedback domination approach to find the explicit formula for choosing the scaling gain and the sampling period which renders the closed-loop system globally asymptotically stable. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.     

Semi-global sampled-data output feedback disturbance rejection control for a class of uncertain nonlinear systems

This paper investigates the semi-global output feedback disturbance rejection control problem for a class of uncertain nonlinear systems with additive disturbances using linear sampled-data control. Aiming to reject the adverse effects caused by the uncertainties and unknown nonlinear perturbations which may not satisfy the strict feedback or feedforward structure, a new generalised discrete-time extended state observer is proposed to estimate the disturbance at sampling points. An output feedback disturbance rejection control law is then constructed in a sampled-data form which facilitates digital implementations. By selecting adequate control gains and a sufficiently small sampling period to restrain the state growth under a zero-order-hold input, the semi-global asymptotic stability of the hybrid closed-loop system and the disturbance rejection ability are proved. Both numerical example and an application of a single-link robot arm system demonstrate the feasibility and efficacy of the proposed method.     

Robust adaptive sampled-data control of a class of systems understructured nonlinear perturbations

A robust adaptive sampled-data feedback stabilization scheme is presented for a class of systems with nonlinear additive perturbations. The proposed controller generates a control input by using high-gain static or dynamic feedback from nonuniform sampled values of the output. A simple adaptation rule adjusts the gain and the sampling period of the controller     

Receding horizon H∞ control problems for sampled-data systems§

In this article, the receding horizon H_∞ control problems for sampled-data systems are considered. Since sampled-data systems can be rewritten as equivalent jump systems, the receding horizon H_∞ control problems for time-varying jump systems are considered first and the design methods of a state feedback receding horizon H_∞ controller and an output feedback receding horizon H_∞ controller are given. Then the obtained results are applied to sampled-data systems and the design methods of a state feedback receding horizon H_∞ controller and an output feedback receding horizon H_∞ controller are given. Two numerical examples are given to illustrate the theory.     

Sampled-Data Asynchronous Fuzzy Output Feedback Control for Active Suspension Systems in Restricted Frequency Domain

This paper proposes a novel sampled-data asynchronous fuzzy output feedback control approach for active suspension systems in restricted frequency domain.In order to better investigate uncertain suspension dynamics,the sampleddata Takagi-Sugeno(T-S)fuzzy half-car active suspension(HCAS)system is considered,which is further modelled as a continuous system with an input delay.Firstly,considering that the fuzzy system and the fuzzy controller cannot share the identical premises due to the existence of input delay,a reconstructed method is employed to synchronize the time scales of membership functions between the fuzzy controller and the fuzzy system.Secondly,since external disturbances often belong to a restricted frequency range,a finite frequency control criterion is presented for control synthesis to reduce conservatism.Thirdly,given a full information of state variables is hardly available in practical suspension systems,a two-stage method is proposed to calculate the static output feedback control gains.Moreover,an iterative algorithm is proposed to compute the optimum solution.Finally,numerical simulations verify the effectiveness of the proposed controllers.     

Practical disturbance rejection of a class of nonlinear systems via sampled output

This paper presents a sampled-data control scheme for the disturbance rejection of nonlinear systems in the output feedback form. The continuous-time controller is designed first using a filtered transformation and the internal model technique. Using the emulation approach, the proposed sampled-data control uses the sampled output and a discretetime implementation of the filter, and the internal model is involved. The proposed control is shown to render the overall system stable in a spirit of fast sampling. In particular, the disturbance is practically rejected in the sense that the ultimate bound of the output is allowed to be arbitrarily small by choosing appropriate gain parameters.     

非线性微分-代数系统的输出反馈镇定:基于线性采样控制

对满足指数1和线性增长条件的非线性微分-代数系统,本文证明其采样输出反馈镇 定控制问题可解.首先,给出一个线性显式非初始化状态观测器设计;然后,构造出线性的采样输出 反馈控制器,使得整个闭环系统渐近稳定.仿真结果表明了所提控制方法的有效性.     

Design of output feedback consensus controllers for nonlinear sampled-data multi-agent systems of strict-feedback form

Design of reduced-order observer-based output feedback consensus controllers for nonlinear sampled-data multi-agent systems of strict-feedback form is considered based on nonlinear sampled-data control and consensus control theories. As a practical application of the proposed design method, output feedback consensus control for sampled-data fully actuated ships is also discussed.     

Nonlinear sampled-data output feedback receding horizon control

In this paper, we present an output feedback receding horizon control for a class of SISO nonlinear systems. A globally stabilizing state feedback receding horizon control scheme is combined with a discretized high gain observer. This is motivated by the fact that measurable system’s outputs are only available at specific sampling intervals. Our result follows from the application of a separation principle applicable to a class of sampled-data nonlinear systems. It is shown that the output-feedback scheme recovers the performance (rate of convergence) achieved under state feedback receding horizon control for a sufficiently large observer gain and sampling frequency.     

An efficient hierarchical identification method for general dual-rate sampled-data systems

For the lifted input–output representation of general dual-rate sampled-data systems, this paper presents a decomposition based recursive least squares (D-LS) identification algorithm using the hierarchical identification principle. Compared with the recursive least squares (RLS) algorithm, the proposed D-LS algorithm does not require computing the covariance matrices with large sizes and matrix inverses in each recursion step, and thus has a higher computational efficiency than the RLS algorithm. The performance analysis of the D-LS algorithm indicates that the parameter estimates can converge to their true values. A simulation example is given to confirm the convergence results.     

Performance recovery under output feedback sampled-data stabilization of a class of nonlinear systems

This paper studies sampled-data output feedback control of a class of nonlinear systems. It is shown that the performance of a stabilizing continuous-time state feedback controller can be recovered by a sampled-data output feedback controller when the sampling period is sufficiently small. The output feedback controller uses a deadbeat discrete-time observer to estimate the unmeasured states. Two schemes are proposed to overcome large initial transients when the controller is switched on.     

Event-driven observer-based output feedback control for linear systems

This paper concerns the problem of event-driven observer-based output feedback control of linear systems. Contrary to normal sampled-data control systems, where the controller is updated periodically, in event-driven systems, it is updated only when an “event” happens, and a typical event is defined as some error signals exceeding a given threshold. Both continuous- and discrete-time event detector cases are considered. It is shown that even with the significantly reduced sampling frequency, the global uniform ultimate boundedness of the event-driven closed-loop systems can also be guaranteed. A numerical example is finally used to illustrate the effectiveness and advantages of the proposed approaches.     

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.     

Preservation of input-to-state stability under sampling and emulation: multi-rate case

The stabilization problem of sampled-data non-linear systems is considered under the low measurement rate constraint. A multi-rate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the current state. We show that if we design a continuous-time controller for a continuous-time plant so that the closed-loop continuous-time system is input-to-state stable and then discretize the controller and implement it using sample and zero order hold devices, then input-to-state stability property will be preserved for the sampled-data multi-rate closed loop system in a practical sense.