Past Output Measurements Research Articles

Observer-based output feedback control for switched T–S fuzzy systems with local nonlinear segments by using past output measurements

This paper researches the observer-based exponential stabilization problem for switched Takagi–Sugeno (T–S) fuzzy systems with unmeasurable premise variables and local nonlinearities. The local nonlinear parts that satisfy the incremental quadratic constraint exist in the systems and observers, which have the merit of being able to contain many common nonlinearities in a unified framework. Because the premise variables are not measurable, the performance of the observers in estimation is critical. Different from existing observer-based control strategies, the strategy of this paper not only depends on the current outputs of the systems but also relates to the past outputs of the systems which can provide a way to improve performance. In order to tackle the difficulties caused by introducing the past outputs and design a set of non-fragile fuzzy controllers to stabilize the systems, a new augmented state vector is constructed. Then, the conditions for designing the observer-based controller are derived by using auxiliary scalars, projection Lemma and S-procedure. Finally, the effectiveness of the control strategy obtained in this paper is proved by two examples.

Finite-time filtering design with past output measurements for interval type-2 fuzzy systems: A descriptor approach

This paper is interested in the design of full-order H∞ memory filters for discrete-time nonlinear systems within finite-time domain. First, the investigated nonlinear systems are modeled by a Takagi–Sugeno fuzzy technique for the interval type-2 case. And to reduce the size of the model, only the past measurements of systems are involved during the memory filters construction. Then, novel design processes with less conservatism are proposed through executing a decoupling transformation for the filtering error dynamics. Based on Lyapunov methods together with several strategies that apply convex optimization techniques and slack variables, some sufficient conditions are presented and certified to solve the memory filter parameters, such that the augmented error dynamics are singular finite-time bounded with prescribed H∞ performance. Finally, an example is introduced to illustrate the effectiveness of the proposed strategy in contrast to existent works.

A novel H∞ memory observer design for uncertain switched nonlinear systems using past output measurements

AbstractThis paper tackles the problem of robust memory observer design problem for discrete‐time switched nonlinear systems by using past output measurements. Different from traditional design strategies of Luenberger‐type observers using the current output measurements, the memory Luenberger‐type observer design strategy introduces the past output measurements of switched systems and observers simultaneously. In addition, in order to better describe the observer error systems, a novel augmented state variable framework of the observer error systems is developed. The highlight of this paper lies that the memory observer design strategy is developed by considering past output measurements and state error values of memory observers, whose performance can be improved by increasing the number of past output measurements used in the observer design, which is an important discovery and significant novelty of this work. By combining the multiple Lyapunov functions approach and average dwell time technique, and introducing matrix variables with free structure, new sufficient conditions for weighted performance analysis of observer error systems are derived. Then, the memory observer synthesis conditions are obtained in the form of linear matrix inequality (LMI), and the memory observers can be obtained by solving these LMIs. Lastly, two examples are presented to show the advantages and effectiveness of the derived results.

Frequency information based memory dynamic output feedback control for discrete‐time systems

AbstractThis article studies the problem of frequency information based memory dynamic output feedback (MDOF) control for discrete‐time systems. A novel design method for MDOF controllers is proposed based on not only the current output measurements and controller states, but also useful past output measurements and controller states, which tend to be less conservative than conventional memoryless controllers. Sufficient conditions are derived to guarantee the asymptotic stability with finite frequency specifications of the closed loop system, and then MDOF controller synthesis results are obtained in the form of linear matrix inequalities, which include the conventional memoryless and/or non‐frequency information based control methods as their special cases. It is also proved that the control performance can be enhanced with the increase of the memory capacity of the MDOF controller. Finally, simulation studies are given to show the effectiveness and advantages of the proposed MDOF controller design method over the conventional memoryless and/or non‐frequency information control approaches.

Robust finite frequency H∞ distributed memory filter design for networked control systems with polytopic uncertainty

AbstractThis paper addresses the robust finite frequency (FF) distributed filtering problem for uncertain networked control system (NCS) that consists of heterogeneous subsystems. By using past output measurements and considering the frequency information of disturbance signals, the designed distributed memory filter is able to guarantee that the filtering error system is well‐posed, stable and has the FF performance. Based on the extended finite frequency bounded realness lemma for uncertain NCSs, the existence condition of robust FF distributed memory filter is derived. Moreover, it is shown that by taking advantage of more past output measurements of NCS, the proposed design procedure can derive a distributed filter that achieves a lower performance bound. Finally, a practical example is given to show the effectiveness of the proposed filter design method.

Finite frequency memory output feedback controller design for discrete‐time systems with state multiplicative noises

AbstractThis article studies the problem of output feedback control for discrete‐time systems with state multiplicative noises. Aiming at reducing the controller design conservatism, a novel finite frequency memory control approach is developed, which makes full use of both current and past output measurements together with the frequency spectrum information of disturbances. By augmenting the control input into the closed‐loop system state, a descriptor system approach is proposed to facilitate the controller synthesis. Then, based on the Fourier transform, Parseval's relation, and Projection lemma, the linear matrix inequalities (LMIs)‐based controller design results are obtained to guarantee the mean‐square asymptotic stability with finite frequency performance for the resulting closed‐loop system. The effectiveness of the developed approach is validated by an antenna motion control system.

Finite-frequency memory filter design for uncertain linear discrete-time systems: A polynomially parameter-dependent approach

This paper investigates the robust filtering problem for linear uncertain systems affected by noises in restricted frequency intervals. Different from traditional filter schemes, a finite-frequency memory filter is designed to generalize conventional memoryless ones in such a way that a sequence of latest output measurements are employed for current estimation. To be specific, a memory filter is sought which ensures that for all admissible uncertainties, the filtering error system is asymptotically stable with a prescribed noise-attenuation level in the restricted frequency range. To accomplish this, the finite-frequency specification is characterized by the generalized Kalman–Yakubovich–Popov (KYP) lemma, aiming at improving the capability of noise-attenuation over the given frequency range. Moreover, the homogeneous polynomially parameter-dependent technique is adopted to facilitate filter design and reduce conservatism further. Based on the proposed scheme, we prove rigorously that additional past output measurements contribute to less conservative results. Finally, a quarter-car model with an active-suspension system is used to validate the proposed scheme.

Homothetic tube-based robust offset-free economic Model Predictive Control

This paper proposes a novel economic Model Predictive Control algorithm aiming at achieving optimal steady-state performance despite the presence of plant-model mismatch or unmeasured nonzero mean disturbances. According to the offset-free formulation, the system’s state is augmented with disturbances and transformed into a new coordinate framework. Based on the new variables, the proposed controller integrates a moving horizon estimator to determine a solution of the nominal system surrounded by a set of potential states compatible with past input and output measurements. The worst cost within a single homothetic tube around the nominal solution is chosen as the economic objective function which is minimized to provide a tightened upper bound for the accumulated real cost within the prediction horizon window. Thanks to the combined use of the nominal system and homothetic tube, the designed optimization problem is recursively feasible and less conservative economic performance bounds are achieved. The proposed controller is demonstrated on a two-tanks system.

A Novel Piecewise Affine Filtering Design for T-S Fuzzy Affine Systems Using Past Output Measurements.

This paper tackles the problem of piecewise affine memory filtering design for the discrete-time norm-bounded uncertain Takagi-Sugeno fuzzy affine systems. The objective is to design an admissible filter using past output measurements of the system, guaranteeing the asymptotic stability of the filtering error system with a given [Formula: see text] performance index. Based on the piecewise fuzzy Lyapunov functions and the projection lemma, a new sufficient condition for [Formula: see text] filtering performance analysis is first derived, and then the filter synthesis is carried out. It is shown that the filter gains can be obtained by solving a set of linear matrix inequalities. In addition, it is also shown that the filtering performance can be improved with the increasing number of past output measurements used in the filtering design. Finally, two examples are presented to show the advantages and effectiveness of the proposed approach.

Finite Frequency Memory Output Feedback Controller Design for T–S Fuzzy Dynamical Systems

In this paper, we will investigate the problem of finite frequency memory fixed-order output feedback controller design for Takagi–Sugeno (T–S) fuzzy affine systems. It is assumed that the disturbances reside in a finite frequency range, i.e., the low, middle, or high frequency range. The objective is to design a memory piecewise affine (PWA) controller by using past output measurements to guarantee the asymptotic stability of the resulting closed-loop system with a prescribed finite frequency $\mathscr H_{\infty }$ performance. Via the system state-input augmentation, a novel descriptor system approach is proposed to facilitate the controller design. All the design conditions are formulated in the form of linear matrix inequalities. It is also proven that the $\mathscr H_{\infty }$ performance can be improved with the memory control strategy. Finally, simulation studies are presented to show the effectiveness of the proposed design method.

Finite Frequency Filtering Design for Uncertain Discrete-Time Systems Using Past Output Measurements

This paper tackles the problem of finite frequency $\mathcal H_{\infty }$ filtering design for polytopic uncertain discrete-time systems using past output measurements. The noise is assumed to be restricted in a finite frequency range, i.e., the low, middle, or high frequency range. The objective is to design an admissible filter with past output measurements of the system, guaranteeing the asymptotic stability of the filtering error system with a prescribed finite frequency $\mathcal H_{\infty }$ disturbance attenuation level. Based on past output measurements together with the parameter-dependent Lyapunov function and projection lemma, a new sufficient condition for robust finite frequency $\mathcal H_{\infty }$ performance is first derived, and then, the filter synthesis is developed. It is shown that the filter gains can be obtained by solving a set of linear-matrix-inequalities. Finally, two examples are given to demonstrate the advantages and effectiveness of the proposed approach.

Robust H ∞ filter design for discrete-time interconnected fuzzy systems with partially unknown membership functions and past output measurements

Abstract This paper is concerned with the H∞ filtering problem for discrete-time interconnected fuzzy systems with partially unknown membership functions and past output measurements. A new H∞ filter with past output measurements is designed by introducing a switching mechanism which depends on the lower and upper bounds of the unknown elements of the membership functions, and graph theory is applied to addressed the interconnections, such that the filtering error system is asymptotically stable and the desired performance is guaranteed. By using Lyapunov analysis method, H∞ filter design conditions are given in terms of convex problem constrained by linear matrix inequalities (LMI). The results of this paper extend the existing filter design methods and obtain less conservative conditions. Finally, a numerical example is given to illustrate the advantages of the proposed design method.

Fault detection for T–S fuzzy systems with past output measurements

This paper is concerned with the fault detection (FD) filter design problem for the discrete-time nonlinear systems with past output measurements and sensor saturation. The considered discrete-time nonlinear systems are described by T–S fuzzy models. A decomposition method is used to deal with the characteristics of sensor saturation. A new FD filter with past output measurements is firstly proposed by using the Lyapunov functional method. Subsequently, the design conditions are given in terms of convex problems constrained by linear matrix inequalities (LMI). Moreover, it is shown that the FD filter with past output measurements can achieve better FD performances than the existing ones with current output measurements. Finally, some simulation results are given to illustrate the advantages of the proposed design method.

Event‐based fault detection for non‐linear networked systems with multi‐data transmission and output quantisation

This study is concerned with the event-triggered fault detection (FD) filter design problem for the discrete-time non-linear systems with multi-data transmission and output quantisation. To reduce the transmission data size, the output signals are quantified by a logarithmic quantiser. Compared with the existing results, past output measurements are first introduced for packaging and transmission only when the event condition is satisfied. Based on this consideration, more data can be used by the FD filter, while using the traditional method, the FD filter can only use the current data. Finally, some simulation results show that the proposed design method can achieve a better FD performance than the existing method with current output measurements transmission.

Robust [formula omitted] filter design with past output measurements for uncertain discrete-time systems

This paper is concerned with the design of robust filters for uncertain discrete-time linear systems. The uncertainty is assumed to be time-invariant belonging to a polytope. An upper bound to the H∞ norm of the transfer-function from the system input to the filtering error is used as performance criterion. The novelty is that the resulting robust filter has order greater than the order of the system being filtered by incorporating past output measurements. The design conditions are expressed in terms of convex problems constrained by Linear Matrix Inequalities. Performance is assessed through parameter-dependent Lyapunov functions. The results generalize existing robust filtering procedures without bringing in any additional conservatism. Simple numerical examples illustrate the procedure.

Robust model predictive controller with output feedback and target tracking

A model predictive controller (MPC) is proposed, which is robustly stable for some classes of model uncertainty and to unknown disturbances. It is considered as the case of open-loop stable systems, where only the inputs and controlled outputs are measured. It is assumed that the controller will work in a scenario where target tracking is also required. Here, it is extended to the nominal infinite horizon MPC with output feedback. The method considers an extended cost function that can be made globally convergent for any finite input horizon considered for the uncertain system. The method is based on the explicit inclusion of cost contracting constraints in the control problem. The controller considers the output feedback case through a non-minimal state-space model that is built using past output measurements and past input increments. The application of the robust output feedback MPC is illustrated through the simulation of a low-order multivariable system.

Self‐tuning control for polynomial systems using a receding horizon observer and control strategy

AbstractA receding horizon observer and control scheme is introduced for non‐linear systems described by polynomial maps. This control scheme has a natural interpretation as a two‐stage adaptive or self‐tuning control algorithm. The non‐linear feedback that results is defined only on the basis of past input and output measurements. The computational complexity aspects of this approach to adaptive or self‐tuning control are briefly discussed. A linear system and a Hénon map example are used to illustrate the ideas. Copyright © 2004 John Wiley & Sons, Ltd.

A RECURSIVE 4SID FROM THE INPUT‐OUTPUT POINT OF VIEW

In this paper, recursive algorithms of subspace state‐space system identification (4SID) for multiple‐input, multiple‐output (MIMO), finite dimensional, linear time‐invariant (FDLTI) systems are proposed. These algorithms are derived based on the Matrix Inversion Lemma. The investigation of our algorithms clarifies that a series of 4SID is the extension of the classical least square method to identification for multivariable systems, and also that our algorithms are the direct extension of the recursive least square algorithm to such ones. For PO‐MOESP (the ordinary MOESP scheme with instrumental variables constructed from Past input and Output measurements), we show the mechanism of how the effect of the process and measurement noises is eliminated asymptotically by a projection related to the input and regressor matrices. “MOESP” is an abbreviation for “the MIMO output‐error state‐space model identification.”