Robust adaptive control of nonlinear systems represented by input-output models

A robust adaptive control scheme is proposed for a class of nonlinear systems represented by input-output models with unmodeled dynamics. The scheme does not require the unknown parameters to satisfy the linear dependence condition and parameter estimation is not needed. With the proposed control scheme, all the variables in the closed-loop system are bounded in the presence of unmodeled dynamics and bounded disturbances. Moreover, the mean-square tracking error can be made arbitrarily small by choosing some design parameters appropriately.     

一种鲁棒模型参考自适应控制*

针对一类参数未知、具有常值扰动和未建模误差的线性离散系统，此文给出了一种模型参考间接自适应控制算法。该方法在未知系统高频增益符号时，可保证系统的非奇异性。同时，对于上述干扰具有鲁棒性，文中提出的自适应控制器可使闭环系统全局渐近稳定。     

Composite Hierarchical Anti-Disturbance Control of a Quadrotor UAV in the Presence of Matched and Mismatched Disturbances

Quadrotor helicopter is an unstable system subject to matched and mismatched disturbances. To stabilize the quadrotor dynamics in the presence of these disturbances, the application of a composite hierarchical anti-disturbance controller, combining a sliding mode controller and a disturbance observer, is presented in this paper. The disturbance observer is used to attenuate the effect of constant and slow time-varying disturbances. Whereas, the sliding mode controller is used to attenuate the effect of fast time-varying disturbances. In addition, sliding mode control attenuates the effect of the disturbance observer estimation errors of the constant and slow time-varying disturbances. In this approach, the upper bounds of the disturbance observer estimation errors are required instead of the disturbances’ upper bounds. The disturbance observer estimation errors are found to be bounded when the disturbance observer dynamics are asymptotically stable and the disturbance derivatives and initial disturbances are bounded. Moreover, due to the highly nonlinear nature of the quadrotor dynamics, the upper bounds of a part of the quadrotor states and disturbance estimates are required. The nonlinear terms in the rotational dynamics are considered as disturbances, part of which is mismatched. This assumption simplifies the control system design by dividing the quadrotor’s model into a position subsystem and a heading subsystem, and designing a controller for each separately. The stability analysis of the closed loop system is carried out using Lyapunov stability arguments. The effectiveness of the developed control scheme is demonstrated in simulations by applying different sources of disturbances such as wind gusts and partial actuator failure.     

PI Adaptive Fuzzy Control With Large and Fast Disturbance Rejection for a Class of Uncertain Nonlinear Systems

Design of controllers for uncertain systems is inherently paradoxical. Adaptive control approaches claim to adapt system parameters against uncertainties, but only if these uncertainties change slowly enough. Alternatively, robust control methodologies claim to ensure system stability against uncertainties, but only if these uncertainties remain within known bounds. This is while, in reality, disturbances and uncertainties remain faithfully uncertain, i.e., may be both fast and large. In this paper, a PI-adaptive fuzzy control architecture for a class of uncertain nonlinear systems is proposed that aims to provide added robustness in the presence of large and fast but bounded uncertainties and disturbances. While the proposed approach requires the uncertainties to be bounded, it does not require this bound to be known. Lyapunov analysis is used to prove asymptotic stability of the proposed approach. Application of the proposed method to a second-order inverted pendulum system demonstrates the effectiveness of the proposed approach. Specifically, system responses to fast versus slow and large versus small disturbances are considered in the presented simulation studies.     

Robust adaptive control of uncertain force/motion constrained nonholonomic mobile manipulators

In this paper, force/motion tracking control is investigated for nonholonomic mobile manipulators with unknown parameters and disturbances under uncertain holonomic constraints. The nonholonomic mobile manipulator is transformed into a reduced chained form, and then, robust adaptive force/motion control with hybrid variable signals is proposed to compensate for parametric uncertainties and suppress bounded disturbances. The control scheme guarantees that the outputs of the dynamic system track some bounded auxiliary signals, which subsequently drive the kinematic system to the desired trajectory/force. Simulation studies on the control of a wheeled mobile manipulator are used to show the effectiveness of the proposed scheme.     

Decentralized robust adaptive control of nonlinear systems withunmodeled dynamics

The authors present a decentralized robust adaptive output feedback control scheme for a class of large-scale nonlinear systems of the output feedback canonical form with unmodeled dynamics. A modified dynamic signal is introduced for each subsystem to dominate the unmodeled dynamics and an adaptive nonlinear damping is used to counter the effects of the interconnections. It is shown that under certain assumptions, the proposed decentralized adaptive control scheme guarantees that all the signals in the closed-loop system are bounded in the presence of unmodeled dynamics, high-order interconnections and bounded disturbances. Furthermore, by choosing the design constants appropriately, the tracking error can be made arbitrarily small regardless of the interconnections, disturbances, and unmodeled dynamics in the system. An illustration example demonstrates the effectiveness of the proposed scheme     

具有降阶模型的多变量鲁棒自适应前馈控制器

本文提出了一种多变量鲁棒自适应前馈控制器。该控制器采用低阶模型来控制参数未知的高阶多变量系统时,在可测干扰和有界不可测干扰作用下能保证自适应系统稳定运行。当可测干扰与系统输出之间存在未建模动态时,它可以对可测干扰实行有效的动静态补偿。当只有有界干扰作用时,它能使有界干扰对系统产生的影响最小。本文还给出了采用所提出的控制器控制某钢厂间歇式余热锅炉的仿真结果。     

线性连续时间系统的鲁棒自适应控制*

本文解决了参数未知，具有非结构性未建模误差和有界恒定扰动的一类线性连续统的自适应控制问题。文中给出的自适应控制器对上述干扰具有鲁棒性，它能保证自适应系统的稳定运行无奇异性产生。     

Finite-Time Convergence Disturbance Rejection Control for a Flexible Timoshenko Manipulator

This paper focuses on a new finite-time convergence disturbance rejection control scheme design for a flexible Timoshenko manipulator subject to extraneous disturbances.To suppress the shear deformation and elastic oscillation,position the manipulator in a desired angle,and ensure the finitetime convergence of disturbances,we develop three disturbance observers(DOs)and boundary controllers.Under the derived DOs-based control schemes,the controlled system is guaranteed to be uniformly bounded stable and disturbance estimation errors converge to zero in a finite time.In the end,numerical simulations are established by finite difference methods to demonstrate the effectiveness of the devised scheme by selecting appropriate parameters.     

On the adaptive control of a class of systems with random parameters and disturbances

The adaptive control of discrete time parameter linear stochastic systems with random parameters is investigated. It is shown that systems whose (unknown) autoregressive parameters undergo bounded martingale difference disturbances may be stabilized by the application of the so-called Modified Least Squares adaptive control algorithm. Asymptotically, the sample mean square performance criterion is equal to the one step ahead minimum variance control loss (which equals the prediction error variance when the system parameters are known) plus a term which is bounded by a quantity proportional to the square of the bound on the parameter disturbance. This latter term may be interpreted as the increase in the prediction error variance due to the random parameter variation.     

A new robust adaptive control algorithm for linear time-varying plants

Robustness is an important property of a control system. Robust adaptive control has been an active research area for more than a decade. Since it was shown that un-modelled dynamics or even a small bounded disturbance can cause most adaptive control algorithms to go unstable, various modifications of the adaptive control algorithms have been developed to counteract instability and improve robustness with respect to unmodelled dynamics and bounded disturbances. However, we know that most of the modified approaches to achieve robustness require knowledge of either the parameter of bounding function on the unmodelled dynamics, or the upper bound on the disturbances, or the bound on the norm of unknown matching controller/plant parameters, and such knowledge can hardly be obtained in practice. A new indirect adaptive control algorithm for linear time-varying plants is proposed to achieve robustness to a class of unmodelled dynamics, bounded disturbances and plant parameter time variations. A modified relative dead zone technique is used, so that knowledge of the parameters of the upper bounding function on the unmodelled dynamics and the disturbances is not required. The stability analysis and the robust performance of adoptively controlled time-varying systems are provided for the new scheme. A simulation example is given to show the effectiveness of the proposed algorithm.     

Adaptive control of linear time-varying systems

Single-input single-output uncertain linear time-varying systems are considered, which are affected by unknown bounded additive disturbances; the uncertain time-varying parameters are required to be smooth and bounded but are neither required to be sufficiently slow nor to have known bounds. The output, which is the only measured variable, is required to track a given smooth bounded reference trajectory. The undisturbed system is assumed to be minimum-phase and to have known and constant relative degree, known sign of the ‘high frequency gain’, known upper bound on the system order. An adaptive output feedback control algorithm is designed which assures: (i) boundedness of all closed-loop signals; (ii) arbitrarily improved transient performance of the tracking error; (iii) asymptotically vanishing tracking error when parameter time derivatives are L₁ signals and disturbances are L₂ signals.     

Event-triggered sliding mode control for a class of nonlinear systems

ABSTRACT

Event-triggering strategy is one of the real-time control implementation techniques which aims at achieving minimum resource utilisation while ensuring the satisfactory performance of the closed-loop system. In this paper, we address the problem of robust stabilisation for a class of nonlinear systems subject to external disturbances using sliding mode control (SMC) by event-triggering scheme. An event-triggering scheme is developed for SMC to ensure the sliding trajectory remains confined in the vicinity of sliding manifold. The event-triggered SMC brings the sliding mode in the system and thus the steady-state trajectories of the system also remain bounded within a predesigned region in the presence of disturbances. The design of event parameters is also given considering the practical constraints on control execution. We show that the next triggering instant is larger than its immediate past triggering instant by a given positive constant. The analysis is also presented with taking delay into account in the control updates. An upper bound for delay is calculated to ensure stability of the system. It is shown that with delay steady-state bound of the system is increased than that of the case without delay. However, the system trajectories remain bounded in the case of delay, so stability is ensured. The performance of this event-triggered SMC is demonstrated through a numerical simulation.     

Robust adaptive control of bilinear plants

A robust model reference adaptive control scheme for bilinear plants with bounded disturbances is developed. Global stability of the closed-loop adaptive system is guaranteed by using a switching-σ modified adaptive law. In the absence of disturbances, the tracking error is shown to go to zero asymptotically with time.     

Adaptive control of nonminimum phase systems subject to unknownbounded disturbances

This paper presents a robust adaptive pole placement control scheme for continuous-time systems with bounded disturbances. The system may possibly be nonminimum phase and unstable. It is shown that for arbitrary bounded disturbances, a global asymptotical bounded-input/bounded-output (BIBO) stability is established through pole placement techniques without either introducing persistent excitation probing signals into the system or assuming any a priori knowledge on the plant parameters. Moreover, the disturbance upper bound is not assumed to be known. The system order is the only a priori knowledge required on the plant. The adaptive control law is free from singularities in the sense that the estimated plant model is always controllable     

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

This paper addresses the output feedback tracking control of a class of multiple‐input and multiple‐output nonlinear systems subject to time‐varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory‐based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time‐varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady‐state tracking accuracy in spite of the presence of time‐varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a Lyapunov‐Krasovskii functional. A specific study on a 2‐link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme.     

高频增益未知的受扰非线性系统输出反馈控制

针对一类具有未知定常参数,包括未知高频增益的受扰非线性最小相位系统,给出了一种鲁棒自适应输出反馈控制策略．系统所受的干扰假设有界,但其界值是未知的．通过采用自适应策略来对其界值进行在线估计,控制算法并不需要高频增益符号的先验知识．同时,系统中的非线性项并不要求满足增长性条件和匹配条件．算法使得估计参数量达到了最小,保证了闭环系统所有信号的有界性,同时使得跟踪误差渐近收敛于零．     

A globally stable APCS in the presence of bounded noises and disturbances

This paper presents a globally stable adaptive predictive control system (APCS) for discrete linear processes with pure time delays in the presence of bounded measurement and process noise plus unmeasured disturbances. The main contribution is the proof of stability in the context of discrete adaptive control schemes. This proof is based on the minimization of the a posteriori estimation error and the convergence of the estimated parameters.     

An adaptive disturbance rejection control scheme for multivariable nonlinear systems

An adaptive disturbance rejection control scheme is developed for uncertain multi-input multi-output nonlinear systems in the presence of unmatched input disturbances. The nominal output rejection scheme is first developed, for which the relative degree characterisation of the control and disturbance system models from multivariable nonlinear systems is specified as a key design condition for this disturbance output rejection design. The adaptive disturbance rejection control design is then completed by deriving an error model in terms of parameter errors and tracking error, and constructing adaptive parameter-updated laws and adaptive parameter projection algorithms. All closed-loop signals are guaranteed to be bounded and the plant output tracks a given reference output asymptotically despite the uncertainties of system and disturbance parameters. The developed adaptive disturbance rejection scheme is applied to turbulence compensation for aircraft fight control. Simulation results from a benchmark aircraft model verify the desired system performance.     

Analysis and control of the cable-supporting system including actuator dynamics

This paper is concerned with modeling, analysis, and control of the cable-supporting system including actuator dynamics for the next generation large spherical radio telescope. According to its 50-m scaled model, to begin with, the dynamic formulations of the electromechanical coupling system including servomechanism dynamics and parabolic curve of the long-span cable sag effects are established; at the same time the relationship among cable force, cable end displacement and cable length variation is obtained by utilizing parabolic equation, and the dynamic modeling for control can be justified by the numerical example. In addition, taking account of the characteristics of nonlinearity, slow time-variant and multivariable coupling, a fuzzy control plus proportional-integral control method is utilized to control the wind-induced vibration of the cable-supporting system. Finally, simulation results from the 50-m scaled model control system, regarding the wind-induced vibration control of the cable-supporting structure in stationary position and the tracking control of the cable-supporting system, show the satisfactory performance of the proposed control scheme as compared with a discrete-time automatic disturbances rejection controller in the presence of internal model uncertainties in both the cable-supporting mechanism and servomechanism dynamics and external disturbances.