A proportional integral extremum-seeking control approach for discrete-time nonlinear systems

This paper proposes a proportional-integral extremum-seeking control technique for a class of discrete-time nonlinear dynamical systems with unknown dynamics. The technique is a generalisation of existing time-varying extremum-seeking control (ESC) techniques that provides fast transient performance of the closed-loop system to the optimum equilibrium of a measured objective function. The main contribution of the proposed technique is the addition of a proportional action that can be used to minimise the impact of a time-scale separation on the transient performance of the ESC system. The integral action fulfils the role of standard ESC techniques to identify optimal equilibrium conditions. The effectiveness of the proposed approach is demonstrated using a simulation example.     

Robust adaptive fault-tolerant control for time delay uncertain nonlinear systems with time-varying performance bounds

In this paper, a robust adaptive fault tolerant controller guaranteeing with time-varying performance bounds is designed for a class of time delay uncertain nonlinear systems subject to actuator failures and external disturbance. The influence of time delay on the system is mitigated and the system performance can be guaranteed by introducing a positive nonlinear control gain function and the generalised restricted potential function. A new method with more design degrees of freedom is developed to ensure the norm of the system state within a-priori, user-defined time varying performance bounds. Using the online estimation information provided by adaptive mechanism, a robust adaptive fault-tolerant control method guaranteeing time varying performance bounds is proposed. It is shown that all the signals of the resulting closed-loop system are bounded and the system state less than a-priori, user-defined performance bounds. Finally, simulation results are given to demonstrate the efficacy of the proposed fault-tolerant control method.     

Global regulation of almost feedforward nonlinear systems by an adaptive event-triggered controller with multi-triggering conditions

We consider a global regulation problem for almost feedforward nonlinear systems with uncertain time-varying parameters using an adaptive event-triggered controller. The systems we consider are called “almost” feedforward systems because, in addition to the feedforward nonlinearity with the unknown linear growth rate, there is a non-zero input-matching term. Notably, this input-matching term is a non-feedforward term and it cannot be directly canceled due to the presence of input uncertainty and the use of event-triggered control. To solve our considered problem, we propose an adaptive event-triggered controller with multi-triggering conditions and dynamic gain. We show that the closed-loop system is globally regulated and the times between executions are positively lower bounded. Moreover, we show that the positive lower bounds of interexecution times can be enlarged by a control parameter. For a clear illustration, a practical example is given.     

Adaptive robust stabilisation for a class of uncertain nonlinear time-delay dynamical systems

The problem of adaptive robust stabilisation is considered for a class of uncertain nonlinear dynamical systems with multiple time-varying delays. It is assumed that the upper bounds of the nonlinear delayed state perturbations are unknown and that the time-varying delays are any non-negative continuous and bounded functions which do not require that their derivatives have to be less than one. In particular, it is only required that the nonlinear uncertainties, which can also include time-varying delays, are bounded in any non-negative nonlinear functions which are not required to be known for the system designer. For such a class of uncertain nonlinear time-delay systems, a new method is presented whereby a class of continuous memoryless adaptive robust state feedback controllers with a rather simpler structure is proposed. It is also shown that the solutions of uncertain nonlinear time-delay systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. Finally, as an application, an uncertain nonlinear time-delay ecosystem with two competing species is given to demonstrate the validity of the results.     

Approximation-based adaptive tracking of a class of uncertain nonlinear time-delay systems in nonstrict-feedback form

This paper investigates a predefined performance control problem for adaptive tracking of uncertain nonlinear time-delay systems in nonstrict-feedback form. Nonstrict-feedback nonlinearities, time-varying delays and external disturbances are assumed to be unknown. Based on the exponential decaying design functions denoting the preassigned bounds of transient and steady-state tracking errors, some variable separation lemmas are derived to design an approximation-based robust adaptive control scheme in the presence of nonstrict-feedback time-delayed nonlinearities. The proposed control system guarantees that a tracking error remains within a predesigned bound for all t ≥ 0 and converges to a preselected neighbourhood of the origin. Compared with the existing results in the literature, the main contribution of this paper is to provide a solution on the guaranteed performance control in the presence of unknown nonstrict-feedback nonlinearities related to all delayed state variables. Simulation results illustrate the effectiveness of the proposed methodology.     

模糊输出反馈实现动态不确定非线性系统的几乎干扰解耦

研究一类单输入单输出动态不确定非线性系统的几乎干扰解耦问题. 首先设计一类新型的模糊高增益观测器估计非线性系统的未知状态; 然后结合自适应模糊backstepping 控制、小增益定理和改变供能函数方法, 给出鲁棒自适应模糊控制器的设计. 所设计的控制器不仅可以保证整个闭环系统在输入到状态实际稳定意义下稳定, 同时抑制了干扰对输出的影响. 仿真结果表明了所提出控制方法的有效性.

     

一类不确定非仿射非线性系统自适应模糊控制

针对一类非仿射非线性系统提出了自适应模糊控制方法,该方法把不确定非线性系统表示为定常线性子系统加非线性项的形式,然后采用模糊逻辑系统设计补偿器来消除非线性项的影响。引入时变死区函数对模糊逻辑系统中的未知参数进行自适应调节,并对时变死区设计了自适应律。证明了该方法可使闭环系统的所有信号均有界,且使跟踪误差收敛到原点的小邻域内。仿真结果表明了该方法的有效性。     

Output feedback adaptive RISE control for uncertain nonlinear systems

In this article, committed to extending the robust integral of the sign of the error (RISE) feedback control to the working condition of output feedback, a novel output feedback controller with a continuously bounded control input which combines the adaptive control and integral robust feedback will be proposed for trajectory tracking of a family of nonlinear systems subject to modeling uncertainties. A novel adaptive state observer (ASO) with disturbance rejection performance is creatively constructed to derive real-time estimation of the unmeasured state signals. Moreover, a projection-type adaption law is integrated to handle parameter uncertainties and an integral robust term is employed to deal with external disturbances. It is shown that asymptotic estimation performance and meanwhile asymptotic tracking result can eventually be derived. Simulation validations are implemented to demonstrate the high tracking performance of the presented controller. Notably, the synthesized control algorithm can be readily extended to the Euler–Lagrange systems. Typically, it can be extended to practical electromechanical equipment such as three-dimensional vector forming robots to improve the real-time forming accuracy.     

Adaptive dynamic surface control for uncertain nonaffine nonlinear systems

This paper focuses on the problem of adaptive control for uncertain nonaffine nonlinear systems. The original nonaffine systems are transformed into the augmented affine systems via adding an auxiliary integrator, which makes the explicit control design possible. By introducing a modified sliding mode filter in each step, a novel adaptive dynamic surface controller is proposed, where the ‘explosion of complexity’ problem inherent in the backstepping design is avoided. It is proven rigorously that for any initial control condition, the proposed adaptive scheme is able to ensure the semiglobal uniformly ultimately boundedness of all signals in the closed loop. An illustrative example is carried out to verify the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

A time-varying extremum-seeking control approach for discrete-time systems

This paper considers the solution of a real-time optimization problem using adaptive extremum seeking control for a class of unknown discrete-time nonlinear systems. It is assumed that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown and that the objective function is measured. The main contribution of the paper is to formulate the extremum-seeking problem as a time-varying discrete-time estimation problem. The proposed approach is shown to avoid the need for averaging results which minimizes the impact of the choice of dither signals on the performance of the extremum seeking control system. Several examples are used to illustrate the effectiveness of the proposed technique.     

基于观测器的不确定非线性系统的自适应鲁棒模糊控制

针对单输入单输出不确定非线性系统提出了一种自适应鲁棒模糊控制算法.该算法通过设计观测器来估计系统的状态向量,因此不要求假设系统的状态向量是可测的.在这个算法中,主要的假设为最优逼近参数向量与标称参数向量之差的范数和逼近误差的界限是未知的.通过只对未知界限估计的调节,该算法减轻了在线计算量并且提高了系统的鲁棒性.所设计的自适应鲁棒模糊控制算法保证了闭环系统的所有信号是一致有界的并且跟踪误差估计收敛到一个小的零邻域内.仿真例子证实了所提方法的可行性.     

一类不确定非线性系统的鲁棒自适应轨迹线性化控制

针对一类不确定非线性系统,研究了一种新的鲁棒自适应轨迹线性化控制方案.利用径向基神经网络的在线逼近能力以及被控对象分析模型的有用信息设计一种径向基神经网络干扰观测器来估计系统中存在的不确定性.观测器输出用于设计补偿控制律抵消不确定性对系统性能的影响,鲁棒自适应控制律用于克服逼近误差.采用Lyapunov方法严格证明了在自适应调节律作用下闭环系统所有误差信号最终有界.最后利用倒立摆系统验证了新方法的有效性.     

A robust adaptive observer for a class of singular nonlinear uncertain systems

This paper proposes a robust adaptive observer for a class of singular nonlinear non-autonomous uncertain systems with unstructured unknown system and derivative matrices, and unknown bounded nonlinearities. Unlike many existing observers, no strong assumption such as Lipschitz condition is imposed on the recommended system. An augmented system is constructed, and the unknown bounds are calculated online using adaptive bounding technique. Considering the continuous nonlinear gain removes the chattering which may appear in practical applications such as analysis of electrical circuits and estimation of interaction force in beating heart robotic-assisted surgery. Moreover, a simple yet precise structure is attained which is easy to implement in many systems with significant uncertainties. The existence conditions of the standard form observer are obtained in terms of linear matrix inequality and the constrained generalised Sylvester's equations, and global stability is ensured. Finally, simulation results are obtained to evaluate the performance of the proposed estimator and demonstrate the effectiveness of the developed scheme.     

不确定高次随机非线性系统的自适应控制

针对一类含有噪声干扰和非线性参数的高次随机非线性系统,研究了依概率全局自适应稳定问题.在噪声的协方差未知的情况下,利用自适应增加幂积分方法和参数分离技术,提出了一种反馈占优设计方法并构造了一个光滑自适应控制器.该控制器能保证闭环系统依概率全局稳定,并且系统的状态几乎必然收敛到零.仿真例子验证了控制方案的有效性.     

Output regulation for a class of uncertain nonlinear systems with nonlinear exosystems and its application

In this paper, we consider the global robust output regulation problem for a class of uncertain nonlinear systems with nonlinear exosystems. By employing the internal model approach, we show that this problem boils down to a global robust stabilization problem of a time-varying nonlinear system in lower triangular form, the solution of which will lead to the solution of the global robust output regulation problem. An example shows the effectiveness of the proposed approach.     

非线性系统的直接自适应输出反馈监督模糊控制

针对一类单输入单输出非线性不确定系统，提出一种稳定的直接自适应模糊输出反馈监督控制算法，该算法不需要系统的状态完全可测的假设条件，监督控制不仅迫使系统的状态在指定的集合内，而且当模糊自适应控制处于良好的工作状态时，监督控制可以关闭，证明了整个模糊自适应输出反馈控制算法可以保证闭环系统稳定。     

不确定非线性系统的鲁棒自适应输出反馈控制

基于自适应非线性阻尼,提出一种鲁棒自适应输出反馈控制方法。该方法适用于带有未建模动态、未知非线性、有界扰动、未知非线性参数和不确定控制系数的多输入多输出非线性系统。理论证明,在一定的假设条件下,该方法能保证闭环系统所有动态信号有界;不论有多少不确定非线性参数、多高阶的非线性系统,只需要一个自适应控制参数和观察参数;而且通过选择适当的控制器和观测器参数,能使控制误差和估计误差达到任意小。仿真结果表明了所提出方法的有效性。     

Adaptive robust stabilisation of uncertain nonlinear dynamical systems: an improved backstepping approach

The main purpose of this paper is to propose a design approach by which some simple adaptive robust controllers can be synthesised for a class of uncertain nonlinear dynamical systems which can be transformed into uncertain strict-feedback nonlinear systems. In this paper, an improved backstepping design approach is presented to synthesising a class of continuous adaptive robust state-feedback controllers with a rather simple structure. The improved backstepping design approach can avoid the repeated differentiation problem which appears in using the conventional backstepping algorithm. In particular, it is not required to know the nonlinear upper bound functions of uncertainties. In the light of the presented approach, the state-feedback controllers can be constructed to be linear in the state, with the time-varying control gains which can be self-tuned by the adaptive laws. Similar to the conventional backstepping algorithm, the improved backstepping approach can be extended to a rather large class of uncertain nonlinear systems, and by combining the improved backstepping approach with other control methods, it may be expected to obtain a number of interesting results.     

未知多变量非线性系统自适应模糊预测控制

对一类未知多变量非线性系统提出了直接自适应模糊预测控制方法,此方法首先对被控对象提出了线性时变子模型加非线性子模型的预测模型,然后直接用模糊逻辑系统组成的向量来设计预测控制器,并基于时变死区函数对控制器中的未知向量和广义误差估计值中的未知矩阵进行自适应调整．文中证明了此方法可使广义误差向量估计值收敛到原点的一个邻域内．