Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.     

Sliding mode disturbance observer‐based adaptive control for uncertain MIMO nonlinear systems with dead‐zone

In this paper, an adaptive integral sliding mode control (ISMC) scheme is developed for a class of uncertain multi‐input and multi‐output nonlinear systems with unknown external disturbance, system uncertainty, and dead‐zone. The research is motivated by the fact that the ISMC scheme against unknown external disturbance and system uncertainty is very important for multi‐input and multi‐output nonlinear systems. The system uncertainty, the unknown external disturbance, and the effect of dead‐zone are integrated as a compounded disturbance, which is well estimated using a sliding mode disturbance observer (SMDO). Then, the adaptive ISMC based on the designed SMDO is presented to guarantee the satisfactory tracking performance in the presence of system uncertainty, external disturbance, and dead‐zone. Finally, the designed adaptive ISMC strategy based on SMDO is applied to the attitude control of the near space vehicle, and simulation results are presented to illustrate the effectiveness of the proposed adaptive ISMC scheme using the SMDO. Copyright © 2016 John Wiley & Sons, Ltd.     

Inverse optimal adaptive control for non‐linear uncertain systems with exogenous disturbances

A Lyapunov‐based inverse optimal adaptive control‐system design problem for non‐linear uncertain systems with exogenous ℒ︁₂ disturbances is considered. Specifically, an inverse optimal adaptive non‐linear control framework is developed to explicitly characterize globally stabilizing disturbance rejection adaptive controllers that minimize a nonlinear‐nonquadratic performance functional for non‐linear cascade and block cascade systems with parametric uncertainty. It is shown that the adaptive Lyapunov function guaranteeing closed‐loop stability is a solution to the Hamilton–Jacobi–Isaacs equation for the controlled system and thus guarantees both optimality and robust stability. Additionally, the adaptive Lyapunov function is dissipative with respect to a weighted input–output energy supply rate guaranteeing closed‐loop disturbance rejection. For special integrand structures of the performance functionals considered, the proposed adaptive controllers additionally guarantee robustness to multiplicative input uncertainty. In the case of linear‐quadratic control it is shown that the operations of parameter estimation and controller design are coupled illustrating the breakdown of the certainty equivalence principle for the optimal adaptive control problem. Finally, the proposed framework is used to design adaptive controllers for jet engine compression systems with uncertain system dynamics. Copyright © 2000 John Wiley & Sons, Ltd.     

轧机液压伺服位置系统的自适应反步滑模控制

针对轧机液压伺服位置系统存在非线性特性、参数不确定性以及控制输入前具有不确定系数的问题,提出了一种自适应反步滑模控制方法.通过对系统非线性模型的等价变换和选择合适的Lyapunov函数,有效解决了由于控制输入前具有不确定系数导致的所设计的控制量与自适应律互相嵌套的难题.把自适应反步法和滑模控制方法相结合,有效克服了系统...     

Adaptive motion/force tracking control of holonomic constrained mechanical systems: a unified viewpoint

This paper proposes a robust adaptive motion/force tracking controller for holonomic constrained mechanical systems with parametric uncertainties and disturbances. First, two types of well‐known holonomic systems are reformulated as a unified control model. Based on the unified control model, an adaptive scheme is then developed in the presence of pure parametric uncertainty. The proposed controller guarantees asymptotic motion and force tracking without the need of extra conditions. Next, when considering external disturbances, control gains are designed by solving a linear matrix inequality (LMI) problem to achieve prescribed robust performance criterion. Indeed, arbitrary disturbance/parametric error attenuation with respect to both motion and force errors along with control input penalty are ensured in the L₂‐gain sense. Finally, applications are carried out on a two‐link constrained robot and two planar robots transporting a common object. Numerical simulation results show the expected performances. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Adaptive robust output‐feedback motion control of hydraulic actuators

Most previous advanced motion control of hydraulic actuators used full‐state feedback control techniques. However, in many cases, only position feedback is available, and thus, there are imperious demands for output‐feedback control for hydraulic systems. This paper firstly transforms a hydraulic model into an output feedback–dependent form. Thus, the K‐filter can be employed, which provides exponentially convergent estimates of the unmeasured states. Furthermore, this observer has an extended filter structure so that online parameter adaptation can be utilized. In addition, it is a well‐known fact that any realistic model of a hydraulic system suffers from significant extent of uncertain nonlinearities and parametric uncertainties. This paper constructs an adaptive robust controller with backstepping techniques, which is able to take into account not only the effect of parameter variations coming from various hydraulic parameters but also the effect of hard‐to‐model nonlinearities such as uncompensated friction forces, modeling errors, and external disturbances. Moreover, estimation errors that come from initial state estimates and uncompensated disturbances are dealt with via certain robust feedback at each step of the adaptive robust backstepping design. After that, a detailed stability analysis for the output‐feedback closed‐loop system is scrupulously checked, which shows that all states are bounded and that the controller achieves a guaranteed transient performance and final tracking accuracy in general and asymptotic output tracking in the presence of parametric uncertainties only. Extensive experimental results are obtained for a hydraulic actuator system and verify the high‐performance nature of the proposed output‐feedback control strategy.     

SMPMSM 系统的无模型反步控制

电动汽车永磁同步电机(PMSM)驱动系统的参数不确定性以及逆变器非线性,将引起电机转速鲁棒性降低,导致电动 汽车速度剧烈波动。 为了提升电动汽车永磁同步电机驱动系统的快速响应性能和鲁棒性,提出了基于无模型的自适应反步控 制(MF-ABC)。 根据无模型控制的代数估计方法,建立超局部模型干扰估计器,再基于自适应反步控制框架,组建适合 PMSM 驱动系统高可靠性运行的 MF-ABC 控制。 研究结果表明,所提出的控制器能够观测、估计和消除各种不确定性,包括系统未建 模动态和外部干扰。 MF-ABC 估计出的干扰值可以用来描述干扰和分析误差。 所提出的方案实时的提升算法计算效益,实现 矢量控制的 PMSM 驱动系统 MTPA 模式高性能稳健运行的研究目标。 通过 dSPACE 台架测试,证实提出的 MF-ABC 和传统反 步控制相比实现了 PMSM 抗转矩干扰能力提升 22%,阶跃响应的快速性提升 0. 02 s。 实验结果证明,MF-ABC 具有强抗干扰性 和响应快速性。     

基于灰狼优化的永磁同步电机自适应反推鲁棒控制策略

针对永磁同步电机存在非线性项的不确定性,以及在运行过程中参数摄动与负载扰动对机械角频率、转速以及系统控制产生的影响,为适应高精度、高稳定的调速应用要求,提出一种基于灰狼优化的永磁同步电机自适应反推鲁棒控制策略.应用非线性反推控制解决电机的非线性问题,并将灰狼优化应用于自适应反推算法中,实现电机转速对期望值的自适应调节跟...     

基于自适应模糊滑模控制的机器人轨迹跟踪算法

针对控制参数的不确定性以及存在未知外部扰动情况下移动机器人的轨迹跟踪问题,提出一种基于光滑非线性饱和函数的自适应模糊滑模轨迹跟踪控制算法。通过建立不确定非线性移动机器人运动控制模型,利用自适应模糊逻辑系统构建自适应模糊滑模控制器。为了增强轨迹跟踪控制算法对随机不确定外部扰动适应能力的同时削弱滑模控制算法中的输入抖振现象,利用有界输入有界输出(BIBO)稳定的方法,通过带有自适应调节算法的模糊系统对滑模控制律中非线性函数项进行自适应逼近,并设计了模糊系统中可调参数的自适应控制律,保证了控制系统的稳定与收敛。实验结果表明,所设计的控制器对系统参数不确定性和外界扰动均具有较强的轨迹跟踪性能和鲁棒性。与传统的滑模控制算法相比,该算法不仅能有效减小输入抖振而且轨迹跟踪控制精度提高了18.89%。     

Accommodation of unknown actuator faults using output feedback‐based adaptive robust control

In this paper, we solve the problem of output tracking for linear uncertain systems in the presence of unknown actuator failures using discontinuous projection‐based output feedback adaptive robust control (ARC). The faulty actuators are characterized as unknown inputs stuck at unknown values experiencing bounded disturbance and actuators losing effectiveness at unknown instants of time. Many existing techniques to solve this problem use model reference adaptive control (MRAC), which may not be well suited for handling various disturbances and modeling errors inherent to any realistic system model. Robust control‐based fault‐tolerant schemes have guaranteed transient performance and are capable of dealing with modeling errors to certain degrees. But, the steady‐state tracking accuracy of robust controllers, e.g. sliding mode controller, is limited. In comparison, the backstepping‐based output feedback adaptive robust fault‐tolerant control (ARFTC) strategy presented here can effectively deal with such uncertainties and overcome the drawbacks of individual adaptive and robust controls. Comparative simulation studies are performed on a linearized Boeing 747 model, which shows the effectiveness of the proposed scheme. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive homo‐backstepping tracking control for strict‐feedback systems in presence of unknown dead‐zones

An adaptive homo‐backstepping control for nonlinear strict‐feedback systems subjected to unknown actuator dead‐zone and disturbance is investigated. A sliding‐mode‐based integral filter is constructed and used to approximate the desired feedback control in the backstepping‐like recursive design technique. Subsequently, the problem of “explosion of complexity” is solved by obviating the analytic derivatives deduction for virtual control in the conventional backstepping technology. The actuator dead‐zone dynamic is modeled as the combination of a line and a disturbance‐like term, which makes the controller design simpler. The interconnected control module and filter module in the resulting closed‐loop system satisfy the input‐to‐state practically stability‐modularity condition, provided that the small‐gain theorem is exploited to ensure the stability of closed‐loop system. The proposed approach cannot only mitigate the effect of dead‐zone but also solve the problem of explosion of complexity in the previous literature. Numerical simulations performed on a manipulator with a brushed DC motor are introduced to illustrate the effectiveness of underlying control scheme.     

Robust adaptive steering control for unmanned surface vehicle with unknown control direction and input saturation

A robust adaptive steering control method is proposed to solve the control problem of the unmanned surface vehicle (USV) with uncertainties, unknown control direction, and input saturation. In the controller design process, the adaptive fuzzy system is incorporated into dynamic surface control (DSC) to approximate the uncertainty term induced by external environmental disturbances and model parameters. Then, the Nussbaum function is used to eliminate the requirement for a priori knowledge of the control direction. Besides, to handle the input saturation, the adaptive fuzzy DSC is extended by a second‐order nonlinear filter and antisaturation auxiliary function to compensate for the magnitude and rate saturation of the rudder. All signals of the closed‐loop system are proven to be uniformly ultimately bounded (UUB) by Lyapunov theorem and the Lemma of Nussbaum gain, and the course error can converge to a small neighborhood of zero through choosing design parameters appropriately. Finally, simulation results and comprehensive comparisons are shown for the USV course system, which is demonstrative of the proposed controller's effectiveness and robustness.     

Direct adaptive control for non‐linear uncertain systems with exogenous disturbances

A direct adaptive non‐linear control framework for multivariable non‐linear uncertain systems with exogenous bounded disturbances is developed. The adaptive non‐linear controller addresses adaptive stabilization, disturbance rejection and adaptive tracking. The proposed framework is Lyapunov‐based and guarantees partial asymptotic stability of the closed‐loop system; that is, asymptotic stability with respect to part of the closed‐loop system states associated with the plant. In the case of bounded energy L₂ disturbances the proposed approach guarantees a non‐expansivity constraint on the closed‐loop input–output map. Finally, several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.     

Adaptive finite‐time actuator fault‐tolerant coordinated attitude control of multispacecraft with input saturation

In this study, for nonrigid spacecraft formation, a distributed adaptive finite‐time actuator fault‐tolerant (FTAFT) coordinated attitude tracking control (CATC) issue is addressed. Aiming at stabilizing the spacecraft formation flying system during a limited time, two distributed adaptive FTAFT CATC strategies are presented. Initially, on basis of distributed finite‐time observer (DFTO), adaptive control, consensus approach, graph theory, and finite‐time theory, we develop a distributed adaptive FTAFT coordinated attitude tracking controller to repress the impact of the external state‐dependent and state‐independent disturbance, unknown time‐varying inertia uncertainty, and actuator fading or fault. Then, combining with the proposed controller, a distributed adaptive FTAFT control law with input saturation subjected to physical limitations of actuator is further designed. In addition, a self‐adjusting matrix (SAM) is proposed to improve the actuators' performance. With the two proposed CATC strategies, the followers can synchronize with the leader. Simulations demonstrated the validity of the designed control laws.     

永磁直线同步电机自适应互补滑模控制

针对永磁直线同步电机(PMLSM)易受非线性因素影响而降低伺服系统鲁棒性的问题,提出一种自适应互补滑模控制方法。永磁直线同步电机的非线性因素包括系统参数变化、电机端部效应及外部不确定性的扰动。互补滑模控制将积分滑模面与广义误差滑模面相结合,将系统状态轨迹限定在两个面的交线上,缩短了状态轨迹达到滑模面的时间,提高了位置跟踪精度。为了进一步改善系统鲁棒跟踪性能,利用自适应控制对不确定扰动因素的上界进行估计,减小不确定因素对系统的影响,改善滑模控制的抖振现象。实验结果表明所提出的控制方法是有效可行的,自适应互补滑模控制不仅提高了系统的跟踪性能,而且更有效地抑制了不确定因素对控制系统的影响。     

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。     

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.     

Adaptive robust output feedback control for attitude tracking of quadrotor unmanned aerial vehicles

This work proposes a new adaptive robust output feedback control method for attitude reference tracking of a quadrotor unmanned aerial vehicle without using the angular velocity measurements. By using the K-filters well known in the adaptive control community, the necessity of velocity measurements or estimating is avoided. The attitude system model is transformed into a second-order model where the angular velocity measurements are not involved. However, the model includes mismatched uncertainties which should be estimated and compensated by the disturbance observers (DOBs). The controller is designed in a backstepping manner, and the dynamic surface technique is adopted to avoid the explosion of the controller complexity. For each Euler angle axis, the prescribed performance control technique is adopted to ensure a prescribed performance, the lumped disturbance is compensated by a DOB, and furthermore an adaptive law is introduced to adaptively update the corresponding uncertain inertia parameter which affects the control performance significantly. The control performance of the overall control system is analyzed rigorously from the viewpoint of input-to-state practical stability. In addition, it is shown how the adaptive laws contribute to improving the control performance. And simulation examples are provided to demonstrate the performance of the proposed method.     

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.