Robust nonlinear generalised predictive control for a class of uncertain nonlinear systems via an integral sliding mode approach

In this paper, a robust nonlinear generalised predictive control (GPC) method is proposed by combining an integral sliding mode approach. The composite controller can guarantee zero steady-state error for a class of uncertain nonlinear systems in the presence of both matched and unmatched disturbances. Indeed, it is well known that the traditional GPC based on Taylor series expansion cannot completely reject unknown disturbance and achieve offset-free tracking performance. To deal with this problem, the existing approaches are enhanced by avoiding the use of the disturbance observer and modifying the gain function of the nonlinear integral sliding surface. This modified strategy appears to be more capable of achieving both the disturbance rejection and the nominal prescribed specifications for matched disturbance. Simulation results demonstrate the effectiveness of the proposed approach.     

Robust control for a class of high-order uncertain nonlinear systems via measurement feedback

This paper considers the problem of global stabilisation for a class of uncertain nonlinear systems, which are of high order and have unknown measurement functions. Based on the notion of homogeneity with monotone degrees (HWMD), the new definition of HWMD indexes is introduced not only to provide an explicit manner to select the homogeneous weights, but also to guarantee the solvability of this problem. By subtly designing a series of Lyapunov functions with indeterministic homogeneous degrees, a measurement feedback controller is proposed to globally stabilise the nonlinear system under different sensors with certain conditions.     

Robust control of a class of uncertain nonlinear systems

This paper considers the robust control of a class of nonlinear systems with real time-varying parameter uncertainty. Interest is focused on the design of linear dynamic output feedback control and two problems are addressed. The first one is the robust stabilization and the other is the problem of robust performance in an H_∞ sense. A technique is proposed for designing stabilizing controllers for both problems by converting them into ‘scaled’ H_∞ control problems which do not involve parameter uncertainty.     

Adaptive stabilization of a class of uncertain nonlinear systems: A differential inclusion approach

Within the framework of controlled differential inclusions, a stabilizing strategy is developed for a class of uncertain nonlinear dynamical systems. The strategy has a linear plus discontinuous output feedback structure with bounded adaptive scalar gain.     

Practical stabilization of a class of uncertain nonlinear systems

In this paper the problem of robust control of a class of nonlinear systems with internal and input channel uncertainties is addressed. The proposed control algorithm reflects the two-level structure of the plant and guarantees the system uniform asymptotic stability with respect to an arbitrary neighbourhood of the nominal system stability point.     

Robust control of a class of nonlinear uncertain systems

Robust control of a general class of uncertain nonlinear systems is investigated. The class of nonlinear systems includes many physical systems as special cases and has an important feature that the uncertainties in the system do not satisfy the matching conditions. Several robust control laws are proposed to make the system stable in the sense of either asymptotic stability or uniformly ultimately bounded stability. The results require no knowledge about the structure of the uncertainties. Although the uncertainties are assumed to be bounded in the Euclidean norm by a polynomial-type bounding function, there is no size restriction imposed on the bounding functions of the uncertainties. The extension to the trajectory tracking problem is also discussed     

Unknown inputs observer for a class of nonlinear uncertain systems: An LMI approach

This paper deals with the simultaneous estimation of states and unknown inputs for a class of Lipschitz nonlinear systems using only the measured outputs. The system is assumed to have bounded uncertainties that appear on both the state and output matrices. The observer design problem is formulated as a set of linear constraints which can be easily solved using linear matrix inequalities (LMI) technique. An application based on manipulator arm actuated by a direct current (DC) motor is presented to evaluate the performance of the proposed observer. The observer is applied to estimate both state and faults.     

Output-feedback stabilization of a class of uncertain non-minimum-phase nonlinear systems

The problem of global output-feedback stabilization for a class of nonlinear systems whose zero dynamics are not necessarily stable is addressed in this paper. It is shown that, using a novel observer design tool together with standard backstepping and small-gain techniques, it is possible to design a stabilizing output feedback controller which ensures robustness with respect to dynamic uncertainties. The proposed stabilization method generalizes existing tools in several directions. As an example, the method is applied to the stabilization of the benchmark translational oscillator/rotational actuator (TORA) using only measurements of the rotational position.     

一类不确定非线性系统的鲁棒自适应控制

针对一类MIMO不确定非线性系统的输出跟踪问题, 基于自适应反步法和滑模控制为其设计了鲁棒自适应控制器. 模型包含3种不确定性: 1) 参数不确定性; 2) 输入增益的不确定性; 3) 代表系统未建模动态和干扰的不确定函数, 该函数有界. 以非完整移动机械臂的输出跟踪控制为目标, 对其进行仿真实验, 实验结果表明所提出的控制算法是正确有效的.     

Global finite-time stabilization of a class of uncertain nonlinear systems

This paper studies the problem of finite-time stabilization for nonlinear systems. We prove that global finite-time stabilizability of uncertain nonlinear systems that are dominated by a lower-triangular system can be achieved by Hölder continuous state feedback. The proof is based on the finite-time Lyapunov stability theorem and the nonsmooth feedback design method developed recently for the control of inherently nonlinear systems that cannot be dealt with by any smooth feedback. A recursive design algorithm is developed for the construction of a Hölder continuous, global finite-time stabilizer as well as a C¹ positive definite and proper Lyapunov function that guarantees finite-time stability.     

Robust adaptive control of a class of nonlinear uncertain systems

A smooth robust dynamic feedback controller is constructed, and the problem of robust H∞ almost disturbance attenuation with internal stability is solved for high-order nonlinear systems with parameter uncertainties. Finally, illustrative example and simulation results demonstrate the effectiveness of the proposed method.     

Dissipative control for a class of uncertain nonlinear control systems

A general dissipative controller is proposed to achieve robust tracking control performance for a class of uncertain single‐input single‐output (SISO) nonlinear systems. The feedback linearization technique is employed to transform the nonlinear system into an assignable inner linear system with a differential control input so that the relationship of the external (input) power and the stored energy of system can be shown clearly. Then, a dissipative controller with an assignable attenuation level is proposed to make the system energy dynamics fit a required dissipative inequality. The unstable factors of the system can then be attenuated accordingly. The system stability is guaranteed even if the system has permanent unavoidable uncertainties. The proposed design can be achieved without the use of traditional means, i.e. optimal control, which requires solution of a Hamilton inequality (or Riccati equation). The Lyapunov stable condition is assured in our approach when the system uncertainties belong to L _∞. Moreover, due to the compatibility of the proposed controller, the controller can be embedded into the designs of other controllers. In those designs, knowledge of the system functions is not required. Basically, the proposed dissipative controller is independent of the system functions. The use of the bounds of the system function is considered to prove the system stability only. Two simulations are given to illustrate the effectiveness of the proposed controller. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Tracking periodic signals for a class of uncertain nonlinear systems

In this paper, a conditional learning control (CLC) is proposed to track periodic signals for a class of nonlinear systems with unknown dynamics. The main advantage of the CLC over the conventional iterative learning control is that monotonic convergence of the control sequence in the iteration domain is achieved, as the CLC ensures the learning is based on the steady‐state output, and hence the effect of the vanishing and unknown transient output is minimized. Following this result, the convergence of the tracking errors is obtained. Further, the optimal setting of the learning gains can be obtained in a min–max sense. A simulation example is presented to illustrate the performance and implementation of the CLC. Copyright © 2009 John Wiley & Sons, Ltd.     

不确定非线性系统的高阶滑模控制器设计

针对一类不确定非线性SISO系统,结合系统有限时间稳定理论与积分滑模控制理论,提出了一种新的高阶滑模控制器设计方法,改善了现有高阶滑模控制中存在的缺陷.积分滑模保证了系统初始时刻就具有抗扰能力,同时采用有限时间稳定观测器实现了高阶滑模的输出反馈控制.仿真结果表明该控制器可使系统在有限时间内收敛,并有效地减小了系统抖振.     

一类非线性不确定系统的模糊自适应控制

利用模糊逻辑系统具有逼近连续函数的性质,研究了一类非线性不确定系统的自适应模糊控制问题.控制器和自适应律的构成直接利用了系统的结构信息和模糊逻辑系统的输出信息,在较弱的假设条件下,这种控制器使被控系统的状态及参数估计误差一致终极有界.最后的仿真算例说明了本文所采用方法的有效性.     

An asymptotically stable robust controller formulation for a class of MIMO nonlinear systems with uncertain dynamics

In this work, we present a novel continuous robust controller for a class of multi-input/multi-output nonlinear systems that contains unstructured uncertainties in their drift vectors and input matrices. The proposed controller compensates uncertainties in the system dynamics and achieves asymptotic tracking while requiring only the knowledge of the sign of the leading principal minors of the input gain matrix. A Lyapunov-based argument backed up with an integral inequality is applied to prove the asymptotic stability of the closed-loop system. Simulation results are presented to illustrate the viability of the proposed method.     

A new approach to adaptive control design without overparametrization for a class of uncertain nonlinear systems

This paper considers the globally stabilizing adaptive controller design for a class of more general uncertain high-order nonlinear systems with unknown control coefficients.Although the existing literature has solved the problem,for n-dimensional systems,the existing methods need at least n + 1 dynamic updating laws for the unknown parameters to construct the stabilizing adaptive controller;that is,the dimension of the dynamic compensator is not less than n + 1,and therefore,there exists serious overparame...     

一类不确定非线性系统无过参数自适应控制设计新方法

文中研究了一类控制系数未知的更一般高阶不确定非线性系统的全局稳定自适应控制设计问题.尽管现有文献已解决了该问题,但对于n维系统,现有构造稳定自适应控制的方法至少需要设计n+1个未知参数的动态调节律,即动态补偿器的维数至少为n+1,存在较为严重的过参数问题.文中通过定义新的需动态调节的未知参数,运用增加幂积分和有关自适应技术,成功地解决了已有方法中的过参数问题,给出了构造只含有一个参数调节律的稳定自适应控制设计新方法.仿真算例验证了文中所给方法的有效性.     

Robust global stabilization of a class of uncertain feedforward nonlinear systems

The problem of global asymptotically stabilizing a certain class of uncertain feedforward nonlinear systems is considered. The control law is obtained by nesting saturation functions whose amplitude can be rendered arbitrarily small. With respect to previous works on the subject the design procedure is able to deal with uncertain (possibly time-varying) parameters ranging within the prescribed compact sets which can affect also the linear approximation of the system. The small gain theorem for nonlinear systems which are input to state stable “with restrictions” is shown to be a key tool for designing a state feedback saturated control law.