Decentralized adaptive stabilization in the presence of unknown backlash-like hysteresis

Due to the difficulty of handling both hysteresis and interactions between subsystems, there is still no result available on decentralized stabilization of unknown interconnected systems with hysteresis, even though the problem is practical and important. In this paper, we provide solutions to this challenging problem by proposing two new schemes to design decentralized output feedback adaptive controllers using backstepping approach. For each subsystem, a general transfer function with arbitrary relative degree is considered. The interactions between subsystems are allowed to satisfy a nonlinear bound with certain structural conditions. In the first scheme, no knowledge is assumed on the bounds of unknown system parameters. In case that the uncertain parameters are inside known compact sets, we propose an alternative scheme where a projection operation is employed in the adaptive laws. In both schemes, the effects of the hysteresis and the effects due to interactions are taken into consideration in devising local control laws. It is shown that the designed local adaptive controllers can ensure all the signals in the closed-loop system bounded. A root mean square type of bound is obtained for the system states as a function of design parameters. This implies that the transient system performance can be adjusted by choosing suitable design parameters. With Scheme II, the proposed control laws allow arbitrarily strong interactions provided their upper bounds are available. In the absence of hysteresis, perfect stabilization is ensured and the L₂ norm of the system states is also shown to be bounded by a function of design parameters when the second scheme is applied.     

Decentralized adaptive stabilization for interconnected systems with dynamic input-output and nonlinear interactions

This paper considers the problem of robust decentralized adaptive output feedback stabilization for a class of interconnected systems with dynamic input and output interactions and nonlinear interactions by using MT-filters and the backstepping design method. It is shown that the closed-loop decentralized system based on MT-filters is globally uniformly bounded, all the signals except for the parameter estimates can be regulated to zero asymptotically, and the L₂ and L_∞ norms of the system outputs are also be bounded by functions of design parameters. The scheme is demonstrated by a simulation example.     

Adaptive backstepping control of uncertain systems with unknown input time-delay

In this paper, we establish the robustness of adaptive controllers designed using the standard backstepping technique with respect to unmodeled dynamics involving unknown input time delay. While noting that some results on robust stabilization of non-minimum phase systems using the backstepping technique are available, we realize that the standard adaptive backstepping technique has only been shown applicable to unknown minimum phase systems. Another significance of our result is to enable the class of systems stablizable by adaptive backstepping controllers to cross the boundary of minimum phase systems, since systems with input time delay belong to non-minimum phase systems. Moreover, the L₂ and L_∞ norms of the system output are also established as functions of design parameters. This implies that the transient system performance can be adjusted by choosing suitable design parameters.     

四旋翼无人机L1 自适应块控反步姿态控制器设计

针对四旋翼无人机的姿态控制问题,提出一种L1自适应块控反步控制方法.将四旋翼姿态运动模型转化为一类多输入多输出不确定非线性系统的形式;根据该系统严格反馈的结构特点,对外回路设计了块控反步控制器;针对内回路存在的外部干扰和内部参数摄动等不确定性,引入L1自适应控制思想补偿其影响.稳定性分析表明闭环系统内所有信号一致有界.仿真和姿态稳定实验验证了所提控制策略的有效性和鲁棒性.     

Decentralized adaptive regulation with unknown high-frequency-gainsigns

We propose for the first time a decentralized adaptive control scheme without requiring a priori information on subsystem high-frequency-gain signs. This is achieved by introducing Nussbaum-type functions in local adaptive controllers, and developing a new analysis approach which is quite different from the conventional one used in centralized adaptive control involving a Nussbaum-type function. With the help of integrator backstepping, the decentralized control scheme can also be applied to high-relative-degree systems. The results of this paper enlarge the class of uncertain large-scale systems for which decentralized adaptive control can be designed     

State derivative feedback for adaptive cancellation of unmatched disturbances in unknown strict-feedback LTI systems

Solutions exist for the problem of canceling sinusoidal disturbances by the measurement of the state or by the measurement of an output for linear and nonlinear systems. In this paper, an adaptive backstepping controller is designed to cancel sinusoidal disturbances forcing an unknown linear time-invariant system in controllable canonical form which is augmented by a linear input subsystem with unknown system parameters. The state-derivatives of the original subsystem and the state of the input subsystem are the only measurements that are used in the design of the controller. The design is based on four steps, (1) parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters, (2) design of an adaptive disturbance observer for both disturbance and its derivative, (3) design of an adaptive controller for the virtual control input, and (4) design of the final adaptive controller by using the backstepping procedure. It is proven that the equilibrium of the closed-loop adaptive system is stable and the state of the considered original subsystem converges to zero as t→∞$t\to \infty$ with perfect disturbance estimation. The effectiveness of the controller is illustrated with a simulation example of a third order system.     

严格反馈互联系统分散式backstepping自适应迭代学习控制

基于Lyapunov分析方法,针对具有严格反馈形式的非线性互联系统,本文设计了一种分散式backstepping自适应迭代学习控制器.子系统之间的互联项为所有子系统输出项线性有界,为每个子系统设计的控制器仅采用该子系统的信息,不需要子系统之间相互传递信息.在控制器中,引入在时间轴和迭代轴上同时更新的自适应参数,以补偿子系统之间的互联项影响.通过采用本文给出的控制器,可使得每个子系统的输出跟踪相应的参考模型输出,仿真结果验证了本文算法的有效性.     

Design of decentralized robust controller for voltage regulation and stabilization of multimachine power systems

This paper presents a decentralized state-feedback controller design based on robust control theory to ensure system stability and voltage regulation in multimachine power systems. The power system is decomposed in n subsystems each represented by a state-space model with bounded parameter uncertainties and unknown input disturbances of class L _∞ which model couplings with the generators of the others subsystems. The proposed controller designed according to a Riccati-based approach is robust with respect to uncertain network parameters and counteracts the effects of the disturbances. A stability analysis in presence of L _∞ disturbances is also given. The control law is straightforward and cost effective because it is function of constant gains and of local measurable machine variables. Numerical simulations give evidence of the achievements in terms of system transient stability as well as voltage regulation, also in comparison with another design technique.     

Transient performance analysis in robust nonlinear adaptive control

This paper deals with the problem of controlling unknown linear systems in the presence of strictly proper unmodelled dynamics and bounded disturbances. Adaptive controllers that ensure the closed-loop global (uniform) stability and asymptotic performances can be designed following either the backstepping approach or the certainty-equivalence method. The main shortcoming of the involved controllers is that they do not allow quantification of the closed-loop transient behaviour. In this paper, the transient issue is addressed for backstepping adaptive controllers. A L_∞ bound on the tracking error is explicitly given as a function of the design parameters. This shows that the error can be made arbitrarily small by sufficiently increasing the design gains.     

Adaptive backstepping controller design for nonlinear uncertain systems using fuzzy neural systems

In this article, we propose an adaptive backstepping control scheme using fuzzy neural networks (FNNs), ABC_FNN, for a class of nonlinear non-affine systems in non-triangular form. The nonlinear non-affine system contains the uncertainty, external disturbance or parameters variations. Two kinds of FNN systems are used to estimate the unknown system functions. According to the FNN estimations, the adaptive backstepping control (ABC_FNN) signal can be generated by backstepping design procedure such that the system output follows the desired trajectory. To ensure robustness and performance, a proportional-integral-surface function and robust controller are designed to improve the control performance. Based on the Lyapunov stability theory, the stability of a closed-loop system is guaranteed and the adaptive laws of the FNN parameters are obtained. This approach is also valid for nonlinear affine system with uncertainty or disturbance. The uncertainty and disturbance terms are estimated by FNNs and treated by the ABC_FNN scheme. Finally, the effectiveness of the proposed ABC_FNN is demonstrated through the simulation of controlling a nonlinear non-affine system and the continuously stirred tank reactor plant to demonstrate the performances of our approach.     

Adaptive fuzzy decentralized control for nonlinear large-scale systems based on high-gain observer

An adaptive fuzzy decentralized backstepping output-feedback control approach is proposed for a class of nonlinear large-scale systems with completely unknown functions,the interconnections mismatched in control inputs,and without the measurements of the states.Fuzzy logic systems are employed to approximate the unknown nonlinear functions,and an adaptive high-gain observer is developed to estimate the unmeasured states.Using the designed high-gain observer,and combining the fuzzy adaptive control theory with backstepping approach,an adaptive fuzzy decentralized backstepping output-feedback control scheme is developed.It is proved that the proposed control approach can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded(SUUB),and that the observer errors and the tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters.Finally,a simulation example is provided to show the eectiveness of the proposed approach.     

Adaptive fuzzy decentralized output feedback control for stochastic nonlinear large‐scale systems using DSC technique

In this paper, an adaptive fuzzy decentralized backstepping output feedback control approach is proposed for a class of uncertain large‐scale stochastic nonlinear systems without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. Using the designed fuzzy state observer, and by combining the adaptive backstepping technique with dynamic surface control technique, an adaptive fuzzy decentralized output feedback control approach is developed. It is shown that the proposed control approach can guarantee that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by choosing appropriate design parameters. A simulation example is provided to show the effectiveness of the proposed approaches. Copyright © 2011 John Wiley & Sons, Ltd.     

Architecture Induced by Distributed Backstepping Design

An important problem in the distributed control of large-scale and infinite dimensional systems is related to the choice of the appropriate controller architecture. We utilize backstepping as a tool for distributed control of nonlinear infinite dimensional systems on lattices, and provide the answer to the following question: what is the controller architecture induced by distributed backstepping design? In particular, we study the case in which we start backstepping design with decentralized control Lyapunov function (CLF), and cancel all interactions at each step of backstepping. For this control law we quantify the number of control induced interactions necessary to guarantee desired dynamical behavior of the infinite dimensional system. We also demonstrate how the controllers with favorable architectures can be designed     

Adaptive dynamic surface control for linear multivariable systems

In this paper, an output-feedback adaptive control is presented for linear time-invariant multivariable plants. By using the dynamic surface control technique, it is shown that the explosion of complexity problem in multivariable backstepping design can be eliminated. The proposed scheme has the following features: (1) The L_∞ performance of the system’s tracking error can be guaranteed, (2) it has least number of updated parameters in comparison with other multivariable adaptive schemes, and (3) the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.     

Adaptive fuzzy output feedback decentralized control of pure‐feedback nonlinear large‐scale systems

In this paper, an adaptive fuzzy decentralized output feedback control approach is presented for a class of uncertain nonlinear pure‐feedback large‐scale systems with immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the immeasurable states. On the basis of the adaptive backstepping recursive design technique, an adaptive fuzzy decentralized output feedback is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed‐loop system are semiglobally uniformly ultimately bounded (SUUB), and that the observer and tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters. Simulation studies are included to illustrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive nonlinear excitation control with L2 disturbance attenuation for power systems

This paper presents a design approach to nonlinear feedback excitation control of power systems with unknown disturbance and unknown parameters. It is shown that the stabilizing control law with desired L₂ gain from the disturbance to a penalty signal can be designed by a recursive way without linearization. A state feedback law is presented for the case of the system with known parameters, and then the control law is extended to adaptive controller for the case when the parameters of the electrical dynamics of the power system are unknown. Simulation results demonstrate that the proposed controllers guarantee transient stability of the system regardless of the system parameters and faults.     

Adaptive dynamic surface control for a class of output-feedback nonlinear systems with guaranteed ℒ∞ tracking performance

In this article, an output-feedback adaptive dynamic surface control (DSC) is proposed for a class of nonlinear systems. It is proved that, by using the new scheme, the explosion of the complexity problem in a traditional backstepping design can be eliminated, the semi-global stability of a closed-loop system can be guaranteed and, in particular, by choosing the design parameters and initialising the filters and the update law properly, we show that the ?_∞ performance of the system-tracking error can be achieved without over-parametrisation. Another advantage of the proposed scheme compared with those traditional backstepping control and current adaptive DSC schemes, whose adaptive control law is obtained through a series of steps recursively, is that the adaptive law is needed only at the first design step, and therefore significantly reduces the design procedure.     

具有动态和静态关联项大系统的鲁棒分散自适应镇定

对于一类具有动态和静态关联项的大系统，利用MT-滤波器和反推设计方法设计了一种鲁棒分散自适应输出反馈控制器．在各子系统为最小相位、静态关联项满足Lipschitz条件、动态关联项稳定且严格正则的假设下，证明了闭环系统的所有信号全局一致有界，且除了参数估计外的其他信号皆以指数速率收敛到零，该结果好于其他相关文献中的结果，仿真结果进一步验证了该方法的有效性。     

Adaptive neural decentralized control for strict feedback nonlinear interconnected systems via backstepping

An approximation based adaptive neural decentralized output tracking control scheme for a class of large-scale unknown nonlinear systems with strict-feedback interconnected subsystems with unknown nonlinear interconnections is developed in this paper. Within this scheme, radial basis function RBF neural networks are used to approximate the unknown nonlinear functions of the subsystems. An adaptive neural controller is designed based on the recursive backstepping procedure and the minimal learning parameter technique. The proposed decentralized control scheme has the following features. First, the controller singularity problem in some of the existing adaptive control schemes with feedback linearization is avoided. Second, the numbers of adaptive parameters required for each subsystem are not more than the order of this subsystem. Lyapunov stability method is used to prove that the proposed adaptive neural control scheme guarantees that all signals in the closed-loop system are uniformly ultimately bounded, while tracking errors converge to a small neighborhood of the origin. The simulation example of a two-spring interconnected inverted pendulum is presented to verify the effectiveness of the proposed scheme.