Adaptive fuzzy output feedback backstepping control of pure‐feedback nonlinear systems via dynamic surface control technique

In this paper, an adaptive fuzzy backstepping dynamic surface control approach is considered for a class of uncertain pure‐feedback nonlinear systems with immeasurable states. Fuzzy logic systems are first employed to approximate the unknown nonlinear functions, and then an adaptive fuzzy state observer is designed to estimate the immeasurable states. By the combination of the adaptive backstepping design with a dynamic surface control technique, an adaptive fuzzy output feedback backstepping control approach is developed. It is proven that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded, and the observer and tracking errors converge to a small neighborhood of the origin by choosing the design parameters appropriately. Simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Observer‐based nonlinear feedback decentralized neural adaptive dynamic surface control for large‐scale nonlinear systems

This paper presents a nonlinear gain feedback technique for observer‐based decentralized neural adaptive dynamic surface control of a class of large‐scale nonlinear systems with immeasurable states and uncertain interconnections among subsystems. Neural networks are used in the observer design to estimate the immeasurable states and thus facilitate the control design. Besides avoiding the complexity problem in traditional backstepping, the new nonlinear feedback gain method endows an automatic regulation ability into the pioneering dynamic surface control design and improvement in dynamic performance. Novel Lyapunov function is designed and rigorous stability analysis is given to show that all the closed‐loop signals are kept semiglobally uniformly ultimately bounded, and the output tracking errors can be guaranteed to converge to sufficient area around zero, with the bound values characterized by design parameters in an explicit manner. Simulation and comparative results are shown to verify effectiveness.     

A small‐gain approach for adaptive output‐feedback NN control of switched pure‐feedback nonlinear systems

This paper investigates the problem of adaptive output‐feedback neural network (NN) control for a class of switched pure‐feedback uncertain nonlinear systems. A switched observer is first constructed to estimate the unmeasurable states. Next, with the help of an NN to approximate the unknown nonlinear terms, a switched small‐gain technique‐based adaptive output‐feedback NN control scheme is developed by exploiting the backstepping recursive design scheme, input‐to‐state stability analysis, the common Lyapunov function method, and the average dwell time (ADT) method. In the recursive design, the difficulty of constructing an overall Lyapunov function for the switched closed‐loop system is dealt with by decomposing the switched closed‐loop system into two interconnected switched systems and constructing two Lyapunov functions for two interconnected switched systems, respectively. The proposed controllers for individual subsystems guarantee that all signals in the closed‐loop system are semiglobally, uniformly, and ultimately bounded under a class of switching signals with ADT, and finally, two examples illustrate the effectiveness of theoretical results, which include a switched RLC circuit system.     

Adaptive robust output‐feedback motion control of hydraulic actuators

Most previous advanced motion control of hydraulic actuators used full‐state feedback control techniques. However, in many cases, only position feedback is available, and thus, there are imperious demands for output‐feedback control for hydraulic systems. This paper firstly transforms a hydraulic model into an output feedback–dependent form. Thus, the K‐filter can be employed, which provides exponentially convergent estimates of the unmeasured states. Furthermore, this observer has an extended filter structure so that online parameter adaptation can be utilized. In addition, it is a well‐known fact that any realistic model of a hydraulic system suffers from significant extent of uncertain nonlinearities and parametric uncertainties. This paper constructs an adaptive robust controller with backstepping techniques, which is able to take into account not only the effect of parameter variations coming from various hydraulic parameters but also the effect of hard‐to‐model nonlinearities such as uncompensated friction forces, modeling errors, and external disturbances. Moreover, estimation errors that come from initial state estimates and uncompensated disturbances are dealt with via certain robust feedback at each step of the adaptive robust backstepping design. After that, a detailed stability analysis for the output‐feedback closed‐loop system is scrupulously checked, which shows that all states are bounded and that the controller achieves a guaranteed transient performance and final tracking accuracy in general and asymptotic output tracking in the presence of parametric uncertainties only. Extensive experimental results are obtained for a hydraulic actuator system and verify the high‐performance nature of the proposed output‐feedback control strategy.     

Observer‐based adaptive control for stochastic nonstrict‐feedback systems with unknown backlash‐like hysteresis

This paper studies an observer‐based adaptive fuzzy control problem for stochastic nonlinear systems in nonstrict‐feedback form. The unknown backlash‐like hysteresis is considered in the systems. In the design process, the unknown nonlinearities and unavailable state variables are tackled by introducing the fuzzy logic systems and constructing a fuzzy observer, respectively. By using adaptive backstepping technique with dynamic surface control technique, an adaptive fuzzy control algorithm is developed. For the closed‐loop system, the proposed controller can guarantee all the signals are 4‐moment semiglobally uniformly ultimately bounded. Finally, simulation results further show the effectiveness of the presented control scheme.     

Robust adaptive control for non‐linear systems in generalized output‐feedback canonical form

Design of global robust adaptive output‐feedback dynamic compensators for stabilization and tracking of a class of systems that are globally diffeomorphic into systems in generalized output‐feedback canonical form is investigated. This form includes as special cases the standard output‐feedback canonical form and various other forms considered previously in the literature. Output‐dependent non‐linearities are allowed to enter both additively and multiplicatively. The system is allowed to contain unknown parameters multiplying output‐dependent non‐linearities and, also, unknown non‐linearities satisfying certain bounds. Under the assumption that a constant matrix can be found to achieve a certain property, it is shown that a reduced‐order observer and a backstepping controller can be designed to achieve practical stabilization of the tracking error. If this assumption is not satisfied, it is shown that the control objective can be achieved by introducing additional dynamics in the observer. Sufficient conditions under which asymptotic tracking and stabilization can be achieved are also given. This represents the first robust adaptive output‐feedback tracking results for this class of systems. Copyright © 2003 John Wiley & Sons, Ltd.     

Integral barrier Lyapunov function-based adaptive fuzzy output feedback control for nonlinear delayed systems with time-varying full-state constraints

In this article, an adaptive fuzzy output feedback control method is presented for nonlinear time-delay systems with time-varying full state constraints and input saturation. To overcome the problem of time-varying constraints, the integral barrier Lyapunov functions (IBLFs) integrating with dynamic surface control (DSC) are applied for the first time to keep the state from violating constraints. The effects of unknown time delays can be removed by using designed Lyapunov-Krasovskii functions (LKFs). An auxiliary design system is introduced to solve the problem of input saturation. The unknown nonlinear functions are approximated by the fuzzy logic systems (FLS), and the unmeasured states are estimated by a designed fuzzy observer. The novel controller can guarantee that all signals remain semiglobally uniformly ultimately bounded and satisfactory tracking performance is achieved. Finally, two simulation examples illustrate the effectiveness of the presented control methods.     

Output‐feedback adaptive tracking control of stochastic nonlinear systems using multi‐dimensional Taylor network

In this paper, an adaptive multi‐dimensional Taylor network (MTN) control scheme based on the backstepping and dynamic surface control (DSC) is developed to solve the tracking control problem for the stochastic nonlinear system with immeasurable states. The MTNs are used to approximate the unknown nonlinearities, and then based on the multivariable analog of circle criterion, an observer is first introduced to estimate the immeasurable states. By combining the adaptive backstepping technique and the DSC technique, an adaptive MTN output‐feedback backstepping DSC approach is developed. It is shown that the proposed controller ensures that all signals of the closed‐loop system are remain bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of probability. Finally, the effectiveness of the design approach is illustrated by simulation results.     

Dual high‐gain‐based adaptive output‐feedback control for a class of nonlinear systems

We propose an adaptive output‐feedback controller for a general class of nonlinear triangular (strict‐feedback‐like) systems. The design is based on our recent results on a new high‐gain control design approach utilizing a dual high‐gain observer and controller architecture with a dynamic scaling. The technique provides strong robustness properties and allows the system class to contain unknown functions dependent on all states and involving unknown parameters (with no magnitude bounds required). Unlike our earlier result on this problem where a time‐varying design of the high‐gain scaling parameter was utilized, the technique proposed here achieves an autonomous dynamic controller by introducing a novel design of the observer, the scaling parameter, and the adaptation parameter. This provides a time‐invariant dynamic output‐feedback globally asymptotically stabilizing solution for the benchmark open problem proposed in our earlier work with no magnitude bounds or sign information on the unknown parameter being necessary. Copyright © 2007 John Wiley & Sons, Ltd.     

Adaptive neural prescribed performance output feedback control of pure feedback nonlinear systems using disturbance observer

In this study, an adaptive output feedback control with prescribed performance is proposed for unknown pure feedback nonlinear systems with external disturbances and unmeasured states. A novel prescribed performance function is developed and incorporated into an output error transformation to achieve tracking control with prescribed performance. To handle the unknown non-affine nonlinearities and avoid the algebraic loop problem, the radial basis function neural network (RBFNN) is adopted to approximate the unknown non-affine nonlinearities with the help of Butterworth low-pass filter. Based on the output of the RBFNN, the coupled design between sate observer and disturbance observer is presented to estimate the unmeasured states and compounded disturbances. Then, the adaptive output feedback control scheme is proposed for unknown pure feedback nonlinear systems, where a first-order filter is introduced to tackle with the issue of “explosion of complexity” in the traditional back-stepping approach. The boundedness and convergence of the closed-loop system are proved rigorously by utilizing the Lyapunov stability theorem. Finally, simulation studies are worked out to demonstrate the effectiveness of the proposed scheme.     

Predictor‐based adaptive dynamic surface control for consensus of uncertain nonlinear systems in strict‐feedback form

This paper investigates the leader–follower consensus problem of uncertain nonlinear systems in strict‐feedback form. By parameterizations of unknown nonlinear dynamics of the agents, an adaptive dynamic surface control with the aid of predictors, tracking differentiators is proposed to realize output consensus of the multi‐agent systems. Unlike the existing adaptive consensus methods, the predictor errors are used to learn the unknown parameters, which can achieve fast learning without high‐frequency signals in control inputs. As a fast precise signal filter, the tracking differentiator is used in the control design instead of first‐order filters, which can further improve the control performance. Based on graph theory and Lyapunov stability theory, it is shown that the outputs of all followers ultimately synchronize to that of the leader with bounded tracking errors. Simulation results are provided to validate the effectiveness and advantage of the proposed consensus algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive finite-time consensus tracking control for nonlinear multiagent systems in nonstrict feedback form with full-state constraints

In this article, the fuzzy adaptive finite-time consensus tracking control problem for nonstrict feedback nonlinear multiagent systems with full-state constraints is studied. The finite-time control based on command filtered backstepping is proposed to guarantee the finite-time convergence and eliminate the explosion of complexity problem caused by backstepping process, and the errors in the filtering process are compensated by using error compensation mechanism. Furthermore, based on the fuzzy logic systems, the uncertain nonlinear dynamics are approximated and the problem of state variables in nonstrict feedback form is solved by using the property of basis functions. The barrier Lyapunov functions are introduced to guarantee that all system states and compensated tracking error signals are constrained in the designed regions. A simulation example is given to verify the superiority of the proposed algorithm.     

Finite‐time prescribed performance adaptive fuzzy fault‐tolerant control for nonstrict‐feedback nonlinear systems

This paper focuses on a finite‐time adaptive fuzzy control problem for nonstrict‐feedback nonlinear systems with actuator faults and prescribed performance. Compared with existing results, the finite‐time prescribed performance adaptive fuzzy output feedback control is under study for the first time. By designing performance function, the transient performance of the corresponding controlled variable is maintained in a prescribed area. Combining the finite‐time stability criterion with backstepping technique, a feasible adaptive fault‐tolerant control scheme is proposed to guarantee that the system output converges to a small neighborhood of the origin in finite time, and the closed‐loop signals are bounded. Finally, simulation results are shown to illustrate the effectiveness of the presented control method.     

Quasi‐passivity‐based adaptive stabilization for switched nonlinearly parameterized systems

This paper investigates the adaptive quasi‐passification‐based stabilization problem for a class of switched nonlinearly parameterized systems via average dwell time method. First, when all the subsystems have any same relative degree, the global practical stability is achieved by combining the recursive feedback quasi‐passification design technique with a switched adaptive control technique. The states and parameter estimation errors converge to the ball whose sizes can be reduced by choosing appropriate design parameters. Second, when the system states are unavailable for measurements, adaptive output feedback controllers are designed to stabilize the system using quasi‐passivity. The proposed output feedback controllers do not depend on any state observer. Finally, three examples show the effectiveness of the proposed methods.     

Adaptive robust control of a class of nonlinear systems in semi‐strict feedback form with non‐uniformly detectable unmeasured internal states

This paper proposes a novel control method for a special class of nonlinear systems in semi‐strict feedback form. The main characteristic of this class of systems is that the unmeasured internal states are non‐uniformly detectable, which means that no observer for these states can be designed to make the observation error exponentially converge to zero. In view of this, a projection‐based adaptive robust control law is developed in this paper for this kind of system. This method uses a projection‐type adaptation algorithm for the estimation of both the unknown parameters and the internal states. Robust feedback term is synthesized to make the system robust to uncertain nonlinearities and disturbances. Although the estimation error for both the unknown parameters and the internal states may not converge to zero, the tracking error of the closed‐loop system is proved to converge to zero asymptotically if the system has only parametric uncertainties. Furthermore, it is theoretically proved that all the signals are bounded, and the control algorithm is robust to bounded disturbances and uncertain nonlinearities with guaranteed output tracking transient performance and steady‐state accuracy in general. The class of system considered here has wide engineering applications, and a practical example—control of mechanical systems with dynamic friction—is used as a case study. Simulation results are obtained to demonstrate the applicability of the proposed control methodology. Copyright © 2010 John Wiley & Sons, Ltd.     

Observer‐based fuzzy adaptive quantized control for uncertain nonlinear multiagent systems

This paper focuses on consensus quantized control design problem for uncertain nonlinear multiagent systems with unmeasured states. Every follower can be denoted through a system with unmeasurable states, hysteretic quantized input, and unknown nonlinearities. Fuzzy state observer and Fuzzy logic systems are employed to estimate unmeasured states and approximate unknown nonlinear functions, respectively. The hysteretic quantized input can be split into two bounded nonlinear functions to avoid chattering problem. By combining adaptive backstepping and first‐order filter signals, an observer‐based fuzzy adaptive quantized control scheme is designed for each follower. All signals exist in closed‐loop systems are semiglobally uniformly ultimately bounded, and all followers can accomplish a desired consensus results. Finally, a numerical example is employed to elaborate the effectiveness of proposed control strategy.     

Observer‐based adaptive neural control of uncertain MIMO nonlinear systems with unknown control direction

This paper investigates adaptive neural network output feedback control for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems with an unknown sign of control gain matrix. Because the system states are not required to be available for measurement, an observer is designed to estimate the system states. In order to deal with the unknown sign of control gain matrix, the Nussbaum‐type function is utilized. By using neural network, we approximated the unknown nonlinear functions and perfectly avoided the controller singularity problem. The stability of the closed‐loop system is analyzed by using Lyapunov method. Theoretical results are illustrated through a simulation example. Copyright © 2012 John Wiley & Sons, Ltd.     

Global output‐feedback control of systems with dynamic nonlinear input uncertainties through singular perturbation‐based dynamic scaling

A general class of uncertain nonlinear systems with dynamic input nonlinearities is considered. The system structure includes a core nominal subsystem of triangular structure with additive uncertain nonlinear functions, coupled uncertain nonlinear appended dynamics, and uncertain nonlinear input unmodeled dynamics. The control design is based on dual controller/observer dynamic high‐gain scaling with an additional dynamic scaling based on a singular perturbation‐like redesign to address the non‐affine and uncertain nature of the input appearance in the system dynamics. The proposed approach yields a constructive global robust adaptive output‐feedback control design that is robust to the dynamic input uncertainties and to uncertain nonlinear functions allowed throughout the system structure. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive finite-time output feedback control for Markov jumping nonlinear systems

In this article, the problem of output feedback tracking control for uncertain Markov jumping nonlinear systems is studied. A finite-time control scheme based on command filtered backstepping and adaptive neural network (NN) technique is given. The finite-time command filter solves the problem of differential explosions for virtual control signals, the NN is utilized to approximate the uncertain nonlinear dynamics and the adaptive NN observer is applied to restructure the state of system. The finite-time error compensation mechanism is established to compensate the errors brought by filtering process. The proposed finite-time tracking control algorithm can ensure that the solution of the closed-loop system is practically finite-time stable in mean square. Two simulation examples are employed to demonstrate the effectiveness of the proposed control algorithm.     

Unifying adaptive control with the nonlinear PI methodology: Designs for unknown strict‐feedback nonlinear systems with nonsmooth actuator nonlinearities

In this paper, we extend the nonlinear PI control methodology within an adaptive control framework. An adaptive nonlinear PI controller is proposed for output tracking of strict‐feedback nonlinear systems with nonsmooth actuator nonlinearities and unknown control directions. The current approach relaxes the standard assumption of known bounds for the associated system nonlinearities made in earlier nonlinear PI schemes. New theoretical boundedness results have been proved that enable the successful combination of backstepping and linear parametric approximators with the nonlinear PI approach and ensure semiglobal approximate tracking of the output to some reference trajectory. Following recent extensions of the nonlinear PI method to strict‐feedback systems, the intermediate virtual control laws are derived through suitable integral equations. Simulation results are also presented in this paper that verify our theoretical analysis.