Experience replay–based output feedback Q‐learning scheme for optimal output tracking control of discrete‐time linear systems

This paper focuses on solving the adaptive optimal tracking control problem for discrete‐time linear systems with unknown system dynamics using output feedback. A Q‐learning‐based optimal adaptive control scheme is presented to learn the feedback and feedforward control parameters of the optimal tracking control law. The optimal feedback parameters are learned using the proposed output feedback Q‐learning Bellman equation, whereas the estimation of the optimal feedforward control parameters is achieved using an adaptive algorithm that guarantees convergence to zero of the tracking error. The proposed method has the advantage that it is not affected by the exploration noise bias problem and does not require a discounting factor, relieving the two bottlenecks in the past works in achieving stability guarantee and optimal asymptotic tracking. Furthermore, the proposed scheme employs the experience replay technique for data‐driven learning, which is data efficient and relaxes the persistence of excitation requirement in learning the feedback control parameters. It is shown that the learned feedback control parameters converge to the optimal solution of the Riccati equation and the feedforward control parameters converge to the solution of the Sylvester equation. Simulation studies on two practical systems have been carried out to show the effectiveness of the proposed scheme.     

Adaptive output feedback control of uncertain nonlinear systems with input delay and output constraint

This paper proposes an adaptive neural‐network control design for a class of output‐feedback nonlinear systems with input delay and unmodeled dynamics under the condition of an output constraint. A coordinate transformation with an input integral term and a Nussbaum function are combined to solve the problem of the input possessing both time delay and unknown control gain. By utilizing a barrier Lyapunov function and designing tuning functions, the adjustment of multiparameters is handled with a single adaptive law. The uncertainty of the system is approximated by dynamic signal and radial basis function neural networks (RBFNNs). Based on Lyapunov stability theory, an adaptive tracking control scheme is developed to guarantee all the signals of the closed‐loop systems are semiglobally uniformly ultimately bounded, and the output constraint is not violated.     

Adaptive fuzzy logic load frequency control of multi-area power system

Based on indirect adaptive fuzzy control technique, a new load frequency control (LFC) scheme for multi-area power system is proposed. The power systems under study have the characterization of unknown parameters. Local load frequency controller is designed using the frequency and tie-line power deviations of each area. In the controller design, the approximation capabilities of fuzzy systems are employed to identify the unknown functions, formulate suitable adaptive control law and updating algorithms for the controller parameters. It is proved that the proposed controller ensures the boundedness of all variables of the closed-loop system and the tracking error. Moreover, in the proposed controller an auxiliary control signal is introduced to attenuate the effect of fuzzy approximation error and to mitigate the effect of external disturbance on the tracking performance. Simulation results of a three-area power system are presented to validate the effectiveness of the proposed LFC and show its superiority over a classical PID controller.     

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.     

Adaptive tracking control for a class of plants with uncertain parameters and non-linearities

We consider systems in which the plant parameters and non-linearities can vary unpredictably within known bounds. Their variations can be arbitrarily fast, even discontinuous. The desired plant output is defined as the output response to a governing input of an appropriately selected reference model. For this class of problems the concept of stable and exponentially stable tracking is defined. The problem studied is the synthesis of an adaptive controller having adjustable parameters to guarantee (stable, exponentially stable) tracking for the plant subject to the action of external disturbances. A solution to the problem is established for a class of plants determined by a special structure. Simulation results illustrate excellent tracking behaviour for a second-order plant with unknown parameters and non-linearities having unpredictable variations.     

Adaptive control of non‐linear systems with unknown virtual control coefficients

This paper deals with state feedback adaptive control of parametric‐strict‐feedback (triangular) non‐linear systems with unknown virtual control coefficients. A priori knowledge of the signs of the virtual coefficients is not required, and control signals and adaptive laws are smooth. Asymptotic tracking of smooth reference signals is achieved while all the variables remain bounded. The proposed algorithms make use of backstepping and tuning functions, and enlarge the class of non‐linear systems with unknown parameters for which asymptotic output tracking can be achieved. Copyright © 2000 John Wiley & Sons, Ltd.     

Robust adaptive control for unmatched systems with guaranteed parameter estimation convergence

This paper provides a modified model reference adaptive control (MRAC) scheme to achieve better transient control performance for systems with unknown unmatched dynamics, where an adaptive law with guaranteed convergence is introduced. We first revisit the standard MRAC system and analyze the tracking error bound by using L₂‐norm and Cauchy‐Schwartz inequality. Based on this analysis, we suggest a feasible way to compensate the undesired transient dynamics induced by the gradient descent–based adaptive laws subject to sluggish convergence or even parameter drift. Then, a modified adaptive law with an alternative leakage term containing the parameter estimation error is developed. With this adaptive law, the convergence of both the estimation error and tracking error can be proved simultaneously. This enhanced convergence property can contribute to deriving smoother control signal and improved control response. Moreover, this paper provides a simple and numerically feasible approach to online verify the well‐known persistent excitation condition by testing the positive definiteness of an introduced auxiliary matrix. Comparative simulations based on a benchmark 3‐DOF helicopter model are given to validate the effectiveness of the proposed MRAC approach and show the improved performance over several other MRAC schemes.     

Adaptive fuzzy finite-time fault-tolerant control of nonlinear systems with state constraints and input quantization

This article concentrates on an adaptive finite-time fault-tolerant fuzzy tracking control problem for nonstrict feedback nonlinear systems with input quantization and full-state constraints. By utilizing the fuzzy logic systems and less adjustable parameters method, the unknown nonlinear functions are addressed in each step process. In addition, a dynamic surface control technique combined with fuzzy control is introduced to tackle the variable separation problem. The problem for the effect of quantization and unlimited number of actuator faults is tackled by a damping term with smooth function in the intermediate control law. Finite-time stability is achieved by combining barrier Lyapunov functions and backstepping method. The finite-time controller is designed such that all the responses of the systems are semiglobal practical finite-time stable and ensured to remain in the predefined compact sets while tracking error converges to a small neighborhood of the origin in finite time. Finally, simulation examples are utilized to testify the validity of the investigated strategy.     

Closed‐loop iterative learning control for non‐linear systems with initial shifts

This paper is concerned with the problem of the iterative learning control with current cycle feedback for a class of non‐linear systems with well‐defined relative degree. The tracking error caused by a non‐zero initial shift is detected as extended D‐type learning algorithm is applied. The defect is overcome by adding terms including the output error, its derivatives as well as integrals. Asymptotic tracking of the final output to the desired trajectory is guaranteed. As an alternative approach, an initial rectifying action is introduced in the extended D‐type learning algorithm and shown effective to achieve the desired trajectory jointed smoothly with a transitional trajectory from the starting position. Also these algorithms with adjustable tracking interval ensure better robustness performance in the presence of initial shifts. Numerical simulation is conducted to demonstrate the theoretical results. Copyright © 2002 John Wiley & Sons, Ltd.     

Adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems with input delays and state time‐varying delays

In this paper, an adaptive fuzzy backstepping dynamic surface control (DSC) approach is developed for a class of MIMO nonlinear systems with input delays and state time‐varying delays. The unknown continuous nonlinear functions are expressed as the linearly parameterized form by using the fuzzy logic systems, and then, by combining the backstepping technique, the appropriate Lyapunov–Krasovskii functionals, and the ‘minimal learning parameters’ algorithms with the DSC approach, the adaptive fuzzy tracking controller is designed. Our development is able to eliminate the problem of ‘explosion of complexity’ inherent in the existing backstepping‐based methods. It is proven that the proposed design method can guarantee that all the signals in the closed‐loop system are bounded and the tracking error is smaller than a prescribed error bound. Finally, simulation results are provided to show the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Passivity‐based control for stabilization,regulation and tracking purposes of a class of nonlinear systems

In this paper, a new passivity‐based control (PBC) scheme based on state feedback is proposed in order to solve tracking, regulation and stabilization problems for a class of multi‐input multi‐output (MIMO) nonlinear systems expressed in the normal form, with time‐invariant parameters and locally bounded reference weakly minimum phase. For the proposed control scheme two new different state feedbacks, one non‐adaptive for the case when the system parameters are assumed to be known and the other adaptive for the case of unknown parameters, are developed. For the adaptive case it is assumed that the unknown parameters appear linearly in the equations. Analysis of the transient behaviour of the proposed control schemes is presented through the simulation of two examples. Copyright © 2006 John Wiley & Sons, Ltd.     

Adaptive compensation for infinite number of actuator failures with an application to flight control

In this paper, a new adaptive compensation control scheme is proposed for a class of nonlinear systems with unknown parameters and unknown actuator failures. The normal operation case and different failure cases of actuators are unified through a time‐varying model. By introducing a smooth function, an integrable auxiliary signal, and a bound estimation approach, the effect of failures is successfully compensated for, and the total number of failures is not restricted to be finite. It is shown that all closed‐loop signals are globally uniformly bounded, and the tracking error converges to zero asymptotically regardless of the possibly infinite number of actuator failures. An application to the longitudinal dynamic model of a twin otter aircraft is presented to illustrate the effectiveness of the proposed scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

Nonlinear adaptive filtering using kernel‐based algorithms with dictionary adaptation

Nonlinear adaptive filtering has been extensively studied in the literature, using, for example, Volterra filters or neural networks. Recently, kernel methods have been offering an interesting alternative because they provide a simple extension of linear algorithms to the nonlinear case. The main drawback of online system identification with kernel methods is that the filter complexity increases with time, a limitation resulting from the representer theorem, which states that all past input vectors are required. To overcome this drawback, a particular subset of these input vectors (called dictionary) must be selected to ensure complexity control and good performance. Up to now, all authors considered that, after being introduced into the dictionary, elements stay unchanged even if, because of nonstationarity, they become useless to predict the system output. The objective of this paper is to present an adaptation scheme of dictionary elements, which are considered here as adjustable model parameters, by deriving a gradient‐based method under collinearity constraints. The main interest is to ensure a better tracking performance. To evaluate our approach, dictionary adaptation is introduced into three well‐known kernel‐based adaptive algorithms: kernel recursive least squares, kernel normalized least mean squares, and kernel affine projection. The performance is evaluated on nonlinear adaptive filtering of simulated and real data sets. As confirmed by experiments, our dictionary adaptation scheme allows either complexity reduction or a decrease of the instantaneous quadratic error, or both simultaneously. Copyright © 2015 John Wiley & Sons, Ltd.     

基于Lyapunov稳定性理论的电励磁直线同步电机自适应控制

为了提高直线伺服系统的动态性能,克服电励磁直线同步电机存在的参数时变性,设计模型参考自适应速度控制器。系统内环是基于参考模型的速度跟踪控制器,外环自适应机构在线调整速度跟踪控制器的可调参数并使参考模型输出速度与控制对象输出速度之间的广义速度误差趋近于零。采用基于Lyapunov稳定性理论的模型参考自适应速度控制器设计方法,在保证广义速度跟踪误差收敛至零的同时,还保证了模型参考自适应速度控制系统具有稳定性和收敛性。采用欧拉数值积分方法,经过计算机数值仿真计算得到参考模型与控制对象的速度输出和初级交轴电流状态变量的时域响应曲线,验证了该自适应速度控制系统具有全局收敛性。     

Robust adaptive output‐feedback control for a class of nonlinear systems with hysteresis compensation controller

In this paper, a robust adaptive output‐feedback dynamic surface control scheme is proposed for a class of single‐input single‐output nonlinear systems preceded by unknown hysteresis with the following features: (1) a hysteresis compensator is designed in the control signal to compensate the hysteresis nonlinearities with only the availability of the output of the control system; (2) by estimating the norm of the unknown parameter vector and the maximum value of the hysteresis density function, the number of the estimated parameters is reduced, which implies that the computational burden is greatly reduced; (3) by introducing the initializing technique, the initial conditions of the state observer and adaptive laws of unknown parameters can be properly chosen, and the arbitrarily small norm of the tracking error is achieved. It is proved that all the signals in the closed‐loop system are ultimately uniformly bounded and can be arbitrarily small. Simulation results show the validity of the proposed scheme.     

Distributed cooperative neural control of a class of nonlinear multi-agent systems with unknown time-varying control coefficient

This article studies the leader–follower cooperative tracking problem of a class of multi-agent systems with unknown nonlinear dynamics. As the load of the following agent may be changing throughout the whole work process, we consider the control coefficient of the following agent to be time-varying and nonlinear instead of constant, which is more practical. All agents are connected by the directed communication graph with weighted topology. The followers can have unknown nonidentical nonlinear dynamics and external disturbances. The nonautonomous leader generates the reference trajectory for only part of the followers and others can only receive the information from their neighbors. To achieve the ultimate synchronization of all following agents to the leader, the novel cooperative adaptive control protocols are designed based on the neural approximation and adaptive updating mechanism. A novel singularity-avoided adaptive updating law is proposed to estimate the control coefficient and compensate for the unknown dynamics online. Lyapunov theory is used to prove the ultimate boundedness of the synchronization tracking error. The correctness and effectiveness of the presented control scheme are demonstrated by two simulations in SISO and MIMO cases, respectively.     

A gain‐scheduled control algorithm for input constrained systems to track time‐varying references using controller state resets

In this paper, we propose a control law for a discrete‐time linear system with actuator saturation to track time‐varying reference signals. The proposed control law consists of a feedback controller and a target recalculation mechanism. The feedback controller includes an integrator to achieve zero steady‐state error in the case where the reference signal is constant. The feedback gains of the controller are parameterized by a single scheduling parameter. In the proposed control algorithm, when the tracking error is large, a modified reference signal is computed by the target recalculation mechanism so that feasibility of the algorithm and stability of the control system are guaranteed at all times. At this stage, the controller state is modified online so that the tracking control performance is improved. Further, when the tracking error becomes small, the scheduling parameter and the controller state are updated simultaneously so that the tracking control performance is improved. The problems of determining the scheduling parameter, the controller state, and the modified reference signal are reduced to convex optimization problems with linear matrix inequality constraints. The effectiveness of the proposed control method is shown through an experiment. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Adaptive neural control for nonstrict‐feedback stochastic nonlinear time‐delay systems with input and output constraints

This paper investigates an adaptive neural tracking control for a class of nonstrict‐feedback stochastic nonlinear time‐delay systems with input saturation and output constraint. First, the Gaussian error function is used to represent a continuous differentiable asymmetric saturation model. Second, the appropriate Lyapunov‐Krasovskii functional and the property of hyperbolic tangent functions are used to compensate the time‐delay effects, the neural network is used to approximate the unknown nonlinearities, and a barrier Lyapunov function is designed to ensure that the output parameters are restricted. At last, based on Lyapunov stability theory, a robust adaptive neural control method is proposed, and the designed controller decreases the number of learning parameters and thus reduces the computational burden. It is shown that the designed neural controller can ensure that all the signals in the closed‐loop system are 4‐Moment (or 2 Moment) semi‐globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin. Two examples are given to further verify the effectiveness of the proposed approach.     

Adaptive control for speed‐sensorless induction motors with uncertain load torque and rotor resistance

The problem of controlling a speed‐sensorless induction motor is addressed. Smooth reference signals for rotor speed and flux modulus are required to be tracked for any unknown constant values of load torque and rotor resistance within known bounds. A fourth order non‐linear adaptive tracking control is presented which is based on a novel rotor speed observer and on two identifiers for the uncertain parameters; it guarantees asymptotic rotor speed tracking and exponential rotor flux modulus tracking with an explicitly computed domain of attraction. The closed‐loop performances are illustrated by simulation. Copyright © 2005 John Wiley & Sons, Ltd.     

Decentralized stochastic adaptive control of interconnected systems

This paper considers the stochastic adaptive control problem for a class of large-scale systems formed by arbitrary interconnection of subsystems with unknown parameters and non-linearities. For the estimation of the unknown parameters of the local controllers, stochastic approximation algorithms are used. Conditions sufficient for global stability of the overall system are established. It is shown that the overall tracking error is bounded by a quantity depending on the size of interconnections.