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.     

Semi‐Global Output Feedback Stabilization for a Class of Uncertain Nonlinear Systems

This paper addresses the problem of semi‐global stabilization by output feedback for a class of nonlinear systems whose output gains are unknown. For each subsystem, we first design a state compensator and use the compensator states to construct a control law to stabilize the nominal linear system without the perturbing nonlinearities. Then, combining the output feedback domination approach with block‐backstepping scheme, a series of homogeneous output feedback controllers are constructed recursively for each subsystem and the closed‐loop system is rendered semi‐globally asymptotically stable.     

Deterministic learning from neural control for uncertain nonlinear pure‐feedback systems by output feedback

The essence of intelligence lies in the acquisition/learning and utilization of knowledge. However, how to implement learning in dynamical environments for nonlinear systems is a challenging issue. This article investigates the deterministic learning (DL) control problem for uncertain pure‐feedback systems by output feedback, which achieves the human‐like learning and control in a simple way. To reduce the complexity of control design and analysis, first, by combining an appropriate system transformation, the original pure‐feedback system is transformed into a simple normal nonaffine system. An observer is then introduced to estimate the transformed system states. Based on the backstepping and dynamic surface control techniques, a simple adaptive neural control scheme is first developed to guarantee the finite time convergence of the tracking error using only one neural network (NN) approximator. Second, through DL, the exponential convergence of the NN weights is obtained with the satisfaction of partial persistent excitation condition. Thus, locally accurate approximation/learning of the transformed unknown system dynamics is achieved and stored as constant NNs. Finally, by utilizing the stored knowledge, an experience‐based controller is constructed and a novel learning control scheme is further proposed to improve the control performance without any further adaptation online for the estimate neural weights. Simulation results have been given to illustrate that the proposed scheme not only can learn and memorize knowledge like humans but also can utilize experience to achieve superior control performance.     

Continuous output‐feedback finite‐time control for a class of second‐order nonlinear systems with disturbances

In this paper, a solution to the continuous output‐feedback finite‐time control problem is proposed for a class of second‐order MIMO nonlinear systems with disturbances. First, a continuous finite‐time controller is designed to stabilize system states at equilibrium points in finite time, which is proven correct by a constructive Lyapunov function. Next, because only the measured output is available for feedback, a continuous nonlinear observer is presented to reconstruct the total states in finite time and estimate the unknown disturbances. Then, a continuous output‐feedback finite‐time controller is proposed to track the desired trajectory accurately or alternatively converge to an arbitrarily small region in finite time. Finally, proposed methods are applied to robotic manipulators, and simulations are given to illustrate the applicability of the proposed control approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust control of nonlinear semi‐strict feedback systems using finite‐time disturbance observers

The output tracking controller design problem is dealt with for a class of nonlinear semi‐strict feedback systems in the presence of mismatched nonlinear uncertainties, external disturbances, and uncertain nonlinear virtual control coefficients of the subsystems. The controller is designed in a backstepping manner, and to avoid the shortcoming of ‘explosion of terms’, the dynamic surface control technique that employs a group of first‐order low‐pass filters is adopted. At each step of the virtual controller design, a robust feedback controller employing some effective nonlinear damping terms is designed to guarantee input‐to‐state practical stable property of the corresponding subsystem, so that the system states remain in the feasible domain. The virtual controller is enhanced by a finite‐time disturbance observer that estimates the disturbance term in a finite‐time. The properties of the composite control system are analyzed theoretically. Furthermore, by exploiting the cascaded structure of the control system, a simplified robust controller is proposed where only the first subsystem employs a disturbance observer. The performance of the proposed methods is confirmed by numerical examples. Copyright © 2017 John Wiley & Sons, Ltd.     

Output‐feedback adaptive consensus tracking control for a class of high‐order nonlinear multi‐agent systems

In this paper, an output‐feedback adaptive consensus tracking control scheme is proposed for a class of high‐order nonlinear multi‐agent systems. The agents are allowed to have unknown parameters, unknown nonlinearities, and input quantization simultaneously. The desired trajectory to be tracked is available for only a subset of agents, and only the relative outputs and the quantized inputs need to be measured or transmitted as signal exchange among neighbors regardless of the system order. By introducing a kind of high‐gain K‐filters and a smooth function, the effect among agents caused by the unknown nonlinearities is successfully counteracted, and all closed‐loop signals are proved to be globally uniformly bounded. Moreover, it is shown that the tracking errors converge to a residual set that can be made arbitrarily small. Simulation results on robot manipulators are presented to illustrate the effectiveness of the proposed scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

Distributed containment control for nonlinear multiagent systems in pure‐feedback form

In this paper, the problem of distributed containment control for pure‐feedback nonlinear multiagent systems under a directed graph topology is investigated. The dynamics of each agent are molded by high‐order nonaffine pure‐feedback form. Neural networks are employed to identify unknown nonlinear functions, and dynamic surface control technique is used to avoid the problem of explosion of complexity inherent in backstepping design procedure. The Frobenius norm of the ideal neural network weighting matrices is estimated, which is helpful to reduce the number of the adaptive tuning law and alleviate the networked communication burden. The proposed distributed containment controllers guarantee that all signals in the closed‐loop systems are cooperatively semiglobally uniformly ultimately bounded, and the outputs of followers are driven into a convex hull spanned by the multiple dynamic leaders. Finally, the effectiveness of the developed method is demonstrated by simulation examples.     

Adaptive fuzzy output feedback decentralized control of pure‐feedback nonlinear large‐scale systems

In this paper, an adaptive fuzzy decentralized output feedback control approach is presented for a class of uncertain nonlinear pure‐feedback large‐scale systems with immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the immeasurable states. On the basis of the adaptive backstepping recursive design technique, an adaptive fuzzy decentralized output feedback is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed‐loop system are semiglobally uniformly ultimately bounded (SUUB), and that the observer and tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters. Simulation studies are included to illustrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust adaptive output feedback control of a class of discrete‐time nonlinear systems with nonlinear uncertainties and unknown control directions

In this paper, robust adaptive output feedback control is studied for a class of discrete‐time nonlinear systems with functional nonlinear uncertainties of the Lipschitz type and unknown control directions. In order to construct an output feedback control, the system is transformed into the form of a nonlinear autoregressive moving average with eXogenous inputs (NARMAX) model. In order to avoid the noncausal problem in the control design, future output prediction laws and parameter update laws with the dead‐zone technique are constructed on the basis of the NARMAX model. With the employment of the predicted future outputs, a constructive output feedback adaptive control is proposed, where the discrete Nussbaum gain technique and the dead‐zone technique are used in parameter update laws. The effect of the functional nonlinear uncertainties is compensated for, such that an asymptotic tracking performance is achieved, whereas other signals in the closed‐loop systems are guaranteed to be bounded. Simulation studies are performed to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Global output‐feedback stabilization for a class of stochastic nonlinear systems via sampled‐data control

In this paper, the global sampled‐data output‐feedback stabilization problem is considered for a class of stochastic nonlinear systems. First, based on output‐feedback domination technique and emulation approach, a systematic design procedure for sampled‐data output‐feedback controller is proposed for a class of stochastic lower‐triangular nonlinear systems. It is proved that the proposed sampled‐data output‐feedback controller will stabilize the given stochastic nonlinear system in the sense of mean square exponential stability. Because of the domination nature of the proposed control approach, it is shown that the proposed control approach can also be used to handle the global sampled‐data output‐feedback stabilization problems for a more general class of stochastic non‐triangular nonlinear systems. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2017 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.     

Observer-based adaptive neural dynamic surface control for a class of non-strict-feedback stochastic nonlinear systems

The problem of adaptive output feedback stabilisation is addressed for a more general class of non-strict-feedback stochastic nonlinear systems in this paper. The neural network (NN) approximation and the variable separation technique are utilised to deal with the unknown subsystem functions with the whole states. Based on the design of a simple input-driven observer, an adaptive NN output feedback controller which contains only one parameter to be updated is developed for such systems by using the dynamic surface control method. The proposed control scheme ensures that all signals in the closed-loop systems are bounded in probability and the error signals remain semi-globally uniformly ultimately bounded in fourth moment (or mean square). Two simulation examples are given to illustrate the effectiveness of the proposed control design.     

Global output‐feedback stabilization for high‐order nonlinear systems with unknown growth rate

This paper considers the global stabilization via time‐varying output‐feedback for a class of high‐order uncertain nonlinear systems with rather weak assumptions. Essentially different from the existing literature, the systems under investigation simultaneously have more serious nonlinearities, unknowns, immeasurableness, and time‐variations, which are indicated from the unknown time‐varying control coefficients and the higher‐order and lower‐order unmeasured states dependent growth with the rate of unknown function of time and output. Recognizing that adaptive technique is quite hard to apply, a time‐varying design scheme is proposed by combining time‐varying approach, certainty equivalence principle and homogeneous domination approach. One key point in the design scheme is the selection of the design functions of time, in order to compensate/capture the serious unknowns and serious time‐variations, and another one is the design of a time‐varying observer to rebuild the unmeasured system states. With the appropriate choice of the involved design functions, the designed controller makes all the signals of the closed‐loop system globally bounded and ultimately converge to zero. Copyright © 2016 John Wiley & Sons, Ltd.     

Global output‐feedback stabilization for nonlinear systems with unknown relative degree

This paper is devoted to the global stabilization via output feedback for a class of nonlinear systems with unknown relative degree, dynamics uncertainties, unknown control direction, and nonparametric uncertain nonlinearities. In particular, the unknown relative degree is without known upper bound, which renders us to research for a filter with varying dimension rather than the ones with over dimensions in the existing literature. In comparison with more popular but a bit stronger input‐to‐state stable or input‐to‐state practically stable requirement, only bounded‐input bounded‐state stable requirement is imposed on the dynamics uncertainties, which affect the systems in a persistent intensity rather than in a decaying one. In this paper, to compensate multiple serious system uncertainties and realize global output‐feedback stabilization, a design scheme via switching logic together with varying dimensional filter is developed. In this scheme, 2 switching sequences, which separately generate the gains of the controller and act as the varying dimensions of the filter, are designed to overcome unknown control direction, dynamics uncertainties and nonparametric uncertain nonlinearities, and unknown relative degree, respectively. A 2‐mass lumped‐parameter structure is provided to show the effectiveness of the proposed method in this paper.     

Universal output feedback adaptive control with uncertain nonlinearity and unknown high‐frequency gain sign: A new design

In this paper, we propose a new universal output feedback adaptive controller to globally (or semiglobally) stabilize nonlinear output feedback systems, whose nonlinearities are bounded either by known functions with unknown parameters or by completely unknown functions. In addition, no a priori knowledge of the sign of high‐frequency gain is required. The new design focuses on properly arranging the control gains step by step in the filter backstepping design. Instead of Lyapunov‐based argument, an inductive contradiction argument is employed in the proof of stability, which is not common in literature.     

NN‐Based Output‐Feedback Control for Stochastic Nonlinear Systems with Unknown Control Directions

This paper addresses the neural network‐based output‐feedback control problem for a class of stochastic nonlinear systems with unknown control directions. The restrictions on the drift and diffusion terms are removed and the conditions on unknown control directions are relaxed. By introducing a proper coordinate transformation, and combining dynamic surface control (DSC) technique with radial basis function neural network (RBF NN) approximation approach, we construct an adaptive output‐feedback controller to guarantee the closed‐loop system to be mean square semi‐globally uniformly ultimately bounded (M‐SGUUB). A simulation example demonstrates the effectiveness of the proposed scheme.     

Semi‐global output feedback control for nonlinear systems with uncertain time‐delay and output function

This paper considers semi‐global output feedback control for more general nonlinear systems with unknown time‐delay and output function whose derivative is unbounded from above. By introducing a new observer and using the backstepping design method and the Razumikhin stability theorem, an output feedback controller is constructed to achieve a semi‐global stability. Copyright © 2016 John Wiley & Sons, Ltd.     

Global asymptotic tracking for nonminimum‐phase nonlinear systems in output feedback form

The problem of global asymptotic tracking by output feedback is studied for a class of nonminimum‐phase nonlinear systems in output feedback form. It is proved that the problem is solvable by an n‐dimensional output feedback controller under the two conditions: (a) the nonminimum‐phase nonlinear system can be rendered minimum‐phase by a virtual output; and (b) the internal dynamics of the nonlinear system driven by a desired signal and its derivatives has a bounded solution trajectory. With the help of a new coordinate transformation, a constructive method is presented for the design of a dynamic output tracking controller. An example is given to validate the proposed output feedback tracking control scheme.     

Output‐feedback robust adaptive backstepping control for a class of multivariable nonlinear systems with guaranteed tracking performance

This paper is devoted to output‐feedback adaptive control for a class of multivariable nonlinear systems with both unknown parameters and unknown nonlinear functions. Under the Hurwitz condition for the high‐frequency gain matrix, a robust adaptive backstepping control scheme is proposed, which is able to guarantee the tracking performance and needs only one parameter to be updated online regardless of the system order and input–output dimension. To cope with the unknown nonlinear functions and improve the tracking performance, a kind of high‐gain K‐filters is introduced. It is proved that all signals of the closed‐loop system are globally uniformly bounded. Simulation results on coupled inverted double pendulums are presented to illustrate the effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust control of a family of uncertain nonminimum‐phase systems via continuous‐time and sampled‐data output feedback

The problem of global robust stabilization is studied by both continuous‐time and sampled‐data output feedback for a family of nonminimum‐phase nonlinear systems with uncertainty. The uncertain nonlinear system considered in this paper has an interconnect structure consisting of a driving system and a possibly unstable zero dynamics with uncertainty, ie, the uncertain driven system. Under a linear growth condition on the uncertain zero dynamics and a Lipschitz condition on the driving system, we show that it is possible to globally robustly stabilize the family of uncertain nonminimum‐phase systems by a single continuous‐time or a sampled‐data output feedback controller. The sampled‐data output feedback controller is designed by using the emulated versions of a continuous‐time observer and a state feedback controller, ie, by holding the input/output signals constant over each sampling interval. The design of either continuous‐time or sampled‐data output compensator uses only the information of the nominal system of the uncertain controlled plant. In the case of sampled‐data control, global robust stability of the hybrid closed‐loop system with uncertainty is established by means of a feedback domination method together with the robustness of the nominal closed‐loop system if the sampling time is small enough.