Robust adaptive output feedback control of nonlinearly parameterized systems

The ideas of adaptive nonlinear damping and changing supply functions were used to counteract the effects of parameter and nonlinear uncertainties, unmodeled dynamics and unknown bounded disturbances. The high-gain observer was used to estimate the state of the system. A robust adaptive output feedback control scheme was proposed for nonlinearly parameterized systems represented by input-output models. The scheme does not need to estimate the unknown parameters nor add a dynamical signal to dominate the effects of unmodeled dynamics. It is proven that the proposed control scheme guarantees that all the variables in the closed-loop system are bounded and the mean-square tracking error can be made arbitrarily small by choosing some design parameters appropriately. Simulation results have illustrated the effectiveness of the proposed robust adaptive control scheme. Translated from Journal of Sichuan University (Engineering Science Edition), 2006, 38(4): 136–140 [译自: 四川大学学报 (工程科学版)]     

Direct adaptive neural control of nonlinear strict‐feedback systems with unmodeled dynamics using small‐gain approach

In this paper, a novel direct adaptive neural control approach is presented for a class of single‐input and single‐output strict‐feedback nonlinear systems with nonlinear uncertainties, unmodeled dynamics, and dynamic disturbances. Radial basis function neural networks are used to approximate the unknown and desired control signals, and a direct adaptive neural controller is constructed by combining the backstepping technique and the property of hyperbolic tangent function. It is shown that the proposed control scheme can guarantee that all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded in mean square. The main advantage of this paper is that a novel adaptive neural control scheme with only one adaptive law is developed for uncertain strict‐feedback nonlinear systems with unmodeled dynamics. Simulation results are provided to illustrate the effectiveness of the proposed scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

A combined backstepping and dynamic surface control to adaptive fuzzy state‐feedback control

This paper studies an adaptive fuzzy dynamic surface control for a class of nonlinear systems with fuzzy dead zone, unmodeled dynamics, dynamical disturbances, and unknown control gain functions. The unknown system functions are approximated by the Takagi‐Sugeno–type fuzzy logic systems. There are 3 main features for the presented systematic design scheme. First, by adopting an integrated method, a novel adaptive fuzzy controller is constructed for the nonlinear system with fuzzy dead zone. Second, only 3 online learning parameters need to be tuned, which significantly reduces the computation burden. Third, the possible controller singularity problem in some of the existing adaptive control methods with feedback linearization techniques can be avoided. On the basis of the backstepping technique and dynamic surface control, all the signals of the closed‐loop system are guaranteed to be semiglobally uniformly ultimately bounded. Finally, 2 simulation examples are provided to illustrate the effectiveness of the proposed scheme.     

Global output‐feedback control of systems with dynamic nonlinear input uncertainties through singular perturbation‐based dynamic scaling

A general class of uncertain nonlinear systems with dynamic input nonlinearities is considered. The system structure includes a core nominal subsystem of triangular structure with additive uncertain nonlinear functions, coupled uncertain nonlinear appended dynamics, and uncertain nonlinear input unmodeled dynamics. The control design is based on dual controller/observer dynamic high‐gain scaling with an additional dynamic scaling based on a singular perturbation‐like redesign to address the non‐affine and uncertain nature of the input appearance in the system dynamics. The proposed approach yields a constructive global robust adaptive output‐feedback control design that is robust to the dynamic input uncertainties and to uncertain nonlinear functions allowed throughout the system structure. Copyright © 2015 John Wiley & Sons, Ltd.     

An adaptive dynamic surface control of output constrained stochastic nonlinear systems with unknown control directions

This article is concerned about an adaptive dynamic surface control (DSC) of output constrained stochastic nonlinear systems with unknown control directions and unmodeled dynamics. Nonlinear mapping-based backstepping control design is presented for stochastic nonlinear systems with output constraint. The explosion of complexity exists in tradition backstepping method is avoided by using the DSC technique. The radial basis function neural networks are employed to deal with unknown nonlinear functions. Nussbaum gain technique is employed to handle the unknown control directions. And a dynamic signal is employed to dominate the unmodeled dynamics. The adaptive controller is designed can ensure that the tracking error converges on a small region of the origin. And all signals of the closed-loop systems are semiglobal uniformly ultimately bounded. Finally, the results of the simulation cases are provided to show the effectivity of the designed controller scheme.     

电力系统非线性鲁棒自适应分散励磁控制设计

利用反步法设计了多机电力系统中的非线性鲁棒自适应励磁控制方案,控制目标是调节发电机功角和频率至稳态运行点的极小领域,并使闭环系统对发电机阻尼系数和电抗参数的不确定性具有自适应能力,且对模型误差和外部有界干扰具备鲁棒性,同时保证各控制器是分散化和本地化的。采用4机系统进行的数字仿真结果表明,实施此方案能有效地提高发电机的功角稳定性。     

不确定混沌系统的鲁棒自适应容错同步控制

针对一类带有执行器故障、非线性不确定性以及外界干扰的混沌系统,设计一个鲁棒自适应容错控制器,来实现主从混沌系统之间的同步容错控制。不需要知晓准确的故障信息以及外界干扰的上界,根据自适应律在线估计未知量。结合自适应控制技术,设计鲁棒自适应容错控制器,使得无论执行器是否有故障发生,主从两个混沌系统都能够实现同步。以经典的蔡氏混沌电路系统为例进行数值仿真,仿真结果验证了所设计控制器的有效性和可行性。     

Adaptive control of pure-feedback nonlinear systems with full-state time-varying constraints and unmodeled dynamics

This paper focuses on the problem of adaptive control for a class of pure-feedback nonlinear systems with full-state time-varying constraints and unmodeled dynamics. By introducing a one-to-one nonlinear mapping, the constrained pure-feedback nonlinear system with state and input unmodeled dynamics is transformed into unconstrained pure-feedback system. The controller design based on the transformed novel system is proposed by using a modified dynamic surface control method. Dynamic signal and normalization signal are designed to handle dynamical uncertain terms and input unmodeled dynamics, respectively. By adding nonnegative normalization signal into the whole Lyapunov function and using the introducing compact set in the stability analysis, all signals in the whole system are proved to be semiglobally uniformly ultimately bounded, and all states can obey the time-varying constraint conditions. A numerical example is provided to demonstrate the effectiveness of the proposed approach.     

双轴励磁同步发电机非线性鲁棒自适应控制

利用Backstepping和扰动抑制方法设计了双轴励磁同步发电杌的自适应控制器。对于含有各种不确定参数和有界扰动的非线性双轴励磁同步杌模型，实现了对转子同步的鲁棒调节。文中的方法可用于其他不确定电力系统的控制设计。     

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)     

A new command governor architecture for transient response shaping

In this paper, we develop a control framework for stabilization and command following of nonlinear uncertain dynamical systems. The proposed methodology consists of a new command governor architecture and an adaptive controller. The command governor is a dynamical system that adjusts the trajectory of a given command to follow an ideal reference system capturing a desired closed‐loop dynamical system behavior in transient time. Specifically, we show that the controlled nonlinear uncertain dynamical system can approach the ideal reference system by choosing the design parameter of the command governor. In addition, an adaptive element is used to asymptotically assure that the error between the controlled nonlinear uncertain dynamical system and the ideal reference system is reduced in long term. Therefore, the proposed methodology not only has closed‐loop transient and steady‐state performance guarantees but can also shape the transient response by adjusting the trajectory of the given command with the command governor. We highlight that there exists a trade‐off between the adaptive controller's learning rate and the command governor's design parameter. This key feature of our framework allows rapid suppression of system uncertainties without resorting to a high learning rate in the adaptive controller. Furthermore, we discuss the robustness properties of the proposed approach with respect to high‐frequency dynamical system content such as measurement noise and ∕ or unmodeled dynamics. A numerical example is provided to demonstrate the efficacy of the proposed architecture. Copyright © 2012 John Wiley & Sons, Ltd.     

不确定混沌电力系统的鲁棒自适应跟踪控制

针对混沌电力系统的跟踪控制问题,在考虑系统含有常参数不确定性及未知干扰的前提下,采用动态面控制方法,设计了鲁棒自适应跟踪控制器,保证了闭环系统的半全局渐近稳定,进而使输出渐近跟踪参考轨迹.理论分析及仿真结果表明,所设计的自适应非线性控制器能够有效抑制简单电力系统的混沌振荡,且具有一定的适应性及鲁棒性.     

Adaptive backstepping neural control of state‐delayed nonlinear systems with full‐state constraints and unmodeled dynamics

In this paper, the problem of adaptive neural control is discussed for a class of strict‐feedback time‐varying delays nonlinear systems with full‐state constraints and unmodeled dynamics, as well as distributed time‐varying delays. The considered nonlinear system with full‐state constraints is transformed into a nonlinear system without state constraints by introducing a one‐to‐one asymmetric nonlinear mapping. Based on modified backstepping design and using radial basis function neural networks to approximate the unknown smooth nonlinear function and using a dynamic signal to handle dynamic uncertainties, a novel adaptive backstepping control is developed for the transformed system without state constraints. The uncertain terms produced by state time delays and distributed time delays are compensated for by constructing appropriate Lyapunov‐Krasovskii functionals. All signals in the closed‐loop system are proved to be semiglobally uniformly ultimately bounded. A numerical example is provided to illustrate the effectiveness of the proposed design scheme.     

Small-gain technique-based adaptive fuzzy command filtered control for uncertain nonlinear systems with unmodeled dynamics and disturbances

This article studies the adaptive tracking control problem for a class of uncertain nonlinear systems with unmodeled dynamics and disturbances. First, a fuzzy state observer is established to estimate unmeasurable states. To overcome the problem of calculating explosion caused by the repeated differentiation of the virtual control signals, the command filter with a compensation mechanism is applied to the controller design procedure. Meanwhile, with the help of the fuzzy logic systems and the backstepping technique, an adaptive fuzzy control scheme is proposed, which guarantees that all signals in the closed-loop systems are bounded, and the tracking error can converge to a small region around the origin. Furthermore, the stability of the systems is proven to be input-to-state practically stable based on the small-gain theorem. Finally, a simulation example verifies the effectiveness of the proposed control approach.     

Discrete‐time multivariable robust model reference adaptive control based on Kp = LDS factorization: an input–output approach

A direct scheme of robust model reference adaptive control is reinvestigated, in an input–output approach, for a large class of discrete‐time multivariable systems with unmodeled dynamics and bounded disturbances. Compared with the existing results, in virtue of a high‐frequency gain matrix factorization, the assumptions required in the scheme are further relaxed without overmuch complicating the controller structure, and a permissible range of the gain parameter in a modified adaptive algorithm is clearly specified. Moreover, paralleling the continuous‐time theoretic framework, robust stability and robust tracking performance are analyzed by using the multivariable versions of some important technical lemmas, such as an exponentially weighted norm‐relation lemma and two swapping lemmas. Copyright © 2012 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.     

STATCOM无功电流的鲁棒自适应控制

从器件级、装置级和系统级3个层次讨论电压源型STATCOM的数学建模和控制器设计;提出了一种鲁棒型直接自适应控制算法,以解决STATCOM模型参数未知情况下无功电流的追踪控制问题。在对象系统严格正实性得以验证的基础上,系统地选择了控制器设计参数,并考虑了输入输出噪声对控制系统的影响,从而使控制器具有较好的鲁棒性。数字仿真结果表明,得到的控制器在追踪控制能力和鲁棒特性等方面比PI控制优越。     

Adaptive output feedback actuator failure compensation for a class of non‐linear systems

An adaptive compensation control scheme using output feedback is designed and analysed for a class of non‐linear systems with state‐dependent non‐linearities in the presence of unknown actuator failures. For a linearly parameterized model of actuator failures with unknown failure values, time instants and pattern, a robust backstepping‐based adaptive non‐linear controller is employed to handle the system failure, parameter and dynamics uncertainties. Robust adaptive parameter update laws are derived to ensure closed‐loop signal boundedness and small tracking errors, in general, and asymptotic regulation, in particular. An application to controlling the angle of attack of a non‐linear hypersonic aircraft dynamic model in the presence of elevator segment failures is studied and simulation results show that the developed adaptive control scheme has desired actuator failure compensation performance. Copyright © 2004 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.