一类时变系统鲁棒自适应状态反馈控制的稳定性分析

针对一类离散线性时变参数系统,给出了一种自适应状态反馈控制器,系统的时变参数是已知有界实函数和未知常数的线性组合,该控制器由带有死区的最小二乘辨识算法,状态反馈控制算法和状态观测器构成,文中详细地分析了闭环系统在有界外部干扰和小未建模不确定性影响下的全局稳定性和鲁棒性。     

Adaptive control with optimal robust tracking

The problem of optimal robust tracking in two-parameter adaptive control systems under non-linear time-varying unmodelled dynamics is examined. A new robust stability criterion is derived for analysing the robustness of adaptive control systems with non-linear time-varying model errors. Based on the concept of excess robustness and the theory of the minimum H^∞norm, a simple and feasible design algorithm is presented to synthesize a two-parameter adaptive controller which ensures that adaptive control systems can achieve the object of optimal robust tracking in the presence of non-linear time-varying unmodelled dynamics. Simulation results that demonstrate features of the two-parameter adaptive controller with optimal robust tracking in the light of the design algorithm are included.     

Robust adaptive control of strict-feedback nonlinear systems with unmodelled dynamics and time-varying delays

This paper presents a novel robust adaptive neural control scheme which can be taken as a robustification of the adaptive backstepping design. The considered class of uncertainties contains unknown non-symmetric dead-zone inputs, time-varying delay uncertainties, unknown dynamic disturbances and unmodelled dynamics. The radial basis function neural networks (RBFNNs) are employed to approximate the unknown nonlinear functions obtained by Young’s inequality. By constructing exponential Lyapunov-Krasovskii functionals, the upper bound functions of the time-varying delay uncertainties are compensated for. Using Young’s inequality and RBFNNs, the assumptions with respect to unmodelled dynamics are relaxed. It is demonstrated that the proposed controller guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error eventually converges to a neighbourhood of zero.     

Robust adaptive control for robot manipulators

A composite adaptive control law for robot manipulators in task space, which uses both the tracking error and the prediction error to drive parameter estimation, is developed in this paper. It is shown that global stability and convergence can be achieved for the adaptive control algorithm in the ideal case, and furthermore that the algorithm can be easily modified by using parameter projection to achieve robustness with respect to a class of unmodelled dynamics. In addition, the algorithm has the advantage that no requirement is needed for the inverse of the jacobian matrix or for the bounded inverse of the estimated inertia matrix. A simulation example is provided for performance demonstration.     

不确定性系统的自适应鲁棒跟踪控制

针对存在未知干扰和未建模动态等不确定性的系统的自适应鲁棒跟踪控制问题进行了 探讨.首选将l1优化控制器的有限拍设计方法结合给出了最优鲁棒稳态跟踪控制器的设计方法． 然后利用集员辨识的思想,将名义模型的参数和未建模动态及干扰的大小作为未知参数,提出了 一种递推参数估计方法.最后将上述研究结果结合起来提出了一种自适应鲁棒跟踪控制策略,证 明了自适应算法的全局收敛性并给出了鲁棒跟踪性能指标的一下较紧的上界.与现有的结果相 比,本文提出的自适应控制具有非保守的鲁棒稳定性,具有渐近最优的鲁棒跟踪性能.     

Stable multirate algorithm for robust adaptive control

A new multirate adaptive control algorithm for plants with unmodelled dynamics and bounded disturbances is presented. Different rates are employed for parameter estimation, controller design and controller implemeniation. A modified constant trace least-square algorithm with dead zone and pole placement are used for the algorithm, It is shown that the closed-loop system is globally stable and that set point tracking can be well achieved.     

Robust adaptive pole placement for linear time-varying systems

This paper studies the robustness properties of a basic adaptive control algorithm with respect to plant parameter variation as well as modeling errors and bounded disturbances. The algorithm consists of a projected gradient estimator and a pole assignment controller. A unified method of proof is presented for robust stability of both discrete and continuous-time adaptively controlled time-varying systems. The robust performance of an adaptive pole assignment controller is also discussed     

Adaptive tracking with external force disturbance rejection for uncertain robotic systems

This paper is concerned with the tracking control problem of robotic systems perturbed by time-varying parameters, unmodelled dynamics and external force (and moment) disturbances. The upper bound of system uncertainties and disturbances is not required for controller design. Also, no limitations are assumed on the speed of variation and the magnitude of unknown parameters and perturbations. An adaptive algorithm with simplicity and universality properties is proposed to ensure robust tracking. Presenting the closed loop stability proof analytically, the tracking controller is applied to a two-link robot manipulator and the simulation results are demonstrated to show the effectiveness of the method.     

Practical issues in the implementation of self-tuning control

Implementation aspects of self-tuning regulators are discussed in the paper. There is a large discrepancy between simulation or academic algorithms and practical algorithms. In the idealized environment of simulations it is easy to get different types of adaptive algorithms to perform well. In practice the situation is quite opposite. The adaptive or self-tuning controller must be able to handle nonlinearities, unmodelled dynamics and unmodelled disturbances over a wide range of operating conditions. Some aspects of how to implement self-tuning controllers are discussed in the paper. This includes robustness, signal conditioning, parameter tracking, estimator wind-up, reset action and start-up. Different ways to use the prior knowledge about the process are also discussed.     

A robust adaptive sliding-mode control for rigid robotic manipulators with arbitrary bounded input disturbances

In this paper, a robust adaptive sliding-mode control scheme for rigid robotic manipulators with arbitrary bounded input disturbances is proposed. It is shown that the prior knowledge on the upper bound of the norm of the input disturbance vector is not required in the sliding-mode controller design. An adaptive mechanism is introduced to estimate the upper bound of the norm of the input disturbance vector. The estimate is then used as a controller gain parameter to guarantee that the output tracking error asymptotically converges to zero and strong robustness with respect to bounded input disturbances can be obtained. A simulation example is given in support of the proposed control scheme.     

Stable robust adaptive controller

This paper presents a globally stable adaptive controller for linear discrete systems in the presence of unmodelled dynamics and bounded disturbances. The proposed formulation uses an augmented plant representation that incorporates P, Q and R weighting polynomials for the system output, input and setpoint respectively into the predictive control law. The algorithm also includes a normalized estimation scheme, based on a least-squares estimator, and a parameter adaptation stopping criterion to guarantee stability.     

Unified treatment of internal model principle based adaptive control algorithms

A number of adaptive control algorithms are summarized here for the control of unknown linear discrete time plants with unknown deterministic disturbances. Adaptive implementation of the internal model principle is used for asymptotical cancellation of the deterministic disturbances. The use of the certainty equivalence principle for implementation of these algorithms can be shown to result in a certain type of unmodelled dynamics error for each of these algorithms. A unified analysis of these algorithms is given under a common framework of unmodelled dynamics. With suitable modification of the parameter estimation algorithm, the global convergence and stability of these algorithms are established without the requirement of the persistency of excitation condition. Some simulation results are provided for support of the analysis.     

Adaptive terminal sliding mode control for rigid robotic manipulators

In order to apply the terminal sliding mode control to robot manipulators, prior knowledge of the exact upper bound of parameter uncertainties, and external disturbances is necessary. However, this bound will not be easily determined because of the complexity and unpredictability of the structure of uncertainties in the dynamics of the robot. To resolve this problem in robot control, we propose a new robust adaptive terminal sliding mode control for tracking problems in robotic manipulators. By applying this adaptive controller, prior knowledge is not required because the controller is able to estimate the upper bound of uncertainties and disturbances. Also, the proposed controller can eliminate the chattering effect without losing the robustness property. The stability of the control algorithm can be easily verified by using Lyapunov theory. The proposed controller is tested in simulation on a two-degree-of-freedom robot to prove its effectiveness.     

Adaptive control systems with robustness optimization to non-linear time-varying unmodelled dynamics

In this paper, the robustness properties of adaptive controllers to non-linear time-varying unmodelled dynamics are presented. A new robust stability criterion will be derived for analysing the robustness of adaptive control in deterministic systems under non-linear time-varying model errors. The concept of the excess robustness of adaptive systems is introduced, and the theory of the minimum H^∞ norm will be employed to solve the problem of robustness optimization in adaptive control systems. The results of simulations, which display the good performance of the robust adaptive controller according to our design algorithm, are also presented.     

Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics

This paper examines the robustness properties of existing adaptive control algorithms to unmodeled plant high-frequency dynamics and unmeasurable output disturbances. It is demonstrated thai there exist two infinite-gain operators in the nonlinear dynamic system which determines the time-evolution of output and parameter errors. The pragmatic implication of the existence of such infinite-gain operators is that 1) sinusoidal reference inputs at specific frequencies and/or 2) sinusoidal output disturbances at any frequency (including dc), can cause the loop gain to increase without bound, thereby exciting the unmodeled high-frequency dynamics, and yielding an unstable control system. Hence, it is concluded that existing adaptive control algorithms as they are presented in the literature referenced in this paper, cannot be used with confidence in practical designs where the plant contains unmodeled dynamics because instability is likely to result. Further understanding is required to ascertain how the currently implemented adaptive systems differ from the theoretical systems studied here and how further theoretical development can improve the robustness of adaptive controllers.     

ROBUST ADAPTIVE CONTROL WITH MULTIPLE ESTIMATION MODELS FOR STABILIZATION OF A CLASS OF NON‐INVERSELY STABLE TIME‐VARYING PLANTS

This paper presents an indirect adaptive control scheme for nominally stabilizable non‐necessarily inversely stable continuous‐time systems with unmodelled dynamics. The control objective is the adaptive stabilization of the closed‐loop system with the achievement of a bounded tracking‐error between the system output and a reference signal given by a stable filter. The adaptive control scheme includes several estimation algorithms and a supervisor which selects the appropriate estimator at every certain time and keeping it operating for at least a minimum period of residence time. This selection is based on a performance criterion related to a measure of the estimation errors obtained with each estimator. In this way, the performance of the output signal is improved with regard to the performance achieved with a unique estimation algorithm. All the estimators are either of the least‐squares type or gradient type. However, any well‐posed estimation algorithm is potentially valid for application. These estimators include relative dead‐zones for robustness purposes and parameter ‘a posteriori’ modifications to ensure the controllability of the estimated models of the plant, which is crucial for proving the stabilizability of the plant via adaptive pole‐placement designs.     

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     

Positive-realness in discrete-time adaptive control systems

Most self-tuning and adaptive control methods hinge on the satisfaction of some positive-realness conditions. Alternatively, they require prior knowledge about an upper bound on the order of the controlled plant and about its exact pole-zero excess. Recently it was shown for continuous-time systems that the positive-realness conditions can be satisfied without the need for this prior knowledge. The results are extended here to discrete-time systems. It is shown that the positive-realness conditions can be satisfied in ‘almost stable’ discrete-time multivariate linear systems, namely, systems that can be stabilized via static or dynamic output feedback, including non-minimum-phase systems, at the price of bounded rather than vanishing output tracking errors. It is also shown that satisfaction of the positivity conditions may facilitate implementation of simple adaptive control procedures that maintain robustness in the presence of parasitic dynamics and disturbances     

Robustness analysis of identification and adaptive control for stochastic systems

This paper gives a preliminary robustness analysis for stochastic systems with unmodelled dynamics. The extended least squares algorithm and stochastic adaptive control for tracking are defined on the basis of the modelled part of the system, and it is shown that the parameter estimate is closed to the true one and the tracking error is small if the unmodelled dynamics is small.     

Adaptive control of robot manipulators in task space

Adaptive control of robotic manipulators in task space or Cartesian space is considered. A general Lyapunov-like concept is used to design an adaptive control law. It is shown that the global stability and convergence can be achieved for the adaptive control algorithm. The algorithm has the advantage that the inverse of Jacobian matrix is not required. The algorithm is further modified so that the requirement for the bounded inverse of estimated inertia matrix is also eliminated. In addition, two approaches are presented to achieve robustness to bounded disturbances