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.     

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.     

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.     

Constructive approximation of non‐linear discrete‐time systems

It is known that large classes of approximately‐finite‐memory maps can be uniformly approximated arbitrarily well by the maps of certain non‐linear structures. As an application, it was proved that time‐delay networks can be used to uniformly approximate arbitrarily well the members of a large class of causal nonlinear dynamic discrete‐time input–output maps. However, the proof is non‐constructive and provides no information concerning the determination of a structure that corresponds to a prescribed bound on the approximation error. Here we give some general results concerning the problem of finding the structure. Our setting is as follows. There is a large family 𝒢 of causal time‐invariant approximately‐finite‐memory input‐output maps G from a set S of real d‐vector‐valued discrete‐time inputs (with d⩾1) to the set of ℝ‐valued discrete‐time outputs, with both the inputs and outputs defined on the non‐negative integers 𝒵₊. We show that for each ϵ>0, any Gϵ𝒢 can be uniformly approximated by a structure map H(G, ·) to within tolerance ϵ, and we give analytical results and an example to illustrate how such a H(G, ·) can be determined in principle. Copyright © 2000 John Wiley & Sons, Ltd.     

Adaptive internal model control: the discrete‐time case

This paper considers the design and analysis of a discrete‐time H₂ optimal robust adaptive controller based on the internal model control structure. The certainty equivalence principle of adaptive control is used to combine a discrete‐time robust adaptive law with a discrete‐time H₂ internal model controller to obtain a discrete‐time adaptive H₂ internal model control scheme with provable guarantees of stability and robustness. The approach used parallels the earlier results obtained for the continuous‐time case. Nevertheless, there are some differences which, together with the widespread use of digital computers for controls applications, justifies a separate exposition. Copyright © 2001 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.     

Adaptive control of discrete‐time nonlinear systems by recurrent neural networks in quasi‐sliding mode like regime

The aim of this study was to design an adaptive control strategy based on recurrent neural networks (RNNs). This neural network was designed to obtain a non‐parametric approximation (identification) of discrete‐time uncertain nonlinear systems. A discrete‐time Lyapunov candidate function was proposed to prove the convergence of the identification error. The adaptation laws to adjust the free parameters in the RNN were obtained in the same stability analysis. The control scheme used the states of the identifier, and it was developed fulfilling the necessary conditions to establish a behavior comparable with a quasi‐sliding mode regime. This controller does not use the regular form of the switching function that commonly appears in the sliding mode control designs. The Lyapunov candidate function to design the controller and the identifier simultaneously requires the existence of positive definite solutions of two different matrix inequalities. As consequence, a class of separation principle was proven when the RNN‐based identifier and the controller were designed by the same analysis. Simulations results were designed to show the behavior of the proposed controller solving the tracking problem for the trajectories of a direct current (DC) motor. The performance of the proposed controller was compared with the solution obtained when a classical proportional derivative controller and an adaptive first‐order sliding mode controller assuming poor knowledge of the plant. In both cases, the proposed controller showed superior performance when the relation between the tracking error convergence and the energy used to reach it was evaluated. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust learning controller design for MIMO stochastic discrete‐time systems: An H∞‐based approach

This paper is devoted to designing iterative learning control (ILC) for multiple‐input multiple‐output discrete‐time systems that are subject to random disturbances varying from iteration to iteration. Using the super‐vector approach to ILC, statistical expressions are presented for both expectation and variance of the tracking error, and time‐domain conditions are developed to ensure their asymptotic stability and monotonic convergence. It shows that time‐domain conditions can be tied together with an H_∞‐based condition in the frequency domain by considering the properties of block Toeplitz matrices. This makes it possible to apply the linear matrix inequality technique to describe the convergence conditions and to obtain formulas for the control law design. Furthermore, the H_∞‐based approach is shown applicable to ILC design regardless of the system relative degree, which can also be used to address issues of model uncertainty. For a class of systems with a relative degree of one, simulation tests are provided to illustrate the effectiveness of the H_∞‐based approach to robust ILC design. Copyright © 2011 John Wiley & Sons, Ltd.     

Stability analysis of a combined direct variable structure adaptive control – the discrete‐time case

This paper presents the proofs of robust stability of a discrete‐time robust model reference controller combined with variable structure in an adaptive framework. All the proofs of robust stability are derived for the discrete‐time case and are similar to those already existing for the conventional non‐combined case. The controller is applied to a SISO LTI plant with unmodeled dynamics of multiplicative and additive types. It is shown that the combined controller can arbitrarily improve the convergence of the error while maintaining the robustness if compared with the non–combined case. Simulation results illustrate the performance of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.     

A robust adaptive control with unmodeled dynamic for HVDC transmission systems

Utilizing the feature of quick response of HVDC to improve the performance of AC/DC system has become the emphasis to be researched. This paper introduces firstly the principle of the robust adaptive control of nonlinear systems with unmodeled dynamics, then developed the robust adaptive additional control of HVDC with unmodeled dynamics of generator in order to improve stability of power system. The additional control of HVDC with unmodeled dynamics only uses the local signals and its design is simple, furthermore it can obviously improve the stability of power system in different operational conditions. Experimental results using the presented concepts obtained on single machine infinite bus model are also included. These results prove the efficiency of the control scheme. The design process of controller provided a new idea to design controller by use of simplified model. __________ Translated from Journal of Sichuan University (Engineering Science Edition), 2005, 37(5): 154–158 (in Chinese)     

Adaptive set‐point regulation of discrete‐time nonlinear systems

In this paper, adaptive set‐point regulation controllers for discrete‐time nonlinear systems are constructed. The system to be controlled is assumed to have a parametric uncertainty, and an excitation signal is used in order to obtain the parameter estimate. The proposed controller belongs to the category of indirect adaptive controllers, and its construction is based on the policy of calculating the control input rather than that of obtaining a control law. The proposed method solves the adaptive set‐point regulation problem under the assumption that the target state is reachable for each fixed parameter value. Additional feature of the proposed method is that Lyapunov‐like functions have not been used in the construction of the controllers. Copyright © 2015 John Wiley & Sons, Ltd.     

A discrete‐time indirect adaptive multiple‐model actuator failure compensation scheme

A new discrete‐time actuator failure compensation control scheme is developed, using a multiple‐model adaptive control approach which has the capacity to achieve faster and more accurate compensation of failure uncertainties. An individual adaptive system, for each possible failure pattern in a failure pattern set of interest for compensation, is designed using an indirect model reference adaptive control scheme for actuator failure compensation. A multiple‐model control switching mechanism for discrete‐time systems is set up by finding the minimal performance index to select the most appropriate control law. The performance indices are based on the adaptive estimation errors of individual parameterized systems with actuator failures. Simulation results from an aircraft flight control system example are presented to show the desired closed‐loop system stability and tracking performance despite the presence of uncertain actuator failures. Copyright © 2014 John Wiley & Sons, Ltd.     

filtering for switched discrete‐time systems under asynchronous switching: A dwell‐time dependent Lyapunov functional method

In this article, the filtering problem for switched discrete‐time linear systems under asynchronous switching is addressed in the framework of dwell time, where ‘asynchronous switching’ covers more general and practical cases, for example, the switching lags caused by mode identification process are taken into consideration. Firstly, a novel dwell‐time dependent Lyapunov function (DTDLF) is introduced to solve stability and ?₂ gain analysis problems. The main advantage of DTDLF approach is that the derived conditions are all convex in system matrices, so it is convenient to be applied into filter design with performance instead of weighted performance as many other previous results. Thus, on the basis of DTLDF, a dwell‐time dependent filter with time‐varying structure is proposed to achieve the desirable non‐weighted filtering performance. It is notable that the proposed approach can also easily characterize the relationships among filtering performance, dwell time, and asynchronous time. Two examples are provided to validate the theoretical findings in this paper. Copyright © 2014 John Wiley & Sons, Ltd.     

非最小相位系统的终端滑模控制

在重新定义系统输出方法的基础上，提出一种终端滑模控制策略，解决了非最小相位系统难以控制的问题。首先，重新定义系统的输出，通过输入输出线性化，得到系统的输入输出子系统。然后，设计终端滑模控制策略，使输入输出子系统在有限时间收敛到零，并根据系统性能指标要求选择适当的输出定义参数，使零动态子系统在原点附近渐近稳定，从而保证原系统的渐近稳定。仿真结果验证了提出方法的有效性。     

Stabilization of controlled positive discrete‐time T‐S fuzzy systems by state feedback control

This paper deals with sufficient conditions of asymptotic stability and stabilization for nonlinear discrete‐time systems represented by a Takagi–Sugeno‐type fuzzy model whose state variables take only nonnegative values at all times t for any nonnegative initial state. This class of systems is called positive systems. The conditions of stabilizability are obtained with state feedback control. This work is based on multiple Lyapunov functions. The results are presented in linear matrix inequalities form. A real plant is studied to illustrate this technique. Copyright © 2010 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.     

Fault estimation and tolerant control for discrete‐time switched systems with sojourn probabilities

This paper addresses the issue of fault estimation and accommodation for a discrete‐time switched system with actuator faults. Here, we assume that the sojourn probabilities are known a priori. By using the reduced‐order observer method, the sojourn probability approach, and the Lyapunov technique, a fault estimation algorithm is obtained for the considered system. The main objective of this work is to design a dynamic output feedback fault‐tolerant controller based on the obtained fault estimation information such that the closed‐loop discrete‐time switched system with available sojourn probabilities is robustly mean‐square stable and satisfies a prescribed mixed and passivity disturbance attenuation level in the presence of actuator faults. More precisely, a dynamic output feedback fault‐tolerant controller is established in terms of linear matrix inequalities. Finally, numerical examples are provided to illustrate the usefulness and effectiveness of the proposed design technique.     

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.     

Finite‐time dissipativity‐based filter design for networked control systems

This paper investigates the problem of finite‐time boundedness and dissipativity‐based filter design for networked control systems together with parameter uncertainties and random packet dropouts. The packet transmission information is defined by using Bernoulli distributed white sequence which characterizes the measurement conditions. Some new sufficient conditions are established to ensure that the filtering error system is stochastically finite‐time bounded and strictly finite‐time dissipative. These sufficient conditions to design the filter parameters are derived by using linear matrix inequalities and reciprocally convex approach. Finally, an example is given to validate the effectiveness of the proposed filter design.     

Threshold computation for fault detection in a class of discrete‐time nonlinear systems

In this paper, we address the problem of designing robust thresholds for fault detection in discrete‐time nonlinear uncertain systems in the presence of process disturbances. Both constant and dynamic thresholds are proposed. For the computation of constant thresholds, a generalized framework based on signal norms is developed. Different kinds of constant thresholds are studied in the framework proposed. Using linear matrix inequalities (LMI) techniques, algorithms are derived for the computation of these thresholds. Similarly, the dynamic threshold is designed by deriving an inequality on the upper bound of the modulus of the residual signal. This inequality is based on the solution of discrete‐time nonlinear uncertain systems. The simulation examples illustrate that false alarms are successfully eliminated using the proposed thresholds. Copyright © 2010 John Wiley & Sons, Ltd.