Robust adaptive MPC for constrained uncertain nonlinear systems

In this paper, we consider the problem of adaptive model predictive control subject to exogenous disturbances. Using a novel set‐based adaptive estimation, the problem of robust adaptive MPC is proposed and solved for a class of linearly parameterized uncertain nonlinear systems subject to state and input constraints. Two formulations of the adaptive MPC routine are proposed. A general minmax approach is considered. A Lipschitz‐based formulation is also proposed. The closed‐loop robust stability of both approaches is demonstrated. The Lipschitz‐based approach avoids the need for a minmax optimization problem and is amenable to real‐time computation. A simple chemical reactor simulation example is presented that demonstrates the effectiveness of the technique. Copyright © 2010 John Wiley & Sons, Ltd.     

Mapping filtered forwarding‐based robust adaptive control for uncertain nonlinear systems with input constraint

This work develops a robust adaptive control algorithm for uncertain nonlinear systems with parametric uncertainties and external disturbances satisfying an extended matching condition. This control method is implemented in the framework of a mapping filtered forwarding‐based technique. As an attractive alternative of the adaptive backstepping method, this bottom‐up strategy forms a virtual controller and a parameter updated law at each step of the design, where Lyapunov functions and the prior knowledge of system parameters are not required. The boundedness of all signals is guaranteed by using Barbalat's lemma. According to immersion relationship, a compliant behavior of systems behaves accordingly to the lower‐order target dynamics. Furthermore, input constraints are handled by estimating a saturated scaling. A spring, mass, and damper system is used to demonstrate the controller performances via simulation results.     

一类不确定非线性系统的自适应模糊跟踪控制

针对一类不确定非线性连续系统，用模糊系统对未知函数进行逼近的基础上，利用Lyapunov稳定性理论，提出了一种新的自适应模糊跟踪控制算法，此算法的特点是，无论取多少条模糊系统的规则，自适应学习的参数只有一个，便于实现，而且还能确保闭环系统渐近稳定，并使系统的跟踪误差为零，仿真研究表明，所提出的算法是有效的。     

Self-triggered adaptive prescribed-time tracking control for stochastic nonlinear systems

This paper proposes a self-triggered (ST) adaptive prescribed-time tracking control method for a class of stochastic nonlinear systems. Different from the existing results, an improved ST mechanism is proposed by adding a judgment condition to reduce the negative effect of excessive design interval on system performance. Based on the one-to-one mapping and backstepping technique, an adaptive prescribed-time tracking control method is proposed, which can make the error converge to the predefined precision set within the predetermined time. Simultaneously, applying the Lyapunov stability method, the boundedness of all signals in the closed-loop system can be ensured. Finally, a detailed simulation example is provided to show the effectiveness of the proposed control strategy.     

Adaptive control for nonlinear uncertain systems with actuator amplitude and rate saturation constraints

A direct adaptive nonlinear tracking control framework for multivariable nonlinear uncertain systems with actuator amplitude and rate saturation constraints is developed. To guarantee asymptotic stability of the closed‐loop tracking error dynamics in the face of amplitude and rate saturation constraints, the control signal to a given reference (governor or supervisor) system is modified to effectively robustify the error dynamics to the saturation constraints. Illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2008 John Wiley & Sons, Ltd.     

Finite-time adaptive control for nonlinear systems with uncertain parameters based on the command filters

The trajectory tracking control problem for a class of nonlinear systems with uncertain parameters is considered in this article. A new adaptive finite-time tracking control is designed based on the adaptive backstepping method via the command filters. The command filter mechanism can avoid the calculation of partial derivatives and solve the “explosion of complexity” in the backstepping design. The compensation signals are introduced to eliminate errors produced by the command filters. The proposed adaptive backstepping control can guarantee the tracking error remains in a small neighborhood of the origin in finite time, while the practical finite-time stability of the control systems with uncertain parameters is proven by the stability criterion. The effectiveness of the proposed scheme is verified by some simulation results.     

基于神经网络的一类非线性系统自适应滑模控制

针对可以分解为标称系统和不确定系统两部分的SISO非线性系统,提出了一种基于神经网络的自适应滑模控制方案。控制器由标称控制律和补偿控制律组成,标称控制律用来控制标称系统,补偿控制律是基于Lyapunov稳定性理论设计的自适应神经滑模控制律,用来控制不确定系统,而神经网络用来逼近系统的不确定性。理论分析和计算机仿真都证明,本文提出的控制策略不但能解决这类系统的轨迹跟踪控制问题,而且可以保证闭环系统的渐近稳定性。     

Novel fuzzy adaptive finite-time nonsmooth control for uncertain nonlinear systems

In this article, a novel fuzzy adaptive finite-time nonsmooth controller is developed to handle the finite-time tracking problem for a class of uncertain nonlinear systems. Different from traditional fuzzy adaptive approximation methods, proposed method contains only one adaptive parameter, no matter how many states there are in the system. By constructing a new Lyapunov function with prescribed performance bound, the transient and steady performances of control system can be ensured. Further, based on a criterion of finite-time semiglobal practical stability and backstepping technology, a novel fuzzy adaptive finite-time nonsmooth control method is designed. It can be demonstrated that proposed control can effectively ensure tracking error tends to small neighborhood in a finite time. Finally, two examples have been simulated by the proposed control method, and it shows effective tracking performance.     

An improved adaptive dynamic surface control approach for uncertain nonlinear systems

Dynamic surface control (DSC) was developed to eliminate the “explosion of complexity” problem in backstepping procedure. However, as demonstrated in this paper, the obtained results by the existing DSC technique are somewhat conservative, which may pose difficulties in system debugging for realistic applications. This work addresses a modification that yields an improved adaptive DSC approach for tracking control of a class of semi‐strict feedback systems. The new method introduces nonlinear adaptive filters instead of the first‐order low pass ones to avoid repeatedly differentiating the virtual control signals. Meanwhile, novel flat zone introduced Lyapunov functions, which have dead zones in the prespecified neighborhood of the origin, are employed to design and analyze the improved robust adaptive control law. As a result, the developed control scheme exhibits three distinct features in comparison with the existing DSC strategy as follows: (1) global rather than semiglobal tracking is achieved even in the presence of nonlinear function nonlinearities; (2) the ultimate tracking accuracy can be exactly known before the controller is implemented; and (3) the ranges of the design parameters to guarantee the closed‐loop stability and ultimate tracking accuracy can be completely determined a priori, and the design parameters can be freely chosen from the feasible ranges to improve the control performance. Finally, two examples are presented to confirm the effectiveness of the established approach.     

Global adaptive regulation control for a class of nonlinear systems with unknown control coefficients

This paper is concerned with the global asymptotic regulation control problem for a class of nonlinear uncertain systems with unknown control coefficients. The allowed class of uncertainties include unmeasured input‐to‐state stable (ISS) and/or weaker integral ISS (iISS) inverse dynamics, parametric uncertainties, and uncertain nonlinearities. By using the Nussbaum‐type gain technique and changing the ISS/integral ISS inverse dynamics supply rates, we design a dynamic output feedback controller which could guarantee that the system states are asymptotically regulated to the origin from any initial conditions, and the other signals are bounded in closed‐loop systems. The numerical example of a simple pendulum with all unknown parameters and without velocity measurement illustrates our theoretical results. The simulation results demonstrate its efficacy. Copyright © 2015 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.     

Observer‐based fuzzy adaptive quantized control for uncertain nonlinear multiagent systems

This paper focuses on consensus quantized control design problem for uncertain nonlinear multiagent systems with unmeasured states. Every follower can be denoted through a system with unmeasurable states, hysteretic quantized input, and unknown nonlinearities. Fuzzy state observer and Fuzzy logic systems are employed to estimate unmeasured states and approximate unknown nonlinear functions, respectively. The hysteretic quantized input can be split into two bounded nonlinear functions to avoid chattering problem. By combining adaptive backstepping and first‐order filter signals, an observer‐based fuzzy adaptive quantized control scheme is designed for each follower. All signals exist in closed‐loop systems are semiglobally uniformly ultimately bounded, and all followers can accomplish a desired consensus results. Finally, a numerical example is employed to elaborate the effectiveness of proposed control strategy.     

Observer‐based adaptive neural control of uncertain MIMO nonlinear systems with unknown control direction

This paper investigates adaptive neural network output feedback control for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems with an unknown sign of control gain matrix. Because the system states are not required to be available for measurement, an observer is designed to estimate the system states. In order to deal with the unknown sign of control gain matrix, the Nussbaum‐type function is utilized. By using neural network, we approximated the unknown nonlinear functions and perfectly avoided the controller singularity problem. The stability of the closed‐loop system is analyzed by using Lyapunov method. Theoretical results are illustrated through a simulation example. Copyright © 2012 John Wiley & Sons, Ltd.     

Decentralized prescribed performance adaptive tracking control for Markovian jump uncertain nonlinear systems with input saturation

A decentralized prescribed performance adaptive tracking control problem is investigated for Markovian jump uncertain nonlinear interconnected large‐scale systems. The considered interconnected large‐scale systems contain unknown nonlinear uncertainties, unknown control gains, actuator saturation, and Markovian jump signals, and the Markovian jump subsystems are in the form of triangular structure. First, by defining a novel state transformation with the performance function, the prescribed performance control problem is transformed to stabilization problem. Then, introducing an intermediate control signal into the control design, employing neural network to approximate the unknown composite nonlinear function, and based on the framework of the backstepping control design and adaptive estimation method, a corresponding decentralized prescribed performance adaptive tracking controller is designed. It is proved that all the signals in the closed‐loop system are bounded, and the prescribed tracking performances are guaranteed. A numerical example is provided to illustrate the effectiveness of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.     

一类不确定非线性系统的鲁棒镇定

针对一类含有不确定性的非线性系统,首先通过精确线性化方法,将其变为一种规范型形式,在一定的不确定性的假设条件下,构造了鲁棒控制器,仿真算例说明了方法的有效性。     

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.     

Robust adaptive sliding mode control for uncertain delta operator systems

In this paper, a robust adaptive sliding mode controller is presented for delta operator systems with mismatched uncertainties and exogenous disturbances. The parameters of the delta operator system are taken for norm‐bounded uncertainties. The exogenous disturbance is also assumed to be bounded. After the statement of a sufficient condition for the existence of linear sliding surface based on linear matrix inequality technique, a robust reaching motion control method for delta operator systems is presented. Afterwards, an adaptive sliding mode controller for delta operator systems is designed. A bridge between the robust adaptive sliding mode control and the delta operator system framework is made. Numerical example is given to illustrate the effectiveness of the developed techniques. Copyright © 2009 John Wiley & Sons, Ltd.     

Nonlinear control for uncertain nonlinear systems with unknown control directions using less or no parameter estimates

For the parametric strict‐feedback nonlinear systems with unknown virtual control coefficients and unknown control directions, the control schemes presented in the existing literature have the disadvantage of overparametrization. In this paper, a novel systematic design procedure is developed to solve the overparametrization problem. Two nonlinear controllers are designed by combining the backstepping technique and the Nussbaum gain approach. A main advantage of the proposed controllers is that they contain less or no parameter estimates that need to be updated online. In the first scheme, the number of the estimated parameters is equal to the dimension of the controlled system. In the second scheme, no parameter estimates are required. In both of the control schemes, the boundedness of all the closed‐loop signal is guaranteed, and the asymptotic convergence of the system states is achieved. An example is provided to demonstrate the effectiveness of the proposed design approaches. Copyright © 2014 John Wiley & Sons, Ltd.     

Observer-based finite time adaptive fault tolerant control for nonaffine nonlinear systems with actuator faults and disturbances

This paper studies the problem of observer-based finite time adaptive fault tolerant control for nonaffine nonlinear systems with actuator faults and disturbances. Based on mean value theorem and convex combination method, a adaptive neural observer with virtual control coefficients is designed to estimate the systems states. Then, by using funnel Lyapunov function and backstepping method, a finite time control scheme is designed in the presence of disturbances and actuator faults. The stability analysis proves that tracking errors can converge to the prescribed performance bound in a finite time and all signals are uniformly ultimately bounded. Finally, simulation results verify efficiency of the studied approach.     

Adaptive finite-time output feedback control for Markov jumping nonlinear systems

In this article, the problem of output feedback tracking control for uncertain Markov jumping nonlinear systems is studied. A finite-time control scheme based on command filtered backstepping and adaptive neural network (NN) technique is given. The finite-time command filter solves the problem of differential explosions for virtual control signals, the NN is utilized to approximate the uncertain nonlinear dynamics and the adaptive NN observer is applied to restructure the state of system. The finite-time error compensation mechanism is established to compensate the errors brought by filtering process. The proposed finite-time tracking control algorithm can ensure that the solution of the closed-loop system is practically finite-time stable in mean square. Two simulation examples are employed to demonstrate the effectiveness of the proposed control algorithm.