Adaptive NN output‐feedback decentralized stabilization for a class of large‐scale stochastic nonlinear strict‐feedback systems

In this paper, the decentralized adaptive neural network (NN) output‐feedback stabilization problem is investigated for a class of large‐scale stochastic nonlinear strict‐feedback systems, which interact through their outputs. The nonlinear interconnections are assumed to be bounded by some unknown nonlinear functions of the system outputs. In each subsystem, only a NN is employed to compensate for all unknown upper bounding functions, which depend on its own output. Therefore, the controller design for each subsystem only need its own information and is more simplified than the existing results. It is shown that, based on the backstepping method and the technique of nonlinear observer design, the whole closed‐loop system can be proved to be stable in probability by constructing an overall state‐quartic and parameter‐quadratic Lyapunov function. The simulation results demonstrate the effectiveness of the proposed control scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

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.     

Decentralized adaptive output-feedback control for a class of nonlinear large-scale systems with unknown time-varying delayed interactions

In this paper, the authors investigate a decentralized adaptive output-feedback controller design for large-scale nonlinear systems with input saturations and time-delayed interconnections unmatched in control inputs. The interaction terms with unknown time-varying delays are bounded by unknown nonlinear bounding functions including all states of subsystems. This point is a main contribution of this paper compared with previous output-feedback control approaches which assume that the time-delayed bounding functions only depend on measurable output variables. The bounding functions are compensated by using appropriate Lyapunov–Krasovskii functionals and the function approximation technique based on neural networks. The observer dynamic surface design technique is employed to design the proposed memoryless local controller for each subsystem. In addition, we prove that all signals in the closed-loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin. Finally, an example is provided to illustrate the effectiveness of the proposed control system.     

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.     

A neural composite dynamic surface control for pure‐feedback systems with unknown control gain signs and full state constraints

This paper investigates a composite neural dynamic surface control (DSC) method for a class of pure‐feedback nonlinear systems in the case of unknown control gain signs and full‐state constraints. Neural networks are utilized to approximate the compound unknown functions, and the approximation errors of neural networks are applied in the design of updated adaptation laws. Comparing the proposed composite approximation method with the conventional ones, a faster and better approximation performance result can be obtained. Combining the composite neural networks approximation with the DSC technique, an improved composite neural adaptive control approach is designed for the considered nonlinear system. Then, together with the Lyapunov stability theory, all the variables of the closed‐loop system are semiglobal uniformly ultimately bounded. The infringements of full state constraints can be avoided in the case of unknown control gain signs as well as unknown disturbances. Finally, two simulation examples show the effectiveness and feasibility of the proposed results.     

Decentralized intelligent tracking control for uncertain high‐order stochastic nonlinear strong interconnected systems in drift and diffusion terms

This paper focuses mainly on decentralized intelligent tracking control for a class of high‐order stochastic nonlinear systems with unknown strong interconnected nonlinearity in the drift and diffusion terms. For the control of uncertain high‐order nonlinear systems, the approximation capability of RBF neural networks is utilized to deal with the difficulties caused by completely unknown system dynamics and stochastic disturbances, and only one adaptive parameter is constructed to overcome the overparameterization problem. Then, to address the problem from high‐order strong interconnected nonlinearities in the drift and diffusion terms with full states of the overall system, by using the monotonically increasing property of the bounding functions, the variable separation technique is achieved. Lastly, based on the Lyapunov stability theory, a decentralized adaptive neural control method is proposed to reduce the number of online adaptive learning parameters. It is shown that, for bounded initial conditions, the designed controller can ensure the semiglobally uniformly ultimate boundedness of the solution of the closed‐loop system and make the tracking errors eventually converge to a small neighborhood around the origin. Two simulation examples including a practical example are used to further illustrate the effectiveness of the design 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.     

Output feedback stabilization of time‐delay nonlinear systems with unknown continuous time‐varying output function and nonlinear growth rate

This article addresses the problem of global output feedback stabilization for a class of time‐varying delay nonlinear systems with polynomial growth rate. The systems under investigation possess two remarkable features: the output is perturbed by an unknown sensitivity function that is not differentiable but continuous, and the nonlinearities are bounded by a polynomial function of the output multiplied by unmeasurable state variables. The new full‐order observer is established by introducing a dynamic gain and filtering unknown nonlinearities and time‐varying delay. With the help of the transformation skill and the reasonable combination of several systems, this article proposes a linear output feedback controller with the dynamic gain and completes the performance analysis based on the construction of two integral Lyapunov functions. Finally, a simulation example is presented to demonstrate the effectiveness of control strategy.     

Adaptive Non‐Backstepping Fuzzy Control for a Class of Uncertain Nonlinear Systems with Unknown Dead‐Zone Input

Based on the approximation property of fuzzy logic systems, we propose a novel non‐backstepping adaptive tracking control algorithm for a class of single input single output (SISO) strict‐feedback nonlinear systems with unknown dead‐zone input. In this algorithm, we introduce some novel state variables and coordinate transforms to convert the strict‐feedback form into a normal one, and it is not necessary to consider the traditional approximation‐based the backstepping scheme. Due to new states variables being unavailable, the tracking control is changed from a state‐feedback one to an output‐feedback one. So, observers need to be designed to estimate the indirect nonmeasurable states. According to Lyapunov stability analysis method, the developed controller can guarantee that all of the signals in the closed‐loop system will be ultimately uniformly bounded (UUB), and the output can track the reference signal very well. Simulation results are presented to show the effectiveness of the proposed approach.     

Adaptive Neural Dynamic Surface Control For Nonlinear Pure‐Feedback Systems With Multiple Time‐Varying Delays: A Lyapunov‐Razumikhin Method

This paper focuses on the problem of adaptive neural control for a class of uncertain nonlinear pure‐feedback systems with multiple unknown time‐varying delays. The considered problem is challenging due to the non‐affine pure‐feedback form and the unknown system functions with multiple unknown time‐varying delays. Based on a novel combination of mean value theorem, Razumikhin functional method, dynamic surface control (DSC) technique and neural network (NN) parameterization, a new adaptive neural controller which contains only one parameter is developed for such systems. Moreover, The DSC technique can overcome the problem of ‘explosion of complexity’ in the traditional backstepping design procedure. All closed‐loop signals are shown to be semi‐globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. Two simulation examples are given to verify the effectiveness of the proposed design.     

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.     

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.     

A low‐complexity design for distributed containment control of networked pure‐feedback systems and its application to fault‐tolerant control

This paper addresses a low‐complexity distributed containment control problem and its extension to fault‐tolerant control for networked nonlinear pure‐feedback systems under a directed graph. The multiple dynamic leaders are neighbors of only a subset of the followers described by completely non‐affine multi‐input multi‐output pure‐feedback dynamics. It is assumed that all followers' nonlinearities are heterogeneous and unknown. The proposed containment controller is implemented by using only error surfaces integrated by performance bounding functions and does not require any differential equations for compensating uncertainties and faults. Thus, compared with the previous containment control approaches for multi‐agent systems with unknown non‐affine nonlinearities, the distributed containment control structure is simplified. In addition, it is shown that the proposed control scheme can be applied to the fault‐tolerant containment control problem in the presence of unexpected system and actuator faults, without reconstructing any control structure. It is shown from Lyapunov stability theorem that all followers nearly converge to the dynamic convex hull spanned by the dynamic leaders and the containment control errors are preserved within certain given predefined bounds. Copyright © 2016 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.     

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.     

Output feedback tracking control for lower‐triangular nonlinear time‐delay systems with asymmetric input saturation

In this paper, the problem of output feedback tracking control is investigated for lower‐triangular nonlinear time‐delay systems in the presence of asymmetric input saturation. A novel design program based on a dynamic high gain design approach is proposed to construct an output feedback tracking controller. The innovation here is that the problem of constructing tracking controller can be transformed into the problem of constructing two dynamic equations, with one being utilized to deal with the nonlinear terms and the other one being applied to analyze the influence of asymmetric input saturation. It is proved by an appropriate Lyapunov‐Krasovskii functional that the proposed tracking controller subject to saturation can ensure that all the signals of the closed‐loop system are globally bounded and the tracking error is prescribed sufficiently small when time is long enough. A practical example is given to illustrate 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.     

Adaptive tracking control for a class of random pure‐feedback nonlinear systems with Markovian switching

This note studies the tracking control problem for a class of random pure‐feedback nonlinear systems with Markovian switching and unknown parameters. An adaptive tracking controller is constructed by introducing an auxiliary integrator subsystem and using the improved backstepping method such that the closed‐loop system has a unique solution that is globally bounded in probability. Meanwhile, the tracking error can converge to an arbitrarily small neighborhood of zero via the parameter regulation technique. The efficiency of the tracking controller designed in this paper is demonstrated by simulation examples.