A frequency adaptive control for multidimensional systems

An adaptive control is designed for a multidimensional system with unknown constant coefficients under bounded polyharmonic disturbances containing an infinite number of harmonics of unknown amplitudes and frequencies. It uses a very small test signal. The control aim is to ensure given bounds for the forced oscillations in the output of the system and controller. Adaptation is based on finite-frequency identification of the system and a closed-loop system. By way of example, an adaptive control of a real physical system is given.     

时变输出约束非线性系统的量化反馈 自适应终端滑模控制

针对一类复杂非线性系统,提出一种新型自适应快速非奇异终端滑模控制(IAFNTSMC)方法,用以解决其在输出时变约束及量化输入情形下的轨迹跟踪问题;利用鲁棒自适应方法处理扰动不确定性,并结合反演策略和终端滑模策略设计控制器;构造一种新型的时变约束障碍Lyapunov函数,用于实现对系统的输出误差进行随时间变化的幅值约束;为提高闭环系统的误差收敛速度,提出一种新型的滑模面构造方案.所提控制方法能够保证闭环系统的输出跟踪误差快速收敛到约束边界内,并确保闭环系统所有信号有界.数值仿真验证了所提方法的有效性.     

A Lyapunov-based adaptive control framework for discrete-time non-linear systems with exogenous disturbances

A direct adaptive non-linear control framework for discrete-time 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 ? ₂ disturbances the proposed approach guarantees a non-expansivity constraint on the closed-loop input–output map. Finally, three illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.     

基于无源性的全方位移动机器人自抗扰控制

针对全方位移动机器人轨迹跟踪控制中存在的外界干扰和系统参数不确定性问题,提出基于无源性的自抗扰控制方法.该方法通过扩张状态观测器对系统扰动进行估计,并在基于无源性的控制器中加入扰动补偿项以减小外界干扰和参数不确定性对系统的影响;进而,利用系统的无源特性和Lyapunov 理论证明在该控制器作用下闭环系统有界输入有界输出稳定.仿真结果表明,所提出的控制方法响应速度较快,控制精度较高,对系统外扰和模型参数不确定性具有较强的鲁棒性     

Performance-Oriented Antiwindup for a Class of Linear Control Systems With Augmented Neural Network Controller

This paper presents a conditioning scheme for a linear control system which is enhanced by a neural network (NN) controller and subjected to a control signal amplitude limit. The NN controller improves the performance of the linear control system by directly estimating an actuator-matched, unmodeled, nonlinear disturbance, in closed-loop, and compensating for it. As disturbances are generally known to be bounded, the nominal NN-control element is modified to keep its output below the disturbance bound. The linear control element is conditioned by an antiwindup (AW) compensator which ensures performance close to the nominal controller and swift recovery from saturation. For this, the AW compensator proposed is of low order, designed using convex linear matrix inequalities (LMIs) optimization     

Performance output exponential tracking for a wave equation with a general boundary disturbance

In this paper, we consider performance output tracking for a wave equation with a general boundary disturbance. The control and the disturbance are unmatched. Different from the existing results, the hidden regularity, instead of the high gain or variable structure, is utilized in the adaptive servomechanism design. As a result, we are able to cope with more complicated and general disturbances. Moreover, the performance output can track the reference signal exponentially, and at the same time, all the states of the subsystems involved are uniformly bounded. More specially, the overall closed-loop system is exponentially stable when the disturbance and reference are disconnected to the system. The numerical simulations are presented to illustrate the effect of the proposed scheme.     

Backstepping adaptive fuzzy control of uncertain nonlinear systems against actuator faults

A class of unknown nonlinear systems subject to uncertain actuator faults and external disturbances will be studied in this paper with the help of fuzzy approximation theory. Using backstepping technique, a novel adaptive fuzzy control approach is proposed to accommodate the uncertain actuator faults during operation and deal with the external disturbances though the systems cannot be linearized by feedback. The considered faults are modeled as both loss of effectiveness and lock-in-place （stuck at some unknown place）. It is proved that the proposed control scheme can guarantee all signals of the closed-loop system to be semi-globally uniformly ultimately bounded and the tracking error between the system output and the reference signal converge to a small neighborhood of zero, though the nonlinear functions of the controlled system as well as the actuator faults and the external disturbances are all unknown. Simulation results demonstrate the effectiveness of the control approach.     

Adaptive rejection of multi-periodic disturbances for a class of linear systems

This paper deals with adaptive rejection of general multi-periodic disturbances for a class of linear systems via output feedback. The multi-periodic disturbance is a superposition of several general periodic disturbances. Assume that all periods of the multi-periodic disturbance are known. A method of estimating the multi-periodic disturbance and its derivatives is presented, which can ensure these estimate errors converge to zero. Based on these estimation methods, we present a new adaptive control method for disturbance rejection, which guarantees that in the closed-loop system, all the signals are bounded and the output converges to zero. A simulation example is presented to verify the effectiveness of the control scheme.     

Estimating performance of the robust control system under unknown upper disturbance boundaries and measurement noise

Consideration was given to estimation of the robust performance of the closed-loop control system under unknown upper disturbance boundaries. The linear stationary discrete plant with scalar output and control served as a model of the nominal plant. The disturbances included external bounded disturbance, measurement noise, and operator disturbances in output and control. Consideration was given to calculation of the asymptotic upper boundaries of the measurable and nonmeasurable tracking errors coordinated with the measurement data.     

Decentralized adaptive output feedback design for large-scalenonlinear systems

In this paper, we present a global, decentralized adaptive design procedure for a class of large-scale nonlinear systems, which utilizes only local output feedback. The advocated scheme guarantees robustness to parametric and dynamic uncertainties in the interconnections and also rejects any bounded disturbances entering the system. The systems belonging to this class are those which can be transformed using a global diffeomorphism to the output feedback canonical form, where the interconnections are a function of subsystem outputs only. The uncertainties are assumed to be bounded by an unknown pth-order polynomial in the outputs. The resulting controller maintains global robustness and disturbance rejection properties. The output tracking error is shown to be bounded within a compact set, the size of which can be made arbitrarily small by appropriate choice of the control gains. For the case where the objective is regulation, global asymptotic regulation of all the states of the closed-loop system is achieved     

不确定非线性系统的鲁棒耗散性与保性能控制

考虑了不确定仿射非线性系统的鲁棒耗散性与保性能控制问题,不确定性范数有界,不满足匹配条件.基于HJI不等式,设计了状态反馈控制器.当扰动存在时,控制器能使系统达到耗散,当扰动为零时,所设计的控制器使系统对于给定的性能函数具有上界,最后研究了不确定线性系统的保性能与耗散性控制情形.     

Disturbance tolerance and rejection of linear systems with imprecise knowledge of actuator input output characteristics

We study the robustness of linear systems with respect to the disturbances and the uncertainties in the actuator input output characteristics. Disturbances either bounded in energy or bounded in magnitude are considered. The actuator input output characteristics are assumed to reside in a so-called generalized sector bounded by piecewise linear curves. Robust bounded state stability of the closed-loop system is first defined and characterized in terms of linear matrix inequalities (LMIs). Based on this characterization, the evaluation of the disturbance tolerance and disturbance rejection capabilities of the closed-loop system under a given feedback law is formulated into and solved as optimization problems with LMI constraints.     

基于最小二乘算法及神经网络的非线性离散系统的自适应控制

针对有关文献所设计的控制律，在一较弱的条件下，去掉了符号运算部分，证明该控制律可避免“零除”问题，提高了运算速度。对于这种基于神经网络和LS算法的自适应控制问题，证明了系统状态落入一紧集中，闭环系统的所有信号都是有界的，且系统输出和参考输出之间的跟踪误差收敛于以零为原点的某一有界球中。     

A direct method for robust adaptive nonlinear control with guaranteed transient performance

In this paper, the adaptive control problem is studied for a class of nonlinear systems in the presence of bounded disturbances. By utilizing a nice property of the studied systems, a novel Lyapunov-based control structure is developed, which avoids the possible control singularity problem in adaptive nonlinear control. The transient bounds of output tracking error are shown to be explicit functions of initial conditions and design parameters, and the control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. Simulation study is provided to verify the theoretical results.     

含有不灵敏区非线性系统的增益调度自适应变结构控制

针对具有控制输入不灵敏区及有界不确定性的非线性系统,采用增益调度变结构控制策略,研究其镇定问题.利用增益调度策略和自适应参数估计方法,在同时存在参数、结构及干扰的不确定性和未知控制输入不灵敏区的情形下,提出了新的增益调度自适应变结构镇定控制律设计方法,既节省了控制能量,又消除了控制信号的颤振.所提出的控制律可以保证闭环输出为一致终结有界,并且算法比较简单,便于实现.用数字仿真方法验证了所得控制律设计方法的有效性.     

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.     

Finite-dimensional decentralized VS-MRAC of non-linear interconnected distributed parameter systems

We propose a design method for finite-dimensional decentralized VS-MRAC of a class of large-scale non-linear interconnected distributed parameter systems with bounded input and output disturbances. Each equivalent control is approximated by each average control and the norm of the output error vector can be made asymptotically arbitrarily small without the ?-matrix condition, independently of the reference inputs and in spite of the presence of non-linear interconnections, unmodelled dynamics and disturbances. Furthermore, it is assured that all signals in the closed-loop system are globally ultimately uniformly bounded. Finally, we show the effectiveness of the proposed method by using a numerical example.     

Robust continuous-time adaptive control by parameter projection

The problem of adaptive control of a continuous-time plant of arbitrary relative degree, in the presence of bounded disturbances as well as unmodeled dynamics, is addressed. The adaptation considered is the usual gradient update law with parameter projection, the latter being the only robustness enhancement modification employed. It is shown that if the unmodeled dynamics, which consists of multiplicative as well as additive system uncertainty, is small enough, then all the signals in the closed-loop system are bounded. This shows that extra modifications are not necessary for robustness with respect to bounded disturbances and small unmodeled dynamics. In the nominal case, where unmodeled dynamics and disturbances are absent, the asymptotic error in tracking a given reference signal is zero. Moreover, the performance of the adaptive controller is also robust     

Results on the Robust Observer-based Position Controller for Parallel Kinematic Machines

The problem of state observation and position control by output feedback for a nonlinear three degrees-of-freedom (3-DOF) parallel kinematic machine (PKM) system is considered, based on the limited signal availability (only the moving platform displacement measurements are assumed available). Unknown velocity signals are estimated via a nonlinear robust observer that is designed for the nonlinear system with observable linear dynamics part and bounded nonlinearities and disturbances, and that guarantees global exponential stability of the observation error. A proportional-derivative (PD) controller is designed to solve the position control problem, utilizing the estimated velocity, as well as the gravitation compensation, dynamic friction and external disturbance compensation for the PKM. The closed-loop system is proven to have global asymptotical stability according to the Lyapunov analysis method and LaSalle’s invariance principle. Performance of the resulting observer and controller is illustrated in a simulation study of a 3-DOF PKM. Modifications to the nonlinear observer and control law are discussed, that assure convergence of the position error and state observation error to zero when the upper bounds on the model uncertainties/disturbances are not known a priori.     

Adaptive fuzzy backstepping output feedback control for strict feedback nonlinear systems with unknown sign of high-frequency gain

In this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of SISO nonlinear strict-feedback systems with unknown sign of high-frequency gain and the unmeasured states. The nonlinear systems addressed in this paper are assumed to possess the unmodeled dynamics, dynamical disturbances and unknown nonlinear functions, where the unknown nonlinear functions are not linearly parameterized, and no prior knowledge of their bounds is available. In the recursive designing, fuzzy logic systems are used to approximate the unknown nonlinear functions, K-filters are designed to estimate the unmeasured states, and a dynamical signal and Nussbaum gain functions are introduced to handle the unmodeled dynamics and the unknown sign of the high-frequency gain, respectively. Based on Lyapunov function method, a stable adaptive fuzzy output feedback control scheme is developed. It is mathematically proved that the proposed adaptive fuzzy control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded, the output converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by the simulation examples.