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This article addresses the problem of adaptive tracking control for stochastic nonlinear systems with asymmetric full state constraints. Different from the traditional log‐type or tan‐type barrier Lyapunov functions (BLFs), a new asymmetric BLF is proposed in this article. Then, a state feedback controller is constructed with backstepping method so that all signals of the closed‐system are bounded and the asymmetric state constraint is well kept all the time. Without changing the structure of the controller, the design and the analysis for constrained and unconstrained systems are unified. Finally, the effectiveness of proposed control strategy has been demonstrated by simulations of numerical example and the single‐link robot arm model. [ABSTRACT FROM AUTHOR]

In this paper, by using bound estimation method, Nussbaum function, K‐filters and higher‐order Lyapunov function, an adaptive output feedback compensation control scheme is proposed for uncertain nonlinear systems with infinite number of actuator failures and unknown control direction. A parametric model with unknown system uncertainties and infinite actuator failures is established, which is different from the existing results. This scheme ensures that closed‐loop signals are globally uniformly bounded. By properly selecting the design parameters, the tracking errors converges to a small neighborhood of the origin. Finally, two simulation examples are given to demonstrate its efficiency of the proposed design scheme. [ABSTRACT FROM AUTHOR]

In this article, we extend the adaptive tracking control to more general nonlinear systems with multiple uncertainties, including output constraint, input delay, unknown parameter, and external disturbances for the first time. Without any growth assumptions, the adaptive backstepping technique is combined with the parameter separation technique to solve the parametric nonlinearities while the related results need to apply restrictive assumptions or use an approximation-based scheme to deal with them. To alleviate the serious uncertainties caused by output constraint and input delay, the barrier Lyapunov function (BLF) and the Pade approximation method are employed in a unified framework when the control coefficient is known. Under the case of the unknown control coefficient, the Nussbaum gain technique is further combined to compensate it. Then, under both cases, universal adaptive state-feedback control strategies merged with rigorous stability analysis are proposed, respectively, which guarantees all the signals are uniformly ultimately bounded. In addition, the reference signal tracks the system output into a compact set of the origin and the constraint of output is not violated. Finally, the proposed controllers are applied to an inverted pendulum system, which demonstrates the designed controller is effective. [ABSTRACT FROM AUTHOR]

This work addresses the nonfragile $H_{\infty }$ controller design problem for a class of discrete-time uncertain nonlinear systems. The norm-bounded uncertainty is contained in the nonlinear plant, which is described by the well-known Takagi–Sugeno (T–S) fuzzy model. The controller gain perturbation is also considered. When the input signal is transmitted from the controller to the system through the digital communication channels, it will be quantized by a static quantizer. The main attention is to design the nonfragile $H_{\infty }$ state-feedback controller for the closed-loop quantized uncertain T–S fuzzy system. By introducing some auxiliary scalars and the fuzzy basis-dependent Lyapunov function approach, sufficient conditions are established in the form of linear matrix inequalities (LMIs). The construction for the nonfragile $H_{\infty }$ controller can be completed by solving these LMIs. In the end, the applicability and effectiveness of the proposed method have been illustrated by two simulation examples. [ABSTRACT FROM AUTHOR]

Summary: Second‐order sliding mode (SOSM) control is used to keep exactly a constraint σ of the second relative degree or to avoid chattering phenomenon. Yet, the traditional SOSM controllers are designed based upon the assumption that the uncertainties or their derivatives are bounded by positive constants. In this paper, a global SOSM controller is designed for a general class of single‐input–single‐output nonlinear systems with uncertainties bounded by positive functions. Moreover, a variable‐gain robust exact differentiator is developed such that the SOSM controllers with finite‐time convergence can also be implemented even when the derivative of the constraint σ is unavailable. Simulation results are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time control problem for a class of stochastic nonlinear systems with stochastic integral input-to-state stablility (SiISS) inverse dynamics. Motivated by finite-time stochastic input-to-state stability and the concept of SiISS using Lyapunov functions, a novel finite-time SiISS using Lyapunov functions is introduced firstly. Then, by adopting this novel finite-time SiISS small-gain arguments, using the backstepping technique and stochastic finite-time stability theory, a systematic design and analysis algorithm is proposed. Given the control laws that guarantee global stability in probability or asymptotic stability in probability, our design algorithm presents a state-feedback controller that can ensure the solution of the closed-loop system to be finite-time stable in probability. Finally, a simulation example is given to demonstrate the effectiveness of the proposed control scheme. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

For the parametric strict-feedback nonlinear systems with unknown virtual control coefficients and unknown control directions, the control schemes presented in the existing literature have the disadvantage of overparametrization. In this paper, a novel systematic design procedure is developed to solve the overparametrization problem. Two nonlinear controllers are designed by combining the backstepping technique and the Nussbaum gain approach. A main advantage of the proposed controllers is that they contain less or no parameter estimates that need to be updated online. In the first scheme, the number of the estimated parameters is equal to the dimension of the controlled system. In the second scheme, no parameter estimates are required. In both of the control schemes, the boundedness of all the closed-loop signal is guaranteed, and the asymptotic convergence of the system states is achieved. An example is provided to demonstrate the effectiveness of the proposed design approaches. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper is concerned with the stability of sampled-data systems with state quantization. A new piecewise differentiable Lyapunov functional is first constructed by fully utilizing information about sampling instants. This functional has two features: one is that it is of the second order in time t and of every term being dependent on time t explicitly and the other is that it is discontinuous and is only required to be definite positive at sampling instants. Then, on the basis of this piecewise differentiable Lyapunov functional, a sampling-interval-dependent exponential stability criterion is derived by applying the technique of a convex quadratic function with respect to the time t to check the negative definiteness for the derivative of the piecewise differentiable Lyapunov functional. In the case of no quantization, a new sampling-interval-dependent stability criterion is also obtained. It is shown that the new stability criterion is less conservative than some existing one in the literature. Finally, two examples are given to illustrate the effectiveness of the stability criterion. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the design of the novel observer that synchronizes with the generalized Lorenz chaotic systems. A simple reduced-order observer scheme is proposed by including extra terms. The boundedness of the state variables in the original system is not necessary for the observer design. The prior knowledge on the derivative signal of the system output is not required. It is also shown that by adopting Lyapunov method and choosing appropriate design parameters, the synchronization (observation) errors can converge to zero exponentially. Finally, numerical examples are provided to illustrate the validity of the theoretical result. [Copyright &y& Elsevier]

Abstract: In this paper, an adaptive control scheme is proposed for the synchronization of two single-degree-of-freedom oscillators with unknown parameters. We only assume that the master system has the bounded solutions, which is generally satisfied for chaotic systems. Unlike the existing literature, the boundedness of the states of the slave system with control input is not necessarily known in advance. The boundedness of the controlled states is rigorously proved. The unknown parameters not only in the slave system but also in the master system are estimated by designing adaptive laws. By choosing appropriate Lyapunov function and employing Barbalat’s lemma, it is theoretically shown that the synchronization errors can converge to zero asymptotically. Finally, two illustrative examples are provided to demonstrate the effectiveness of the proposed adaptive control design. [Copyright &y& Elsevier]

The main focus of this paper is to explore the finite-time stabilization of mean-field time-varying stochastic systems that are affected by uncertain parameters, multiple disturbances, and delays. In contrast to prior studies, we present a set of sufficient conditions for achieving finite-time stability in the closed-loop model. Notably, these conditions are established based on the analysis of the state transition matrix (STM). Additionally, we address a sufficient condition based on the Lyapunov function, where the STM significantly simplifies the selection process of the Lyapunov function. Finally, we introduce a linear matrix inequality (LMI)-based approach that facilitates the computation of non-fragile controllers. The effectiveness of the developed theoretical results is verified through a stock investment model. [ABSTRACT FROM AUTHOR]

This paper is concerned with the design of fuzzy controller for networked control systems (NCSs). T-S fuzzy system approach is adopted to study the problem. In account of NCSs, various data missing on both sides of the controller caused by event-triggered scheme, data losses and event-driven controller are involved. For handling this issue, an auxiliary random series method is presented to describe the data transferring in the network. Based on this method, the closed-loop NCSs is constructed and then analyzed via Lyapunov stability theory. Additionally, the probability of random data losses at each instant is supposed to be different which is more practical. For the purpose of obtaining more relaxed stabilization conditions, the fuzzy Lyapunov function obtained on the basis of both plant and controller fuzzy rules is employed. Furthermore, variations of membership functions are taken into account, and consequently, slack matrices are introduced to obtain less conservative result. At last, by considering a cart-damper-spring system, the effectiveness of the proposed method is illustrated. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of event triggering H ∞ synchronization control for discrete-time switched complex networks via quasi-time asynchronous controllers. One event triggering mechanism is introduced with the triggering parameters depending on triggering states. Applying quasi-time dependent multiple Lyapunov functions and the mode-dependent average dwell time technique, quasi-time dependent synchronization conditions are obtained with a lower weighted performance index. And then, a quasi-time dependent asynchronous controller is designed with quasi-time dependent control gains in each triggering interval. In addition, not only no more than one switching, but also multiple switchings are taken into account in each triggering interval, by which the assumption in some existing results is relaxed. Finally, the proposed result is applied to the PWM-driven boost converter. [ABSTRACT FROM AUTHOR]

In modern control theory, it is more applicable for digital computers using a sampled-data controller than a continuous-time controller. Meanwhile, input saturation and disturbance inevitably exist in control systems. Thus, how to propose an applicable sampled-data controller for nonlinear systems considering input saturation together with external disturbances is essential for applications. To deal with this control problem, a novel auxiliary control signal is designed in this paper. Then, by using Lyapunov method, the control design process is simplified compared with the traditional backstepping technique, and only one Lyapunov function is needed. In addition, the state and disturbance observers are proposed with the new auxiliary control signal to track the unavailable states and external disturbances. Finally, we propose a novel controller reflecting the sampled-data output-feedback for the nonlinear systems to ensure the system stability. The effectiveness of proposed control method in this paper is confirmed through two sets of numerical simulation results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the adaptive finite-time flocking problem for a class of second-order nonlinear multi-agent systems with parameter uncertainties. The states of all agents can achieve finite-time consensus by using the proposed control algorithm under an undirected graph. It is shown that connectivity preservation is guaranteed by choosing an appropriate Lyapunov potential function. A numerical example is presented to illustrate the effectiveness of the proposed consensus protocol. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of the exponential synchronization of complex dynamical networks with time-varying inner coupling via event-triggered communication. The network topology is assumed to have a spanning tree. A sufficient condition is derived to guarantee the exponential synchronization by employing the special Lyapunov stability analysis method, which by combining the difference and differential of the Lyapunov function rather than the single difference or differential. The main advantage of this paper is to avoid continuous communication between network nodes, which can decrease the number of information updates, reduce the network congestion and avoid the waste of network resources. Moreover, the Zeno behavior is excluded as well by the strictly positive sampling intervals. Finally, A simulation example is given to show the effectiveness of the proposed exponential synchronization criteria. [ABSTRACT FROM AUTHOR]