Global finite‐time stabilization via time‐varying output‐feedback for uncertain nonlinear systems with unknown growth rate

This paper considers the global finite‐time output‐feedback stabilization for a class of uncertain nonlinear systems. Comparing with the existing related literature, two essential obstacles exist: On the one hand, the systems in question allow serious parametric unknowns and serious time variations coupling to the unmeasurable states, which is reflected in that the systems have the unmeasurable states dependent growth with the rate being an unknown constant multiplying a known continuous function of time. On the other hand, the systems possess remarkably inherent nonlinearities, whose growth allows to be not only low‐order but especially high‐order with respect to the unmeasurable states. To effectively cope with these obstacles, we established a time‐varying output‐feedback strategy to achieve the finite‐time stabilization for the systems under investigation. First, a time‐varying state‐feedback controller is constructed by adding an integrator method, and by homogeneous domination approach, a time‐varying reduced‐order observer is designed to precisely rebuild the unmeasurable states. Then, by certainty equivalence principle, a desired time‐varying output‐feedback controller is constructed for the systems. It is shown that, as long as the involved time‐varying gain is chosen fast enough to overtake the serious parametric unknowns and the serious time variations, the output‐feedback controller renders that the closed‐loop system states converge to zero in finite time. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

Global decentralized sampled‐data output feedback stabilization for a class of large‐scale nonlinear systems with sensor and actuator failures

In this paper, we investigate global decentralized sampled‐data output feedback stabilization problem for a class of large‐scale nonlinear systems with time‐varying sensor and actuator failures. The considered systems include unknown time‐varying control coefficients and inherently nonlinear terms. Firstly, coordinate transformations are introduced with suitable scaling gains. Next, a reduced‐order observer is designed to estimate unmeasured states. Then, a decentralized sampled‐data fault‐tolerant control scheme is developed with an allowable sampling period. By constructing an appropriate Lyapunov function, it can be shown that all states of the resulting closed‐loop system are globally uniformly ultimately bounded. Finally, the validity of the proposed control approach is verified by using two examples.     

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.     

Active disturbance rejection control approach to output‐feedback stabilization of lower triangular nonlinear systems with stochastic uncertainty

In this paper, we apply the active disturbance rejection control approach to output‐feedback stabilization for uncertain lower triangular nonlinear systems with stochastic inverse dynamics and stochastic disturbance. We first design an extended state observer (ESO) to estimate both unmeasured states and stochastic total disturbance that includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance, and uncertainty caused by the deviation of control parameter from its nominal value. The stochastic total disturbance is then compensated in the feedback loop. The constant gain and the time‐varying gain are used in ESO design separately. The mean square practical stability for the closed‐loop system with constant gain ESO and the mean square asymptotic stability with time‐varying gain ESO are developed, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output‐feedback control scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Observer‐based decentralized adaptive control for large‐scale pure‐feedback systems with unknown time‐delayed nonlinear interactions

This paper presents an approximation design for a decentralized adaptive output‐feedback control of large‐scale pure‐feedback nonlinear systems with unknown time‐varying delayed interconnections. The interaction terms are bounded by unknown nonlinear bounding functions including unmeasurable state variables of subsystems. These bounding functions together with the algebraic loop problem of virtual and actual control inputs in the pure‐feedback form make the output‐feedback controller design difficult and challenging. To overcome the design difficulties, the observer‐based dynamic surface memoryless local controller for each subsystem is designed using appropriate Lyapunov‐Krasovskii functionals, the function approximation technique based on neural networks, and the additional first‐order low‐pass filter for the actual control input. It is shown that all signals in the total controlled closed‐loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin. Finally, simulation examples are provided to illustrate the effectiveness of the proposed decentralized control scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Global adaptive stabilization for high‐order uncertain time‐varying nonlinear systems with time‐delays

This paper focuses on the adaptive stabilization problem for a class of high‐order nonlinear systems with time‐varying uncertainties and unknown time‐delays. Time‐varying uncertain parameters are compensated by combining a function gain with traditional adaptive technique, and unknown multiple time‐delays are manipulated by the delicate choice of an appropriate Lyapunov function. With the help of homogeneous domination idea and recursive design, a continuous adaptive state‐feedback controller is designed to guarantee that resulting closed‐loop systems are globally uniformly stable and original system states converge to zero. The effectiveness of the proposed control scheme is illustrated by the stabilization of delayed neural network systems. Copyright © 2016 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.     

Output feedback stabilization for nonholonomic systems with unknown unmeasured states‐dependent growth

This paper is concerned with the global output feedback stabilization for a class of nonholonomic systems with unknown parameter, polynomial‐of‐output, and unmeasurable states dependent growth. A dynamic high‐gain observer is first designed to reconstruct the unmeasurable system states and, in addition, to compensate the serious parameter unknowns in nonlinear drifts. Then, we design a compact adaptive controller without invoking the backstepping technique, which reduces the complexity of controller. Additionally, a switching control strategy is employed to overcome the smooth feedback obstacle associated with nonholonomic systems. It is shown that the proposed control laws guarantee that all closed‐loop system states are globally bounded and ultimately converge to zero. The simulation results demonstrate the effectiveness of the proposed control strategy.     

Adaptive output‐feedback tracking for nonlinear systems with rather general control coefficients

This paper studies the problem of global practical tracking by output feedback for a class of uncertain nonlinear systems with unmeasured state‐dependent growth and unknown time‐varying control coefficients. Compared with the closely related works, the remarkableness of this paper is that the upper and lower bounds of unknown control coefficients are not required to be known a priori. Motivated by our recent works, by combining the methods of universal control and deadzone with the backstepping technique and skillfully constructing a novel Lyapunov function, we propose a new adaptive tracking control scheme with appropriate design parameters. The new scheme guarantees that the state of the resulting closed‐loop system is globally bounded while the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time. Two examples, including a practical example, are given to illustrate 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.     

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.     

Fault reconstruction for delay systems via least squares and time‐shifted sliding mode observers

In this article, we address the problem of fault reconstruction in delayed systems by introducing a time‐shifted sliding mode observer (SMO). While time‐varying delays of arbitrary duration are considered in the measured output signal, the actuator fault is parametrized as a weighted sum of known regressor functions with unknown coefficients. The prediction scheme utilizes the variation of constants formula to obtain the present time estimate of the unmeasured state. The fault is also identified at present time by means of the continuous‐time Least Squares approaches. Ideal sliding mode can be guaranteed in theory, even in the presence of such adverse delays, since there is no chattering in the output estimation error of the SMO. An application to petroleum engineering with numerical simulations is presented to show the effectiveness of the proposed method.     

Adaptive fuzzy decentralized output feedback control for stochastic nonlinear large‐scale systems using DSC technique

In this paper, an adaptive fuzzy decentralized backstepping output feedback control approach is proposed for a class of uncertain large‐scale stochastic nonlinear systems without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. Using the designed fuzzy state observer, and by combining the adaptive backstepping technique with dynamic surface control technique, an adaptive fuzzy decentralized output feedback control approach is developed. It is shown that the proposed control approach can guarantee that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by choosing appropriate design parameters. A simulation example is provided to show the effectiveness of the proposed approaches. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Adaptive fuzzy backstepping output feedback control of nonlinear uncertain systems with unknown virtual control coefficients using MT-filters

In this paper, an adaptive fuzzy output feedback control approach is developed for a class of SISO nonlinear uncertain systems with unmeasured states and unknown virtual control coefficients. The fuzzy logic systems are used to model the uncertain nonlinear systems. The MT-filters and the state observer are designed to estimate the unmeasured states. Using backstepping design principle and combining the Nussbaum gain functions, an adaptive fuzzy output feedback control scheme is developed. It is proved that the proposed adaptive fuzzy control approach can guarantee all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of origin. A simulation is included to illustrate the effectiveness of the proposed approach.     

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L₂ gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

Singularly perturbed implicit control law for linear time‐varying delay MIMO systems

This paper proposes a control scheme for the problem of stabilizing partly unknown multiple‐input multiple‐output linear time‐varying retarded systems. The control scheme is composed by a singularly perturbed controller and a reference model. We assume the knowledge of a number of structural characteristics of the system as the boundedness and the knowledge of the bounds for the unknown parameters (and their derivatives) that define the system matrices, as well as the structure of these matrices. The results presented here are a generalization of previous results on linear time‐varying Single‐Input Single‐Output (SISO) and multiple‐input multiple‐output systems without delays and linear time‐varying retarded SISO systems. The closed‐loop system is a linear singularly perturbed retarded system with uniform asymptotic stability behavior. The uniform asymptotic stability of the singularly perturbed retarded system is guaranteed. We show how to design a control law such that the system dynamics for each output is given by a Hurwitz polynomial with constant coefficients. Copyright © 2015 John Wiley & Sons, Ltd.     

Output feedback regulation control for a class of cascade nonlinear systems by time‐varying Kalman observer

The global output feedback regulation problem is studied for a class of cascade nonlinear systems. The considered system represents more general classes of nonlinear uncertain systems, including the integral input‐to‐state stable (iISS) unmodeled dynamics, the unknown control direction, the parameter uncertainty, and the external disturbance additively in the input channel. Technically, we explore the changing supply rate technique for the iISS system to deal the iISS unmodeled dynamics and apply the Nussbaum‐type gain into the control design to overcome the unknown control direction. Additionally, a dynamic extended state observer in the form of a time‐varying Kalman observer is novelly constructed to overcome the unmeasured state components in the nonlinear uncertainties. It is shown that the global regulation problem is well addressed by the proposed method, and its efficacy is demonstrated by a fan speed control system.