一类非线性系统输出反馈自适应扰动抑制

研究了一类依赖于不可量测状态增长非线性系统的输出反馈自适应扰动抑制问题. 与现有文献不同, 所研究的系统具有更多的未知参数, 尤其是不确定控制系数. 为了解决该 问题, 引入了动态高增益K-滤波器, 进而构造了基于K-滤波器的状态观测器. 在输出反馈控制器的设计过程中, 引入了待定设计参数, 增加了设计的自由度. 结果表明, K-滤 波器的动态增益和设计参数的恰当选择可以保证闭环系统的全局稳定性, 从而实现系统 L2-增益意义的扰动抑制.     

Observer‐based adaptive control for nonlinear strict‐feedback stochastic systems with output constraints

In this paper, an adaptive output‐feedback control problem is investigated for nonlinear strict‐feedback stochastic systems with input saturation and output constraint. A barrier Lyapunov function is used to solve the problem of output constraint. Then, fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. To overcome the difficulties in designing the control signal in the saturation, we introduce an auxiliary signal in the n + 1th step in the deduction. By combining Nussbaum technique and the adaptive backstepping technique, an adaptive output‐feedback control method is developed. The proposed control method not only overcomes the problem of the compensation for the nonlinear term from the input saturation but also overcomes the problem of unavailable state measurements. It is proved that all the signals of the closed‐loop system are semiglobally uniformly ultimately bounded. Finally, the effectiveness of the proposed method is verified by the simulation results.     

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.

     

Adaptive Stabilization of a Class of Reaction–Diffusion Systems

This paper is concerned with adaptive stabilization of a class of reaction–diffusion systems governed by a nonlinear partial differential equation of the first order in time but the fourth order in space. In the presence of bounded deterministic disturbances, the adaptive stabilizer is constructed by the concept of high-gain nonlinear output feedback and the estimation mechanism of the unknown parameters. In the control system the global asymptotic stability and the convergence of the system state to zero will be guaranteed.     

一类线性时变系统的输出反馈控制

基于线性时不变系统能控能观标准型变换及非线性系统高增益观测器方法,本文研究了一类线性时变系统 的输出反馈控制问题. 通过引入时变的状态变量坐标变换,分别设计了线性时变系统的状态反馈控制器、状态观测器以及基于 状态观测器的输出反馈控制器. 进一步地,本文分别证明了观测器动态误差是渐近收敛于零的,而状态反馈控制器以及输出反馈控制器可以 保证闭环系统的渐近稳定性.     

Nonlinear uncertain systems and robustness optimization

An approach to (adaptive) stabilization is developed for a class of uncertain nonlinearly perturbed linear dynamical systems modelled by a controlled differential inclusion on Rⁿ. The essential features are nonlinear feedback and optimization of robustness with respect to unmatched uncertainty. The approach is geometric: (i) a family ?? of proper subspaces V ? Rⁿ is introduced with the property that {0} ? V is an asymptotically stable equilibrium for the projection, onto V, of the unperturbed linear flow; (ii) for the perturbed system, it is then shown that each V ? ?? can be rendered attractive and (almost) invariant by some choice of feedback determined by the nature of the perturbation and other a priori system information; specifically, under differing hypotheses, we can render V ? ?? almost invariant and attractive, or invariant and finite-time attractive, or adaptively attractive via, respectively, linear high-gain feedback or discontinuous feedback, or adaptive feedback. Associated with each V ? ?? is a measure of robustness with respect to unmatched uncertainty (a stability radius), quantified by a real parameter η. The problem of optimizing this measure is formulated as an optimization problem over ??, solvable (in a supremal sense of η-maximizing sequences (V_j) ??) via solutions of particular algebraic Riccati equations of order k ≤ (n - m), where m ≤ n is the control dimension; typically k = n - m..     

Output feedback control of nonlinear systems subject to sensor data losses

In this work, we focus on output feedback control of nonlinear systems subject to sensor data losses. We initially construct an output feedback controller based on a combination of a Lyapunov-based controller with a high-gain observer. We then study the stability and robustness properties of the closed-loop system in the presence of sensor data losses for both the continuous and sampled-data systems. We state a set of sufficient conditions under which the closed-loop system is guaranteed to be practically stable. The theoretical results are demonstrated using a chemical process example.     

Adaptive λ-tracking for a class of infinite-dimensional systems

For a class of high-gain stabilizable multivariable linear infinite-dimensional systems we present an adaptive control law which achieves approximate asymptotic tracking in the sense that the tracking error tends asymptotically to a ball centred at 0 and of arbitrary prescribed radius λ>0. This control strategy, called λ-tracking, combines proportional error feedback with a simple nonlinear adaptation of the feedback gain. It does not involve any parameter estimation algorithms, nor is it based on the internal model principle. The class of reference signals is W^1,∞, the Sobolev space of absolutely continuous functions which are bounded and have essentially bounded derivative. The control strategy is robust with respect to output measurement noise in W^1,∞ and bounded input disturbances. We apply our results to retarded systems and integrodifferential systems.     

Adaptive nonlinear output feedback tracking with a partialhigh-gain observer and backstepping

An adaptive output feedback controller for nonlinear systems with nonlinearities depending on the first r (1⩽r⩽n) derivatives of the output is proposed. The derivatives are estimated with a partial state high-gain observer, and the remaining states are handled using a backstepping method. Compared with methods based on full state high-gain observer, this approach improves robustness with respect to measurement noise and avoids overparametrization. Semiglobal tracking is proven under the assumption that the regressor is persistently exciting     

A global state feedback output regulating control for uncertain systems in strict feedback form

A family of single-input, single-output, nonlinear systems in strict feedback form with uncertain constant parameters which appear linearly and belong to a known compact set Π is considered. A global robust output regulation problem via state feedback is addressed and solved under the assumptions that the regulator equations are solvable in Π, the output equation does not depend on uncertain parameters, no modelled disturbances affect the system and the output reference signal is generated by a known exosystem whose state is bounded and available for feedback. Robust adaptive techniques are used to guarantee closed loop boundedness and to achieve, without requiring persistency of excitation, global asymptotic output regulation for a class of feedback linearizable systems which may have unbounded uncertain tracking dynamics or may not have a well-defined global relative degree.     

Normal forms for multi‐input flat systems of minimal differential weight

We present normal forms for nonlinear control systems that are the closest to static feedback linearizable ones, that is, for systems that become feedback linearizable via the simplest dynamic feedback, which is the one‐fold prolongation of a suitably chosen control. They form a particular class of flat systems, namely those of differential weight n + m + 1, where n is the number of states and m is the number of controls. We also show that the dynamic feedback may create singularities in the control space depending on the state and we discuss them. We also address the issue of the normalization of the system only versus that of the system together with a flat output. Finally, we illustrate our results by several examples.     

一类模糊非线性系统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,提出了 一种模糊自适应输出反馈控制方法.证明了所设计的输出反馈控制器可以获得状态反馈控制 器的性能.仿真结果证明了所提出方法是有效的.     

High-gain feedback in non-linear control systems†

High-gain state and output feedback are investigated for non-linear control systems with a single additive input by using singular perturbation techniques.

Classical approximation results (Tihonov-like theorems) in singular perturbation theory are extended to non-linear control systems by defining a composite additive control strategy, a control-dependent fast equilibrium manifold and non-linear change of coordinates.

Those tools and an appropriate change of coordinates show that high-gain state feedback and variable structure control systems can be equivalently used for approximate non-linearity compensation in feedback-linearizable systems.

Next the effect of high-gain output feedback is shown to be related to the strong invertibility property and the relative order of invertibility. For strongly invertible systems the slow reduced subsystem coincides with the dynamics of the inverse system when zero input is applied and with the unobservable dynamics when a certain input-output feedback-linearizable transformation is applied.     

Semi-global robust output regulation of minimum-phase nonlinear systems based on high-gain nonlinear internal model

We consider the assumption of existence of the general nonlinear internal model that is introduced in the design of robust output regulators for a class of minimum-phase nonlinear systems with rth degree (r ≥ 2). The robust output regulation problem can be converted into a robust stabilisation problem of an augmented system consisting of the given plant and a high-gain nonlinear internal model, perfectly reproducing the bounded including not only periodic but also nonperiodic exogenous signal from a nonlinear system, which satisfies some general immersion assumption. The state feedback controller is designed to guarantee the asymptotic convergence of system errors to zero manifold. Furthermore, the proposed scheme makes use of output feedback dynamic controller that only processes information from the regulated output error by using high-gain observer to robustly estimate the derivatives of the regulated output error. The stabilisation analysis of the resulting closed-loop systems leads to regional as well as semi-global robust output regulation achieved for some appointed initial condition in the state space, for all possible values of the uncertain parameter vector and the exogenous signal, ranging over an arbitrary compact set.     

Adaptive output-feedback control for a class of nonlinear systems with actuator failures and input quantisation

In this paper, an adaptive output feedback control technique is proposed for a class of nonlinear systems with unknown parameters, unknown nonlinear functions, quantised input and possible actuator failures up to infinity. A modified backstepping approach is proposed by the use of high-gain K-filters, hyperbolic tangent function property and bound-estimation approach to compensate for the effect of possible number of actuator failures up to infinity, input quantisation and unknown nonlinear functions. It is proved both mathematically and by simulation that with the proposed controller, all the signals of the closed-loop system are globally bounded despite of input quantisation, unknown nonlinear functions and possible number of actuator failures up to infinity.     

Simple adaptive stabilization of high-gain stabilizable systems

It is shown that the simple adaptive feedback strategy

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is a universal adaptive stabilizer for the class of single-input, single-output, finite-dimensional, linear systems which are stabilizable by either negative or positive high-gain feedback.     

Output feedback control of switched nonlinear systems using multiple Lyapunov functions

This work presents a hybrid nonlinear control methodology for a broad class of switched nonlinear systems with input constraints. The key feature of the proposed methodology is the integrated synthesis, via multiple Lyapunov functions, of “lower-level” bounded nonlinear feedback controllers together with “upper-level” switching laws that orchestrate the transitions between the constituent modes and their respective controllers. Both the state and output feedback control problems are addressed. Under the assumption of availability of full state measurements, a family of bounded nonlinear state feedback controllers are initially designed to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding stability region for each mode. A set of switching laws are then designed to track the evolution of the state and orchestrate switching between the stability regions of the constituent modes in a way that guarantees asymptotic stability of the overall switched closed-loop system. When complete state measurements are unavailable, a family of output feedback controllers are synthesized, using a combination of bounded state feedback controllers, high-gain observers and appropriate saturation filters to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding output feedback stability regions in terms of the input constraints and the observer gain. A different set of switching rules, based on the evolution of the state estimates generated by the observers, is designed to orchestrate stabilizing transitions between the output feedback stability regions of the constituent modes. The differences between the state and output feedback switching strategies, and their implications for the switching logic, are discussed and a chemical process example is used to demonstrate the proposed approach.     

Disturbance-observer-based sampled-data adaptive output feedback control for a class of uncertain nonlinear systems

In this paper, a sampled-data adaptive output feedback controller is proposed for a class of uncertain nonlinear systems with unmeasured states, unknown dynamics and unknown time-varying external disturbances. To approximate uncertain nonlinear functions, radial basis function neural networks (RBFNNs) are employed. The state observer and the disturbance observer (DO) are constructed to estimate the unmeasured state and the external disturbance, respectively. Then, the sampled-data adaptive output feedback controller and adaptive laws are designed by using the backstepping design technique. The allowable sampling period T is derived to guarantee that all states of the resulting closed-loop system are semi-globally uniformly ultimately bounded. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed approach.     

Observer-based tracking control for MIMO pure-feedback nonlinear systems with time-delay and input quantisation

In addressing the adaptive neural backstepping control for multiple-input and multiple-output nonlinear systems in pure-feedback form with time-delay and input quantisation, we construct a high-gain state observer and an output-feedback adaptive control scheme using backstepping method, with neural networks to estimate the uncertain nonlinear functions. Then, we propose an output feedback neural controller that ensures all the state trajectories in the time-delay quantised nonlinear systems are ultimately bounded, with the control signal being quantised by either a hysteretic quantiser or a logarithmic quantiser. An illustrative example is presented to show the applicability of the new control method developed.     

A note on reduced order stabilizing output feedback controllers

In this paper we show that if a certain class of nonlinear systems is globally asymptotically stabilizable through an n-dimensional output feedback controller then it can be always stabilized through an (n − p)-dimensional output feedback controller, where p is the number of outputs and n is the dimension of the state space. This result gives an alternative construction of reduced order controllers for linear systems, and recovers in a more general framework the concept of dirty derivative, used in the framework of rigid and elastic joint robots, and gives an alternative procedure for designing reduced-order controllers for nonlinear systems considered in the existing literature.