Adaptive Output‐Feedback Control of Nonlinear Systems with Multiple Uncertainties

This paper addresses the global stabilization via adaptive output‐feedback for a class of uncertain nonlinear systems. Remarkably, the systems under investigation are with multiple uncertainties: unknown control directions, unknown growth rates and unknown input bias, and can be used to describe more physical plants. Multiple uncertainties, which usually cannot be compensated by a sole compensation technique, may give rise to big technical difficulty for controller design. To overcome such difficulty and to achieve the global stabilization, a new adaptive output‐feedback scheme is proposed in this paper, by flexibly combining Nussbaum‐type function, tuning function technique and extended state observer. It is shown that, under the designed controller, the system states globally converge to zero. A simulation example on non‐zero set‐point regulation is given to demonstrate the effectiveness of the theoretical results.     

Global Output‐Feedback Stabilization for Stochastic Nonlinear Systems with Function Control Coefficients

This paper investigates the global output‐feedback stabilization for a class of stochastic nonlinear systems with function control coefficients. Notably, the systems in question possess control coefficients that are functions of output, rather than constants; hence, they are different from the existing literature on stochastic stabilization. To solve the control problem, an appropriate reduced‐order observer is introduced to reconstruct the unmeasured system states before a smooth output‐feedback controller is designed using the backstepping method, which guarantees that the closed‐loop system is globally asymptotically stable in probability. This paper combines the related results in the deterministic and stochastic setting and gives the first treatment on the global output‐feedback stabilization for the stochastic nonlinear systems with function control coefficients. A simulation example is given also to illustrate the effectiveness of the proposed approach.     

Global Practical Tracking for Nonlinear Systems With More Unknowns via Adaptive Output‐Feedback

This paper investigates the global practical tracking via adaptive output‐feedback for a class of uncertain nonlinear systems. Essentially different from the closely related literature, the system under investigation possesses unknown time‐varying control coefficients and a polynomial‐of‐output growth rate, and meanwhile, the system nonlinearities and the reference signal allow serious unknowns. For this, an adaptive observer is designed to reconstruct the system unmeasured states, where a new dynamic gain is introduced to compensate the serious unknowns in the system nonlinearities and the reference signal. Based on this and by backstepping technique, an adaptive output‐feedback controller is successfully designed, such that all the states of the closed‐loop system are bounded, and the tracking error will be prescribed sufficiently small after a finite time. A numerical simulation is provided to demonstrate the effectiveness of the proposed method.     

一类具有未知控制方向非线性系统的输出反馈自适应控制

研究了一类控制方向未知非线性系统的输出反馈自适应镇定问题. 首先, 通过一线性状态变换, 将未知控制系数集中起来, 从而将原系统变换为适于控制设计的新系统. 然后, 分别引入状态观测器和参数估计器, 并应用积分反推和调节函数方法, 给出了输出反馈稳定控制律的构造性设计过程. 可以证明,所设计的控制器确保原系统状态渐近收敛到原点, 而其它闭环系统状态有界. 仿真结论验证了所提出方法的有效性.     

Robust Adaptive Output‐Feedback Dynamic Surface Control of a Class of Nonlinear Systems with Unmodeled Dynamics

This paper presents a robust adaptive output‐feedback dynamic surface control (DSC) for a class of nonlinear systems with unmodeled dynamics or/and uncertain time‐varying disturbances. Based on traditional K‐filters, the proposed adaptive DSC scheme is able to guarantee semi‐global stability of the closed‐loop system without applying any approximation techniques. The adaptive law is necessary only at the first design step, which, together with the introduction of a first‐order filter at each design step, makes the control law easy to implement. Moreover, it is shown that the tracking error can converge to an arbitrarily small residual set by adjusting only one design parameter.     

Adaptive Output Feedback Control for a Class of Uncertain Stochastic Nonlinear Systems With Unknown Time‐Delays

This paper investigates the problem of output feedback control for a class of stochastic nonlinear systems with time‐delays. Using dynamic gain scaling technique, an adaptive update law is introduced to the observer and controller to deal with the unknown parameters. Based on the Lyapunov‐Krasovskii functional and stochastic Barbalat's lemma, it is proved that the proposed universal‐type adaptive output feedback controller can regulate all the states of the closed‐loop system almost surely. A simulation example is presented to illustrate the effectiveness of the proposed design procedure.     

随机非线性系统鲁棒自适应反馈控制器的积分反推方法设计

考虑了一类随机非线性系统的鲁棒自适应控制问题.采用Ito随机微分方程描述系统,进而在概率意义下研究系统的鲁棒稳定性.应用积分反推(backstepping)方法,系统地给出了设计状态反馈及输出反馈鲁棒自适应控制器的方法.同时构造出了适当形式的四次型的自适应控制Lyapunov函数(CLF).     

虚拟控制增益函数未知的随机非线性系统模糊自适应控制

The problem of track control is studied for a class of strict-feedback stochastic nonlinear systems in which unknown virtual control gain function is the main feature. First, the so-called stochastic LaSalle theory is extended to some extent, and accordingly, the results of global ultimate boundedness for stochastic nonlinear systems are developed. Next, a new design scheme of fuzzy adaptive control is proposed. The advantage of it is that it does not require priori knowledge of virtual control gain function sign, which is usually demanded in many designs. At the same time, the track performance of closed-loop systems is improved by adaptive modifying the estimated error upper bound. By theoretical analysis, the signals of closed-loop systems are globally ultimately bounded in probability and the track error converges to a small residual set around the origin in 4th-power expectation.     

Finite‐Time Stabilization of Stochastic High‐Order Nonlinear Systems

This paper considers the problem of global finite‐time stabilization in probability for stochastic high‐order nonlinear systems in which the power order is greater than or equal to one and the drift and diffusion terms satisfy weaker growth conditions. Based on stochastic Lyapunov theorem on finite‐time stability, via the combined adding one power integrator and sign function method, constructing a Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed‐loop system globally finite‐time stable in probability.     

一类非线性系统的间接自适应输出反馈模糊控制

针对一类未知非线性系统,提出一种输出反馈控制方法。首先在假设系统状态已知的情况下设计状态反馈控制器,实现跟踪性能。然后在系统状态不完全可测的情况下,通过设计高增益观测器对系统的状态进行估计,实现输出反馈控制器设计。最后证明所设计的输出反馈控制器可获得状态反馈控制器所取得的最大最小问题的跟踪性能。     

控制方向未知的时变非线性系统鲁棒控制

针对一类具有未知时变控制方向、不确定时变参数以及未知时变有界干扰的严反馈非线性系统,给出一种带有死区修正算法的鲁棒控制方法.在控制系数符号未知的情况下,通过在反步法中引入Nussbaum增益和死区修正技术,得到一种修正的鲁棒反步设计方法.该方法不需要未知时变控制系数的上下界先验知识以及不确定参数和外界干扰的上界信息.算法保证了闭环系统所有信号的有界性,同时使得跟踪误差收敛于零的任意小邻域内.     

Output‐Feedback Nonlinear Adaptive Control of Single‐Phase Half‐Bridge Ups Systems

We consider the problem of controlling single‐phase half‐bridge power converters in UPS systems operating in the presence of changing load. The control objective is twofold: (i) ensuring a satisfactory power factor correction (PFC) at the grid–UPS connection; (ii) guaranteeing a tight regulation of the DC bus voltage and the half‐bridge inverter output voltage despite changes in load. The considered control problem entails several difficulties including: (i) the high dimension and strong nonlinearity of the system; (ii) the numerous state variables that are inaccessible to measurements; (iii) the uncertainty that prevails on some system parameters. The problem is dealt with using a multi‐loop nonlinear adaptive control system that makes use of the backstepping design technique. The inner loop ensures the PFC objective and involves an adaptive observer estimating the grid voltage and impedance parameters. The intermediary loop regulates the inverter output voltage to its reference, which is a sinusoidal wave, and it also contains an observer estimating the current in the inverter coil. The outer loop regulates the DC bus voltage up to small size ripples. The controller performances are formally analyzed using system averaging theory.     

Dynamic Output‐Feedback Control for T‐S Fuzzy Systems with Input Time‐Varying Delay

This paper considers the problem of the control for T‐S fuzzy systems with input time‐varying delay via dynamic output feedback. Firstly, by applying the reciprocally convex approach, new delay‐dependent sufficient condition for performance analysis is obtained. Then, a less conservative condition for the existence of the controllers is given in terms of linear matrix inequalities (LMIs). Moreover, in the considered system, the time‐delay term is included in the measured output. This results in the difficulty in designing the controllers being increased and the obtained results being applied to a wider class of fuzzy systems than the most existing ones. The main contribution of this work lies in the application of the reciprocally convex inequality and the time‐delay term included in the measured output. Finally, the advantages and effectiveness of the present results are shown by several numerical examples.     

Robust Adaptive Fuzzy Control of Nonlinear Systems with Unknown and Time‐Varying Saturation

In this paper, a robust adaptive fuzzy control approach is proposed for a class of nonlinear systems in strict‐feedback form with the unknown time‐varying saturation input. To deal with the time‐varying saturation problem, a novel controller separation approach is proposed in the literature to separate the desired control signal from the practical constrained control input. Furthermore, an optimized adaptation method is applied to the dynamic surface control design to reduce the number of adaptive parameters. By utilizing the Lyapunov synthesis, the fuzzy logic system technique and the Nussbaum function technique, an adaptive fuzzy control algorithm is constructed to guarantee that all the signals in the closed‐loop control system remain semiglobally uniformly ultimately bounded, and the tracking error is driven to an adjustable neighborhood of the origin. Finally, some numerical examples are provided to validate the effectiveness of the proposed control scheme in the literature.     

一类模糊非线性系统的直接鲁棒自适应输出反馈控制

针对一类未知非线性系统,利用模糊逻辑系统、H^∞控制和高增益观测器,提出一种模糊直接鲁棒自适应输出反馈控制方法。证明了所设计的输出反馈控制方法不但能保证闭环控制系统稳定,而且可获得在状态反馈控制器下的性能。仿真结果进一步验证了所提出方法的有效性。     

模糊CMAC神经网络用于MIMO非线性系统的反馈线性化

针对一类多输入多输出（ＭＩＭＯ）连续时间非线性系统,应用模糊ＣＭＡＣ神经网络,给出一种状态反馈控制器,用于使状态反馈可线笥化的未知的非线性动态系统儿得要求的患 很弱的假设条件下,应用李雅普诺夫稳定性理论严格地证明了闭环系统内的所有信号为一致最终有界（ＵＵＢ）。     

Output‐Feedback Control for Continuous‐time Interval Positive Systems under L1 Performance

This paper is concerned with the design of an L₁‐induced output‐feedback controller for continuous‐time positive systems with interval uncertainties. A necessary and sufficient condition for stability and an L₁‐induced performance of interval positive linear systems is proposed in terms of linear inequalities. Based on this, conditions for the existence of robust static output‐feedback controllers are established and an iterative convex optimization approach is developed to solve the conditions. For special single‐input‐multiple‐output (SIMO) positive systems, the problem of controller synthesis is completely solved with the help of an analytical formula for the L₁‐induced norm. An illustrative example is provided to show the effectiveness and applicability of the theoretical results.     

基于CMAC 神经网络的一类M I MO非线性系统的自适应反馈线性化

在已知系统标称模型的基础上,将ＣＭＡＣ;神经网络用于一类状态反馈可线性化的ＭＩＭＯ连续时间不确定性非线性系统的鲁棒自适应反馈线性化,使系统获得要求的跟踪性能。在很弱的假设条件下,应用李雅普诺夫稳定性理论证明了闭环系统内的所有信号为一致最终有界。仿真算例验证了该方法的正确性与有效性。     

一类具有未知幂次的高阶不确定非线性系统的自适应控制

研究了一类具有未知幂次的高阶不确定非线性系统的自适应跟踪控制问题. 在无需系统函数先验知识的条件下, 采用积分反推技术和障碍李雅普诺夫函数, 提出了一种新颖的自适应跟踪控制算法. 该控制算法的显著特点是所设计的自适应控制器均与系统幂次无关, 并且能够保证闭环系统的所有信号皆有界. 仿真算例验证了该控制算法的有效性.     

Global Robust Stabilization via Sampled‐Data Output Feedback for Nonlinear Systems with Uncertain Measurement and Control Gains

This paper studies the problem of using a sampled‐data output feedback controller to globally stabilize a class of nonlinear systems with uncertain measurement and control gains. A reduced‐order observer and a linear output control law, both in the sampled‐data form, are designed without the precise knowledge of the measurement and control gains except for their bounds. The observer gains are chosen recursively in a delicate manner by utilizing the output feedback domination approach. The allowable sampling period is determined by estimating and restraining the growth of the system states under a zero‐order‐hold input with the help of the Gronwall–Bellman Inequality. A DC–DC buck power converter as a real‐life example will be shown by numerical simulations to demonstrate the effectiveness of the proposed control method.