Multivariable extension of global finite‐time HOSM based differentiator for output‐feedback unit vector and smooth binary control

In this paper, we propose a unit vector control law by output feedback to solve the problem of global exact output tracking for a class of multivariable uncertain plants with nonlinear disturbances. In order to face the nonuniform arbitrary relative degree obstacle, we extend our earlier estimation scheme based on global finite‐time differentiators using dynamic gains to a multivariable architecture. A diagonally stable condition over the system high‐frequency gain (HFG) matrix has to be assumed. Preserving the simplicity of its mono variable framework, variable gain super‐twisting algorithm (STA) is employed to obtain the robust and exact multivariable differentiator. Moreover, state‐norm observers for the unmeasured state variables are constructed to upper bound the disturbances as well as to update the differentiator gains, being both state dependent. Uniform global exponential stability and ultimate exact tracking are proved. As an alternative to chattering alleviation, we appeal to the Emelyanov's concept of binary control in order to obtain a continuous control signal replacing the unit vector function in the controller by a high‐gain gradient adaptive law with parameter projection. As shown in the existing literature for mono variable systems, the proposed multiparameter binary‐adaptive formulation tends to the unit vector control as the adaptation gain increases to infinity, also smoothing the transition from adaptive to sliding mode control. A numerical example is portrayed to illustrate the potentialities of the developed multivariable techniques.     

Output‐feedback tracking in causal nonminimum‐phase nonlinear systems using higher‐order sliding modes

Asymptotic output‐feedback tracking in a class of causal nonminimum phase uncertain nonlinear systems is addressed via sliding mode techniques. Sliding mode control is proposed for robust stabilization of the output tracking error in the presence of a bounded disturbance. The output reference profile and the unknown input/disturbance are supposed to be described by unknown linear exogenous systems of a given order. Local asymptotic stability of the output tracking error dynamics along with the boundedness of the internal states are proven. The unstable internal states are estimated asymptotically via the proposed multistage observer that is based on the method of extended system center. A higher‐order sliding mode observer/differentiator is used for the exact estimation of the input–output states in a finite time. The bounded disturbance is reconstructed asymptotically. A numerical example illustrates the efficiency of the proposed output‐feedback tracking approach developed for causal nonminimum phase nonlinear systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Observer‐based leader‐following consensus of uncertain nonlinear multi‐agent systems

In this paper, the leader‐following consensus problem of uncertain high‐order nonlinear multi‐agent systems on directed graph with a fixed topology is studied, where it is assumed that the relative states of a follower and its neighbors are immeasurable and only the relative outputs are available. Nonlinear adaptive observers are firstly proposed for each follower to estimate the states of it and its neighbors, and an observer‐based distributed adaptive control scheme is constructed to guarantee that all followers asymptotically synchronize to a leader with tracking errors being semi‐globally uniform ultimate bounded. On the basis of algebraic graph theory and Lyapunov theory, the closed‐loop system stability analysis is conducted. Finally, numerical simulations are presented to illustrate the effectiveness and potential of the proposed new design techniques. Copyright © 2017 John Wiley & Sons, Ltd.     

Finite‐time angular velocity observers for rigid‐body attitude tracking with bounded inputs

The attitude tracking of a rigid body without angular velocity measurements is addressed. A continuous angular velocity observer with fractional power functions is proposed to estimate the angular velocity via quaternion attitude information. The fractional power gains can be properly tuned according to a homogeneous method such that the estimation error system is uniformly almost globally finite‐time stable, irrespective of control inputs. To achieve output feedback attitude tracking control, a quaternion‐based nonlinear proportional‐derivative controller using full‐state feedback is designed first, yielding uniformly almost globally finite‐time stable of the attitude tracking system as well as bounded control torques a priori. It is then shown that the certainty equivalent combination of the observer and nonlinear proportional‐derivative controller ensures finite‐time convergence of the attitude tracking error for almost all initial conditions. The proposed methods not only avoid high‐gain injection, as opposed to the semi‐global results, but also overcome the unwinding problem associated with some quaternion‐based observers and/or controllers. Numerical simulations are presented to verify the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Global adaptive regulation of feedforward nonlinear time‐delay systems by output feedback

The problem of global adaptive state regulation is investigated via output feedback for uncertain feedforward nonlinear time‐delay systems. Compared with existing results, our control schemes can be applicable to more general nonlinear time‐delay systems because of combining the low‐gain scaling approach with the backstepping method. In particular, we allow that there exist uncertain output function and uncertain growth rate imposed on nonlinear terms. Also, one considers a class of nonlinear systems with main‐axis delay. By the Lyapunov–Krasovskii theorem, delay‐independent controllers are proposed by constructing novel low‐gain observers driven by system input, to regulate the states of original system while all the closed‐loop signals are globally bounded. Furthermore, two examples are given to illustrate the usefulness of our results. Copyright © 2016 John Wiley & Sons, Ltd.     

High‐gain nonlinear observer‐based impedance control for deformable object cooperative teleoperation with nonlinear contact model

Unmeasurable object deformation and local communication time delays between the slave robots influence the manipulation effect for multirobot multioperator teleoperation. In this article, a distributed control method based on high‐gain nonlinear observer, interactive identification, and impedance control is proposed for this problem. First, we use Hunt‐Crossley contact model and deduce the desired synchronizing object state in cooperative teleoperation. Second, an impedance item expressed by the internal position errors is presented to decrease object position tracking errors. For the unmeasurable object deformation, an interactive identification method is proposed for estimating unknown variables. Third, we consider both varying communication time delays and local time delays in the slave side. Two mirror high‐gain nonlinear observers are designed for estimating other slave robots' real‐time state. Finally, we build the system controllers and prove the stability of the closed‐loop system and the boundless of estimating errors using Lyapunov functions. Comparable simulation results executed by the physical system present that the position and internal force tracking errors of the object decrease in the designated cooperative tasks.     

Synchronization and Tracking Control for Dual‐motor Driving Servo Systems with Friction Compensation

A nonsingular fast terminal sliding mode (NFTSM) controller is designed by incorporating the variable gain neural network (NN) observer, which is utilized to guarantee motor speed synchronization and load position tracking of dual‐motor driving servo systems. By designing the variable gain NN observer, the states and uncertain nonlinearities of servo systems are estimated with fast convergence rate and small steady‐state error, where the effects from external disturbance are suppressed as well. Based on the estimated states, the cross‐coupling synchronization strategy and NFTSM tracking scheme are designed to achieve the rapid speed synchronization and precise load tracking, where the NNs are introduced to approximate and compensate friction nonlinearities. In particular, a novel nonlinear synchronization factor characterizing the degree of speed synchronization is proposed to achieve switching between synchronization control and tracking control, which is proven to deal with the coupling problem of synchronization and tracking. Finally, the comparative simulations and experiments are included to verify the reliability and effectiveness.     

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.     

Reduced‐order observer‐based output‐feedback tracking control of nonlinear systems with state delay and disturbance

In this paper, we investigate the problem of output‐feedback tracking control for a class of nonlinear SISO systems in the strick‐feedback form, which are subject to both uncertain delay‐related functions and disturbances. A reduced‐order observer is first introduced to provide the estimates of the unmeasured states. Then, an output‐feedback controller is recursively designed based on the backsteppng method. By constructing an appropriate Lyapunov–Krasovskii functional, we prove that all the signals in the closed‐loop system are bounded. The tracking performance is guaranteed by suitably choosing the design parameters. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed control algorithm. Copyright © 2009 John Wiley & Sons, Ltd.     

An Active Disturbance Rejection Approach to Leader‐Follower Controlled Formation

This article describes the design of a linearizing, observer‐based, robust dynamic feedback control scheme for output reference trajectory tracking tasks in a leader‐follower non‐holonomic car formation problem. The approach is based on the cars' kinematic models. A radical simplification in the form of a global ultra‐model is proposed on the follower's exact open loop position tracking error dynamics obtained via flatness considerations. This results in a system described by an additively disturbed set of two, second order integrators with non‐linear velocity dependent control input gain matrix. The unknown additive disturbances are modeled as absolutely uniformly bounded time signals which may be locally approximated by arbitrary elements of a sufficiently high degree family of Taylor polynomials. Linear high‐gain Luenberger observers of the generalized proportional integral (GPI) type may be readily designed. These observers include the self updating internal model of the unknown disturbance input vector components in the form of generic, instantaneous, time‐polynomial models. The proposed (GPI) observers, which are the dual counterpart of GPI controllers [17], achieve a simultaneous disturbance estimation and tracking error phase variables estimation. This on‐line gathered information is used to advantage on the follower's feedback controller thus allowing for a simple, yet efficient, disturbance and control input gain cancelation effort. The results are applied to have the follower track a time‐delayed version of the actual leader's trajectory. Experimental results are presented which illustrate the robustness and viability of the proposed approach.     

Composite disturbance‐observer‐based control and H ∞ control for nonlinear time‐delay systems

A novel type of control scheme combined the distance‐observer‐based control (DOBC) with H_∞ control is proposed for a class of nonlinear time‐delay systems subject to disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other is supposed to have the bounded H₂ norm. The disturbance observers based on regional pole placement and D‐stability theory are presented, which can be designed separately from the controller design. By integrating disturbance‐observer‐based control with H_∞ control laws, the disturbances can be rejected and attenuated, simultaneously, the desired dynamic performances can be guaranteed for nonlinear time‐delay systems with unknown nonlinear dynamics. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Fractional‐order–dependent global stability analysis and observer‐based synthesis for a class of nonlinear fractional‐order systems

This paper focuses on proposing novel conditions for stability analysis and stabilization of the class of nonlinear fractional‐order systems. First, by considering the class of nonlinear fractional‐order systems as a feedback interconnection system and applying small‐gain theorem, a condition is proposed for L₂‐norm boundedness of the solutions of these systems. Then, by using the Mittag‐Leffler function properties, we show that satisfaction of the proposed condition proves the global asymptotic stability of the class of nonlinear fractional‐order systems with fractional order lying in (0.5, 1) or (1.5, 2). Unlike the Lyapunov‐based methods for stability analysis of fractional‐order systems, the new condition depends on the fractional order of the system. Moreover, it is related to the H_∞‐norm of the linear part of the system and it can be transformed to linear matrix inequalities (LMIs) using fractional‐order bounded‐real lemma. Furthermore, the proposed stability analysis method is extended to the state‐feedback and observer‐based controller design for the class of nonlinear fractional‐order systems based on solving some LMIs. In the observer‐based stabilization problem, we prove that the separation principle holds using our method and one can find the observer gain and pseudostate‐feedback gain in two separate steps. Finally, three numerical examples are provided to demonstrate the advantage of the novel proposed conditions with the previous results.     

Observer‐based controller for constrained uncertain stochastic nonlinear discrete‐time systems

In this paper, an observer‐based control approach is proposed for uncertain stochastic nonlinear discrete‐time systems with input constraints. The widely used extended Kalman filter (EKF) is well known to be inadequate for estimating the states of uncertain nonlinear dynamical systems with strong nonlinearities especially if the time horizon of the estimation process is relatively long. Instead, a modified version of the EKF with improved stability and robustness is proposed for estimating the states of such systems. A constrained observer‐based controller is then developed using the state‐dependent Riccati equation approach. Rigorous analysis of the stability of the developed stochastically controlled system is presented. The developed approach is applied to control the performance of a synchronous generator connected to an infinite bus and chaos in permanent magnet synchronous motor. Simulation results of the synchronous generator show that the estimated states resulting from the proposed estimator are stable, whereas those resulting from the EKF diverge. Moreover, satisfactory performance is achieved by applying the developed observer‐based control strategy on the two practical problems. Copyright © 2015 John Wiley & Sons, Ltd.     

Decentralized output feedback stabilization for a class of large‐scale feedforward nonlinear time‐delay systems

This paper is concerned with the decentralized stabilization problem for a class of large‐scale feedforward nonlinear time‐delay systems. The uncertain nonlinearities involved in the systems are assumed to be bounded by continuous functions of the inputs and delayed inputs multiplied by unmeasured states and delayed states. An observer‐based decentralized output feedback control scheme is proposed by using the dynamic gain control design approach. On the basis of the Lyapunov–Krasovskii stability theory, the global asymptotic stability of the closed‐loop control system is proved. Contrary to many existing control designs for feedforward nonlinear systems, the celebrated forwarding design and saturation design are not utilized here. An example is finally given to demonstrate the effectiveness of the proposed design procedure. Copyright © 2013 John Wiley & Sons, Ltd.     

Global stabilization of uncertain stochastic nonlinear time‐delay systems by output feedback

Constructive control techniques have been proposed for controlling strict feedback (lower triangular form) stochastic nonlinear systems with a time‐varying time delay in the state. The uncertain nonlinearities are assumed to be bounded by polynomial functions of the outputs multiplied by unmeasured states or delayed states. The delay‐independent output feedback controller making the closed‐loop system globally asymptotically stable is explicitly constructed by using a linear dynamic high‐gain observer in combination with a linear dynamic high‐gain controller. A simulation example is given to demonstrate the effectiveness of the proposed design procedure. Copyright © 2007 John Wiley & Sons, Ltd.     

Global tracking sliding mode control for a class of nonlinear systems via variable gain observer

A novel output‐feedback sliding mode control strategy is proposed for a class of single‐input single‐output (SISO) uncertain time‐varying nonlinear systems for which a norm state estimator can be implemented. Such a class encompasses minimum‐phase systems with nonlinearities affinely norm bounded by unmeasured states with growth rate depending nonlinearly on the measured system output and on the internal states related with the zero‐dynamics. The sliding surface is generated by using the state of a high gain observer (HGO) whereas a peaking free control amplitude is obtained via a norm observer. In contrast to the existing semi‐global sliding mode control solutions available in the literature for the class of plants considered here, the proposed scheme is free of peaking and achieves global tracking with respect to a small residual set. The key idea is to design a time‐varying HGO gain implementable from measurable signals. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust estimation‐free decentralized prescribed performance control of nonaffine nonlinear large‐scale systems

In this paper, a low‐complexity robust estimation‐free decentralized prescribed performance control scheme is proposed and analyzed for nonaffine nonlinear large‐scale systems in the presence of unknown nonlinearity and external disturbance. To tackle the high‐order dynamics of each tracking error subsystem, a time‐varying stable manifold involving the output tracking error and its high‐order derivatives is constructed, which is strictly evolved within the envelope of user‐specialized prescribed performance. Sequentially, a robust decentralized controller is devised for each manifold, under which the output tracking error and its high‐order derivatives are proven to converge asymptotically to a small residual domain with prescribed fast convergence rate. Additionally, no specialized approximation technique, adaptive scheme, and disturbance observer are needed, which alleviates the complexity and difficulty of robust decentralized controller design dramatically. Finally, 3 groups of illustrative examples are used to validate the effectiveness of the proposed low‐complexity robust decentralized control scheme for uncertain nonaffine nonlinear large‐scale systems.     

Output‐feedback control strategies of lower‐triangular nonlinear nonholonomic systems in any prescribed finite time

In this paper, output‐feedback control strategies are proposed for lower‐triangular nonlinear nonholonomic systems in any prescribed finite time. Specifically, by employing the input‐state–scaling technique, the controlled systems are firstly converted into lower‐triangular nonlinear systems, which makes it possible to study such systems using the high‐gain technique. Then, by introducing a scaling of the state by a function that grows unbounded toward the terminal time and proposing a high‐gain observer–prescribed finite time recovering the system states, the output‐feedback regulation control problem in any prescribed finite time is firstly achieved for nonlinear nonholonomic systems with unknown constant incremental rate. Moreover, by designing another time‐varying high gain, the output‐feedback stabilization control problem in any prescribed finite time is then achieved for nonlinear nonholonomic systems with a time‐varying incremental rate. Finally, a numerical example is introduced to show the effectiveness of proposed control strategies.     

Event‐triggered cascade high‐gain observer and its application

In this article, we consider the event‐triggered cascade high‐gain observer (ETCHGO) for a class of nonlinear systems. By cascading lower dimensional observers, we design a cascade high‐gain observer together with a Zeno‐free event‐triggered mechanism to estimate the state of the plant. We show that the ETCHGO has the same steady‐state performance as the continuous‐time cascade high‐gain observer, that is, there is a finite time after which the estimation error will not exceed the given threshold, and moreover, the finite time and the threshold can be made sufficiently small by adjusting some design parameters. We also investigate an ETCHGO with saturation, which will reduce the peaking value while maintaining the steady‐state estimation performance. Furthermore, we use the ETCHGO with saturation to solve the output feedback stabilization problem for a class of nonlinear systems. An example is given to illustrate our results.