An improved finite frequency approach to robust filter design for LTI systems with polytopic uncertainties

In this paper, the finite frequency robust filtering problem (‐FFRFP), design of a robust filter minimizing the norm from the disturbance input to the estimation error evaluated over a prescribed finite frequency domain, is considered for continuous‐time and discrete‐time linear time‐invariant (LTI) systems with polytopic parameter uncertainties. By means of the generalized Kalman–Yakubovich–Popov (KYP) lemma in combination with a result known as Finsler's lemma, the ‐FFRFP is cast as a linear matrix inequality (LMI) optimization. Examples are given to demonstrate that the proposed condition can achieve improvement over the previous ones in the literature. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust H∞ filtering for switched linear discrete‐time systems with polytopic uncertainties

In this paper, the problem of robust H_∞ filtering for switched linear discrete‐time systems with polytopic uncertainties is investigated. Based on the mode‐switching idea and parameter‐dependent stability result, a robust switched linear filter is designed such that the corresponding filtering error system achieves robust asymptotic stability and guarantees a prescribed H_∞ performance index for all admissible uncertainties. The existence condition of such filter is derived and formulated in terms of a set of linear matrix inequalities (LMIs) by the introduction of slack variables to eliminate the cross coupling of system matrices and Lyapunov matrices among different subsystems. The desired filter can be constructed by solving the corresponding convex optimization problem, which also provides an optimal H_∞ noise‐attenuation level bound for the resultant filtering error system. A numerical example is given to show the effectiveness and the potential of the proposed techniques. Copyright © 2006 John Wiley & Sons, Ltd.     

Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.     

Stability and stabilization in switched discrete‐time systems

In this paper, we investigate the stability and stabilization problem for discrete‐time switched systems. We consider a probabilistic case where the system is switched among different subsystems, and the probability of each subsystem being active is defined as its occurrence probability. The relationship between the developed model of the switched system and the Markovian jump system is analyzed. For a switched system with a known subsystem occurrence probabilities, we give a stochastic stability criterion in terms of a linear matrix inequality. Then, we extend the results to a more practical case where the subsystem occurrence probabilities of switching are known to be constant, but their specific values are only known with some uncertainty. A new iterative approach is employed to choose the switching law between the subsystems. For unstable switched systems, mode‐dependent state feedback and static output feedback controllers are developed to achieve the stabilization objective. Finally, several simulation examples are presented to show the efficacy of the proposed criteria and methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Immersion and invariance adaptive control for discrete‐time systems in strict‐feedback form with input delay and disturbances

This work presents a new adaptive control algorithm for a class of discrete‐time systems in strict‐feedback form with input delay and disturbances. The immersion and invariance formulation is used to estimate the disturbances and to compensate the effect of the input delay, resulting in a recursive control law. The stability of the closed‐loop system is studied using Lyapunov functions, and guidelines for tuning the controller parameters are presented. An explicit expression of the control law in the case of multiple simultaneous disturbances is provided for the tracking problem of a pneumatic drive. The effectiveness of the control algorithm is demonstrated with numerical simulations considering disturbances and input‐delay representative of the application.     

Robust adaptive iterative learning control for discrete‐time nonlinear systems with both parametric and nonparametric uncertainties

A new robust adaptive iterative learning control approach is proposed for discrete‐time nonlinear systems with both parametric and nonparametric uncertainties. By virtue of a well‐designed dead‐zone function, the learning of the parametric and nonparametric uncertainties can be performed concurrently. Rigorous Lyapunov function‐based analysis ensures that the effect of system uncertainties can be fully compensated, and the tracking error will converge to zero asymptotically in the iteration domain, even under random initial conditions and iteration‐varying reference trajectories. The efficacy of the proposed controller is demonstrated by simulating a single‐link robot manipulator with unknown frictions. Copyright © 2015 John Wiley & Sons, Ltd.     

带有多胞型摄动的线性切换系统的二次稳定性

研究了带有多胞型摄动的线性切换系统的二次稳定性问题。这种摄动是由若干已知常数矩阵所张成的多胞构成的。利用完备性给出二次稳定的充要条件和切换律的设计方法,利用凸组合技术给出了二次稳定的一个充分条件。这些方法能够分析含有不稳定子系统的多胞型切换系统的稳定性。仿真例子说明了文中结果的正确性。     

An indirect adaptive pole‐placement control for MIMO discrete‐time stochastic systems

In this paper, an indirect adaptive pole‐placement control scheme for multi‐input multi‐output (MIMO) discrete‐time stochastic systems is developed. This control scheme combines a recursive least squares (RLS) estimation algorithm with pole‐placement control design to produce a control law with self‐tuning capability. A parametric model with a priori prediction outputs is adopted for modelling the controlled system. Then, a RLS estimation algorithm which applies the a posteriori prediction errors is employed to identify the parameters of the model. It is shown that the implementation of the estimation algorithm including a time‐varying inverse logarithm step size mechanism has an almost sure convergence. Further, an equivalent stochastic closed‐loop system is used here for constructing near supermartingales, allowing that the proposed control scheme facilitates the establishment of the adaptive pole‐placement control and prevents the closed‐loop control system from occurring unstable pole‐zero cancellation. An analysis is provided that this control scheme guarantees parameter estimation convergence and system stability in the mean squares sense almost surely. Simulation studies are also presented to validate the theoretical findings. Copyright © 2005 John Wiley & Sons, Ltd.     

Adaptive iterative learning control of discrete‐time varying systems with unknown control direction

Without using Nussbaum gain, a novel method is presented to solve the unknown control direction problem for discrete‐time systems. The underlying idea is to fully exploit the convergence property of parameter estimates in well‐known adaptive algorithms. By incorporating two modifications into the control and the parameter update laws, respectively, we present an adaptive iterative learning control scheme for discrete‐time varying systems without the prior knowledge of the sign of control gain. It is shown that the proposed adaptive iterative learning control can achieve perfect tracking over the finite time interval while all the closed‐loop signals remain bounded. An illustrative example is presented to verify effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Global adaptive finite‐time stabilization of a class of switched nonlinear systems with parametric uncertainty

This paper investigates the global adaptive finite‐time stabilization of a class of switched nonlinear systems, whose subsystems are all in p (p≤1) normal form with unknown control coefficients and parametric uncertainties. The restrictions on the power orders and the nonlinear perturbations are relaxed. By using the parameter separation technique, the uncertain parameters are separated from nonlinear functions. A systematic design procedure for a common state feedback controller and a switching adaptive law is presented by employing the backstepping methodology. It is proved that the closed‐loop system is finite‐time stable under arbitrary switching by utilizing the common Lyapunov function. Finally, with the application to finite‐time control of chemical reactor systems, the effectiveness of the proposed method is demonstrated. Copyright © 2015 John Wiley & Sons, Ltd.     

Fault‐tolerant saturated control for switching discrete‐time systems with delays

In this paper, fault‐tolerant control problem for discrete‐time switching systems with delay and saturated input is studied. Sufficient conditions of building an observer are obtained by using multiple Lyapunov function. These conditions are worked out using cone complementarity technique, to obtain LMIs with slack variables and multiple weighted residual matrices. The obtained results are applied on a numerical example showing fault detection, localization of fault, and reconfiguration of the control to maintain asymptotic stability even in the presence of a permanent sensor fault and saturation on the control. Copyright © 2014 John Wiley & Sons, Ltd.     

On the radius of stabilizability of lti systems: Application to projection implementation in indirect adaptive control

In this paper we solve the problem of finding the ‘largest sphere’ around a linear time-invariant (LTI) stabilizable plant such that all plants of the same order in the sphere are also stabilizable and there exists a plant in its boundary that is not stabilizable. The sphere is described in the plant parameter space and an explicit expression for its radius is given. This result solves the open problem in indirect adaptive control of determining the region to which the parameter search procedure should be constrained so that stabilizability of the estimated plant is preserved.     

Robust adaptive tracking control of uncertain discrete time systems

In this paper, the problem of robust adaptive tracking for uncertain discrete‐time systems is considered from the slowly varying systems point of view. The class of uncertain discrete‐time systems considered is subjected to both 𝓁_∞ to 𝓁_∞ bounded unstructured uncertainty and external additive bounded disturbances. A priori knowledge of the dynamic model of the reference signal to be tracked is not completely known. For such problem, an indirect adaptive tracking controller is obtained by frozen‐time controllers that at each time optimally robustly stabilize the estimated models of the plant and minimize the worst‐case steady‐state absolute value of the tracking error of the estimated model over the model uncertainty. Based on 𝓁_∞ to 𝓁_∞ stability and performance of slowly varying system found in the literature, the proposed adaptive tracking scheme is shown to have good robust stability. Moreover, a computable upper bound on the size of the unstructured uncertainty permitted by the adaptive system and a computable tight upper bound on asymptotic robust steady‐state tracking performance are provided. Copyright © 2005 John Wiley & Sons, Ltd.     

Lyapunov‐stable discrete‐time model reference adaptive control

Discrete‐time model reference adaptive control (MRAC) is considered with both least squares and projection algorithm parameter identification. For both cases complete Lyapunov proofs are given for stability and convergence. The results extend the approach of Johansson (Int. J. Control 1989; 50 (3):859–869) to include Lyapunov stability for MRAC when the normalized projection algorithm is used for parameter identification. Copyright © 2005 John Wiley & Sons, Ltd.     

Robust adaptive tracking control for nontriangular time-delay nonlinear systems with input dead-zone and multiple uncertainties

This article studies the robust adaptive tracking control problem of nontriangular nonlinear systems that are affected by multiple state delays rather than the input-delay. Different from the related studies, the considered systems involve input dead-zone and various uncertainties arising in the control coefficients, structure parameters, time delays, and disturbances. A new adaptive control strategy is presented by introducing a dynamic-gain-based Lyapunov-Krasovskii functional and by generalizing the tuning function method in the framework of time-delay system theory. All the states of the closed-loop system are bounded and the tracking error can be adjusted sufficiently small. In the simulation, the delayed chemical system is studied to demonstrate the validity of the strategy.     

The optimal fuzzy robust regulator for TS discrete‐time systems: An LMI approach

In this work, the problem of designing an optimal regulator for discrete‐time nonlinear systems when the plant can be modelled by a Takagi–Sugeno (TS) fuzzy system is addressed. The approach analyzed in this paper, under certain conditions, guarantees the tracking of references and allows the performance of the controller to be improved by means of the inclusion of some cost functions. The main result is given in terms of linear matrix inequality techniques, meaning that the design of the controller can be obtained in a practical way. Finally, numerical simulations are carried out in order to illustrate the validity of the fuzzy regulator. Copyright © 2008 John Wiley & Sons, Ltd.     

Quantized feedback stabilization of linear discrete‐time systems with constraints

This paper addresses the quantization of control systems. The state of the system is quantized by means of a quantizer. In addition, constraints on the input and/or state are considered explicitly. For a linear system with no constraints, some quantized feedback control methods have been proposed. In this paper, a control methodology for a constrained system is proposed. Specifically, the idea of a positively invariant set is introduced so that the performance is improved while the constraints are satisfied. The effectiveness of the proposed method is verified through both simulation and experiment. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 178(3): 53–61, 2012; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21122     

A finite frequency approach to filter design for uncertain discrete‐time systems

This paper studies the problem of finite frequency filter design for linear time‐invariant discrete‐time systems with polytopic uncertainties. Generalized Kalman–Yakubovich–Popov lemma is exploited to formulate the filter design problem in finite frequency domain. A design method is presented in terms of solutions to a set of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

A note on global convergence of adaptive control in a discrete‐time non‐linear case

Adaptive control is applied to a particular class of SISO discrete‐time non‐linear systems. Global boundedness and convergence are obtained by introducing a modification to a classical adaptive scheme. Copyright © 1999 John Wiley & Sons, Ltd.