Adaptive stabilization of a class of high‐order uncertain nonholonomic systems with unknown control coefficients

This paper is concerned with the globally stabilizing control design for a class of high‐order nonholonomic systems. Compared with the existing literature, the high‐order nonholonomic systems under investigations have more uncertainties and unknowns, such as neither lower nor upper bound is known for each control coefficient of the systems. This renders the existing control methods highly difficult to the control problems of the systems or even inapplicable. In this paper, by defining two new unknown parameters whose dynamic updating laws are properly chosen and also by using the discontinuous coordinates transformation and the method of adding a power integrator, a new design approach is given to the adaptive stabilizing controllers for the systems. A numerical simulation is provided to demonstrate the effectiveness of the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive robust control of nonlinear systems with dynamic uncertainties

In this paper, the discontinuous projection‐based adaptive robust control (ARC) approach is extended to a class of nonlinear systems subjected to parametric uncertainties as well as all three types of nonlinear uncertainties—uncertainties could be state‐dependent, time‐dependent, and/or dynamic. Departing from the existing robust adaptive control approach, the proposed approach differentiates between dynamic uncertainties with and without known structural information. Specifically, adaptive robust observers are constructed to eliminate the effect of dynamic uncertainties with known structural information for an improved steady‐state output tracking performance—asymptotic output tracking is achieved when the system is subjected to parametric uncertainties and dynamic uncertainties with known structural information only. In addition, dynamic normalization signals are introduced to construct ARC laws to deal with other uncertainties including dynamic uncertainties without known structural information not only for global stability but also for a guaranteed robust performance in general. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive robust dynamic surface control with composite adaptation laws

This paper focuses on an adaptive robust dynamic surface control (ARDSC) with composite adaptation laws (CAL) for a class of uncertain nonlinear systems in semi‐strict feedback form. A simple and effective controller has been obtained by introducing dynamic surface control (DSC) technique and designing novel adaptation laws. First, the ‘explosion of terms’ problem caused by backstepping method in the traditional adaptive robust control (ARC) is avoided. Meanwhile, through a new proof philosophy the asymptotical output tracking that the ARC possesses is theoretically preserved. Second, when persistent excitation (PE) condition satisfies, true parameter estimates could be acquired via designing CALs which integrate the information of estimation errors. Finally, simulation results are presented to illustrate the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive estimator-based formation maneuvering control of nonholonomic mobile robots

In this paper, the formation maneuvering control problem for a group of nonholonomic mobile robots with the objective of having a desired formation shape described by distances between pairs of robots and an overall maneuvering velocity is studied. The desired maneuvering velocity, which can be constant or time-varying, is only known to a set of agents. A control scheme consisting of an adaptive estimator and a modified gradient control law is proposed to solve this problem. The adaptive estimator is designed to estimate the desired maneuvering velocity in either constant or time-varying situation. Utilizing the estimated velocity, a modified gradient control law is designed based on the nonholonomic kinematic model so that the objective is achieved. Local asymptotic convergence of the overall system is guaranteed by choosing appropriate control parameters. The effectiveness of the proposed control scheme is demonstrated through simulation results.     

Adaptive state feedback stabilization of more general stochastic high‐order nonholonomic systems

This paper investigates adaptive state feedback stabilization for a class of more general stochastic high‐order nonholonomic systems. By constructing the appropriate Lyapunov function, skillfully combining parameter separation, sign function, and backstepping design methods, an adaptive state feedback controller is designed to eliminate the phenomenon of uncontrollability and guarantee global asymptotic stability in probability of the closed‐loop system. Two simulation examples are used to demonstrate the effectiveness of this method.     

Adaptive fuzzy control for nontriangular form systems with time-varying full-state constraints

This article investigates an adaptive fuzzy tracking control problem for a class of nontriangular form systems with asymmetric time-varying full state constraints. Unknown functions are approximated by the fuzzy logic systems. A domination approach is employed to tackle the nontriangular form structure. Time-varying asymmetric barrier Lyapunov functions (ABLFs) are adopted to ensure full-state constraints satisfaction. Based on the backstepping technique and time-varying ABLFs, an adaptive controller is proposed and guarantees that all the signals in the closed-loop system are ultimately bounded and the time-varying full state constraints are met. Simulation examples are presented to further demonstrate the effectiveness of the proposed approach.     

基于动态面控制的间接自适应神经网络块控制

针对一类可转化为"标准块控制形"的多输入多输出的非线性系统,基于动态面控制技术,提出一种间接自适应神经网络控制器的设计方案.该方法通过引入1阶滤波器,消除了后推设计中由于反复对虚拟控制的求导而导致的复杂性问题,同时完全避免了反馈线性化方法中可能出现的控制器奇异性问题,且无需控制增益矩阵正定、可逆的条件.利用李亚普诺夫方法,证明了闭环系统是半全局一致终结有界,通过适当选取设计常数,跟踪误差可收敛到原点的一个小邻域内.仿真结果表明所提控制方法的有效性.     

Adaptive neural dynamic surface control of MIMO stochastic nonlinear systems with unknown control directions

In this paper, an adaptive neural output‐feedback control approach is considered for a class of uncertain multi‐input and multi‐output (MIMO) stochastic nonlinear systems with unknown control directions. Neural networks (NNs) are applied to approximate unknown nonlinearities, and K‐filter observer is designed to estimate unavailable system's states. Due to utilization of Nussbaum gain function technique in the proposed approach, the singularity problem and requirement to prior knowledge about signs of high‐frequency gains are removed, simultaneously. Razumikhin functional method is employed to deal with unknown state time‐varying delays, so that the offered control approach is free of common assumptions on derivative of time‐varying delays. Also, an adaptive neural dynamic surface control is developed; hence, explosion of complexity in conventional backstepping method is eliminated, effectively. The boundedness of all the resulting closed‐loop signals is guaranteed in probability; meanwhile, convergence of the tracking errors to adjustable compact set in the sense of mean quartic value is also proved. Finally, simulation results are shown to verify and clarify efficiency of the offered approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Reinforcing robustness of adaptive dynamic surface control

Adaptive dynamic surface control (ADSC) design was proposed as an alternative to adaptive backstepping, capable of curing the ‘explosion of complexity’ problem, caused by the repeated differentiations of the so called intermediate control signals. However, as it is clearly demonstrated in this work, ADSC schemes are sensitive to modeling uncertainties and/or additive external disturbances. In fact, it is shown that a uniformly bounded exogenous perturbation of unknown upper bound may easily destabilize the closed‐loop system. Subsequently, a constructive methodology based on the recently developed by the authors prescribed performance control technique, is proposed, which combined with an ADSC design, results in a modified scheme possessing significantly increased robustness properties. Simulation studies illustrate the approach. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Adaptive finite‐time formation tracking control for multiple nonholonomic UAV system with uncertainties and quantized input

An adaptive finite‐time formation tracking control approach is proposed for multiple unmanned aerial vehicle (UAV) system with quantized input signals in this paper. The UAVs are described by nonholonomic kinematic model and autopilot model with uncertainties. An enhanced hysteretic quantizer is introduced to avoid chattering, and some restrictions are released by using a new quantization decomposition method. Based on backstepping technique and finite‐time Lyapunov stability theory, the adaptive finite‐time controller is designed for the trajectory tracking of the multi‐UAV formation. The nonholonomic constraints are solved by a transverse function. A transformation is introduced to the control input signals to eliminate the quantization effect. Stability analysis proves that the tracking errors can converge to a small neighborhood of the origin within finite time and all the closed‐loop signals are semiglobally finite‐time bounded. The effectiveness of the proposed control approach is validated by simulation and experiment.     

Adaptive dynamic surface control of stochastic nonstrict-feedback constrained nonlinear systems with input and state unmodeled dynamics

In this paper, the issue of adaptive neural control is discussed for a class of stochastic nonstrict-feedback constrained nonlinear systems with input and state unmodeled dynamics. A dynamic signal produced by the first-order auxiliary system is employed to deal with the dynamical uncertain terms. Radial basis function neural networks are used to reconstruct unknown nonlinear continuous functions. With the help of the mean value theorem and Young's inequality, only one learning parameter is adjusted online at recursive each step. Using the hyperbolic tangent function as nonlinear mapping, the output constrained stochastic nonstrict-feedback system in the presence of unmodeled dynamics is transformed into a novel unconstrained stochastic nonstrict-feedback system. Based on dynamic surface control technology and the property of Gaussian function, adaptive neural control is developed for the transformed stochastic nonstrict-feedback system. The output abides by stochastic constraints in probability. By the Lyapunov method, all signals of the closed-loop control system are proved to be semi-global uniform ultimate bounded (SGUUB) in probability. The obtained theoretical findings are verified by two numerical examples.     

Adaptive fuzzy output feedback backstepping control of pure‐feedback nonlinear systems via dynamic surface control technique

In this paper, an adaptive fuzzy backstepping dynamic surface control approach is considered for a class of uncertain pure‐feedback nonlinear systems with immeasurable states. Fuzzy logic systems are first employed to approximate the unknown nonlinear functions, and then an adaptive fuzzy state observer is designed to estimate the immeasurable states. By the combination of the adaptive backstepping design with a dynamic surface control technique, an adaptive fuzzy output feedback backstepping control approach is developed. It is proven that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded, and the observer and tracking errors converge to a small neighborhood of the origin by choosing the design parameters appropriately. Simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

A simplified adaptive tracking control for nonlinear pure-feedback systems with input delay and full-state constraints

This article investigated the adaptive backstepping tracking control for a class of pure-feedback systems with input delay and full-state constraints. With the help of mean value theorem, the system is transformed into strict-feedback one. By introducing the Pade approximation method, the effect of input delay was compensated. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. Furthermore, in order to reduce the computational burden by introducing backstepping design technique, dynamic surface control technique was employed. In addition, the number of the adaptive parameters that should be updated online was also reduced. By utilizing the barrier Lyapunov function, the closed-loop nonlinear system is guaranteed to be semi-globally ultimately uniformly bounded. Finally, a numerical simulation example is given to show the effectiveness of the proposed control strategy.     

Adaptive output feedback dynamic surface control of stochastic nonlinear systems with state and input unmodeled dynamics

In this paper, an adaptive neural output feedback control scheme is investigated for a class of stochastic nonlinear systems with unmeasured states and four kinds of uncertainties including uncertain nonlinear function, dynamic disturbance, input unmodeled dynamics, and stochastic inverse dynamics. The unmeasured states are estimated by K‐filters, and stochastic inverse dynamics is dealt with by constructing a changing supply function. The considered input unmodeled dynamic subsystem possesses nonlinear feature, and a dynamic normalization signal is introduced to counteract the unstable effect produced by the input unmodeled dynamics. Combining dynamic surface control technique with stochastic input‐to‐state stability, small‐gain condition, and Chebyshev's inequality, the designed robust adaptive controller can guarantee that all the signals in the closed‐loop system are bounded in probability, and the error signals are semi‐globally uniformly ultimately bounded in mean square or the sense of four‐moment. Simulation results are provided to verify the effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.     

感应电机的神经网络鲁棒自适应动态面控制

针对感应电机的高阶、强耦合的非线性,设计一种具有自适应性和鲁棒性的动态面控制律,以实现对感应电机的控制。首先通过变量代换,将五阶感应电机模型变为块三角形式;接着采用神经网络逼近,将模型转化为含有结构不确定性和参数不确定性的参数化模型。对于感应电机系统中的参数不确定性,在动态面控制方法的基础上设计参数自适应律,在线估计其未知参数;对于感应电机系统中的结构不确定性,设计鲁棒控制律,使得电机控制系统具有鲁棒性。最后通过仿真实现,以验证所提出的控制方法的有效性与实用性。     

SVG控制系统的稳定性研究

根据静止无功发生器SVG(Static Var Generator)的结构特点,建立了相应的微分方程。考虑到实际系统的非线性周期性时变系数的影响,将逆变器的外部电气性能,用直流量与交流量之间的矢量关系进行了线性化处理,并根据劳斯一胡尔维茨稳定性判据得出了电力电子技术应用时的非线性控制参数与系统参数之间的稳定性关系,根据稳定性的表达式得到了静态稳定结果。     

Distributed adaptive control for multiple nonholonomic systems with nonlinearly parameterized uncertainties

This paper investigates the distributed adaptive control problem for multiple nonholonomic systems with nonlinearly parameterized uncertainties. Under the assumption that the graph topology is directed and the leader is globally reachable, distributed adaptive controllers are designed recursively by using backstepping technique and algebra graph theory. It is shown that all the followers' outputs will exponentially converge to the reference output signal while all the signals of the closed‐loop system are bounded. Finally, two simulation examples are given to demonstrate the effectiveness of the control scheme.     

Multiple‐model adaptive robust dynamic surface control with estimator resetting

A multiple‐model adaptive robust dynamic surface control with estimator resetting is investigated for a class of semi‐strict feedback nonlinear systems in this paper. The transient performance is mainly considered. The multiple models are composed of fixed models, one adaptive model, and one identification model that can be obtained when the persistent exciting condition is satisfied. The transient performance of the final tracking system can be improved significantly by designing proper switching mechanism during the parameter tuning procedure. The semi‐globally uniformly ultimately bounded stability of the closed‐loop system can be easily achieved because of the framework of adaptive robust dynamic surface control. Numerical examples are provided to demonstrate the effectiveness of the proposed multiple‐model controller. Copyright © 2014 John Wiley & Sons, Ltd.