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This paper presents a novel perspective on fully distributed adaptive protocol design for bipartite consensus under directed communication graphs. It is revealed that the fully distributed protocol is indeed a PI‐gain design approach. Based on such PI‐gain method, fully distributed observer‐based protocols are proposed to solve the consensus problem of nonlinear multi‐agent systems over directed cooperative‐antagonistic networks, where the neural network approximation is introduced to tackle the unknown nonlinearity. Fully distributed continuous protocols are further presented by modifying the sign function with a decaying variable, which takes the advantage of avoiding chattering problem. Theoretical analysis and numerical simulations are given to support our main results. [ABSTRACT FROM AUTHOR]

Summary: This paper concerns the analysis of an iterative scheme delivering approximate control laws for the tracking regulation problems for nonlinear systems. The procedure can be applied to finite‐ and infinite‐dimensional systems, and the underlying methodology derives from the geometric methods, which have been developed for both linear and nonlinear systems. In the nonlinear case, the main tool is the center manifold theorem. Indeed, in the geometric methodology, under the assumption that the signals to be tracked are generated by a finite‐dimensional exo‐system, the desired control is obtained by solving a pair of operator equations called the regulator equations. In this paper, we extend the concept of regulator equations to what we refer to as the dynamic regulator equations. Just as it is generally quite difficult to solve the regulator equations, it can be equally difficult to solve the dynamic regulator equations. As the authors have already shown in the linear case, a straightforward attempt to solve the dynamic regulator equations leads to a singular system, which can be regularized to obtain an iterative scheme that provides approximate control laws that provide accurate tracking with very a small tracking error after only a couple of iterations. In this paper, we generalize the iterative scheme to nonlinear systems and provide error estimates for the first 3 iterations. Both finite‐ and infinite‐dimensional examples are given to validate the estimates. We comment that the method has also been applied to a wide range of nonlinear distributed parameter examples described in the references. [ABSTRACT FROM AUTHOR]

Traditionally, an anti-windup compensator is activated when control signal saturation occurs. An alternative approach is to activate the compensator at a level below that of the physical control constraints: the anti-windup compensator is activated in anticipation of actuator saturation. Recent studies have proposed systematic methods for the construction of such anticipatory anti-windup compensators, but a pseudo-LPV representation of the saturated system has been central to these results. This paper approaches the anticipatory anti-windup problem for open-loop stable plants using a 'non-square' sector condition, which is associated with a combination of deadzone nonlinearities. The advantage of this approach is that it leads to synthesis routines, which bear a close resemblance to those associated with traditional immediately activated anti-windup compensators. A by-product of this approach also appears to be that the arising compensators are better numerically conditioned. Some simulation examples illustrating the effectiveness of anticipatory anti-windup compensators and some comments on their wider use complete the paper. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a finite‐time stability results of linear delay fractional‐order systems is investigated based on the generalized Gronwall inequality and the Caputo fractional derivative. Sufficient conditions are proposed to the finite‐time stability of the system with the fractional order. Numerical results are given and compared with other published data in the literature to demonstrate the validity of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the practical leader‐following consensus via the sampled‐data protocol is investigated for second‐order nonlinear multiagent systems with external disturbances, where the velocity information of all agents are assumed to be unmeasurable. The consensus problem of the multiagent system is first transformed to a stabilization problem of the constructed error system. Because of the unknown of the agents' velocities, an observer is then proposed for the constructed error system to estimate the velocity errors. By the backstepping approach, a new protocol is designed with only position measurements and sampled‐data information. Furthermore, the upper bound of the sampling period is given. It is proved that the practical leader‐following consensus can be achieved by the proposed sampled‐data protocol with a proper sampling period. The result is then extended to the multiagent systems with multiple leaders. Finally, two numerical examples are provided to illustrate the effectiveness of the designed protocols. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the pth moment exponential input‐to‐state stability (ISS) of nonlinear discrete‐time impulsive stochastic delay systems. By employing Lyapunov functionals, some pth moment exponential ISS criteria are provided. The obtained results show that a discrete‐time stochastic delay system can become pth moment exponential input‐to‐state stable by impulsive controls even if it may be not input‐to‐state stable itself. On the other hand, the original system without impulses can retain its ISS property with appropriate destabilizing impulses. As an application, the theoretical results are used to test the ISS for a class of recurrent neural networks under stochastic perturbations. Finally, a numerical example is presented to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

Summary: This paper concerns the consensus analysis of multiagent systems made of the interconnection of identical nonlinear agents interacting with one another through an undirected and connected graph topology. Drawing inspiration from the theory of linear "decomposable systems," we provide a method for proving the convergence (or consensus) of such multiagent sytems in the case of polynomial dynamics. The method is based on a numerical test, namely a set of linear matrix inequalities providing sufficient conditions for the convergence. We also show that the use of a generalized version of the famous Kalman‐Yakubovic‐Popov lemma allows the development of a linear matrix inequalities test whose size does not directly depend on the number of agents. The method is validated in simulation on three examples, which also show how the numerical test can be used to properly tune a controller. [ABSTRACT FROM AUTHOR]

Summary: Domain of attraction plays an important role in stability analysis and safety verification of nonlinear control systems. In this paper, based on the concept of multiple Lyapunov‐like functions, we propose iteration algorithms for computing inner estimates of domains of attraction for a class of switched hybrid systems, where the state space is composed of several regions and each region is described by polyhedral sets. Starting with an initial inner estimate of domain of attraction, we firstly present a theoretical framework for obtaining a larger inner estimate by iteratively computing multiple Lyapunov‐like functions. Successively, the theoretical framework is underapproximatively realized by using S‐procedure and sums of squares programming, associated with the coordinatewise iteration method. Afterwards, for obtaining a required initial inner estimate of domain of attraction, we propose an alternative higher‐order truncation and linear semidefinite programming based method for computing a common Lyapunov function. Especially, a bisection method based improvement is proposed for obtaining better estimates in each iteration step. Finally, we implement proposed algorithms and test them on numerical examples with comparisons. These computation and comparison results show that the advantages of our multiple Lyapunov‐like functions based algorithm. Especially, we provide alternative underapproximations for avoiding the possible numerical problem. [ABSTRACT FROM AUTHOR]

This paper presents LMI conditions for local, regional, and global robust asymptotic stability of rational uncertain nonlinear systems. The uncertainties are modeled as real time varying parameters with magnitude and rate of variation bounded by given polytopes and the system vector field is a rational function of the states and uncertain parameters. Sufficient LMI conditions for asymptotic stability of the origin are given through a rational Lyapunov function of the states and uncertain parameters. The case where the time derivative of the Lyapunov function is negative semidefinite is also considered and connections with the well known LaSalle's invariance conditions are established. In regional stability problems, an algorithm to maximize the estimate of the region of attraction is proposed. The algorithm consists of maximizing the estimate for a given target region of initial states. The size and shape of the target region are recursively modified in the directions where the estimate can be enlarged. The target region can be taken as a polytope (convex set) or union of polytopes (non-convex set). The estimates of the region of attraction are robust with respect to the uncertain parameters and their rate of change. The case of global and orthant stability problems are also considered. Connections with some results found in sum of squares based methods and other related methods found in the literature are established. The LMIs in this paper are obtained by using the Finsler's Lemma and the notion of annihilators. The LMIs are characterized by affine functions of the state and uncertain parameters, and they are tested at the vertices of a polytopic region. It is also shown that, with some additional conservatism, the use of the vertices can be avoided by modifying the LMIs with the S-Procedure. Several numerical examples found in the literature are used to compare the results and illustrate the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a novel robust sliding mode learning control scheme is developed for a class of non-minimum phase nonlinear systems with uncertain dynamics. It is shown that the proposed sliding mode learning controller, designed based on the most recent information of the stability status of the closed-loop system, is capable of adjusting the control signal to drive the sliding variable to reach the sliding surface in finite time and remain on it thereafter. The closed-loop dynamics including both observable and non-observable ones are then guaranteed to asymptotically converge to zero in the sliding mode. The developed learning control method possesses many appealing features including chattering-free characteristic, strong robustness with respect to uncertainties. More importantly, the prior information of the bounds of uncertainties is no longer required in designing the controller. Numerical examples are presented in comparison with the conventional sliding mode control and backstepping control approaches to illustrate the effectiveness of the proposed control methodology. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper presents a robust fault estimation approach for a class of nonlinear discrete-time systems. In particular, two sources of uncertainty are present in the considered class of systems, that is, an unknown input and an exogenous external disturbance. Thus, apart from simultaneous state and fault estimation, the objective is to decouple the effect of an unknown input while minimizing the influence of the exogenous external disturbance within the [ABSTRACT FROM AUTHOR]

This paper deals with the robust consensus tracking problem for a class of heterogeneous second-order nonlinear multi-agent systems with bounded external disturbances. First, a distributed adaptive control law is proposed based on the relative position and velocity information. It is shown that for any connected undirected communication graph, the proposed control law solves the robust consensus tracking problem. Then, by introducing a novel distributed observer and employing backstepping design techniques, a distributed adaptive control law is constructed based only on the relative position information. Compared with the existing results, the proposed adaptive consensus protocols are in a distributed fashion, and the nonlinear functions are not required to satisfy any globally Lipschitz or Lipschitz-like condition. Numerical examples are given to verify our proposed protocols. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper focuses on the robust output precise tracking control problem of uncertain nonlinear systems in pure-feedback form with unknown input dead zone. By designing an extended state observer, the states unmeasurable problem in traditional feedback control is solved, and the lumped uncertainty, which is caused by system unknown functions and input dead zone, is estimated. In order to apply separation principle, finite-time extended state observer is designed to obtain system states and estimate the lumped uncertainty. Then, by introducing tracking differentiator, a modified dynamic surface control approach is developed to eliminate the 'explosion of complexity' problem and guarantee the tracking performance of system output. Because tracking differentiator is a fast precise signal filter, the closed-loop control performance is significantly improved when it is used in dynamic surface control instead of first-order filters. The L ∞ stability of the whole closed-loop system, which guarantees both the transient and steady-state performance, is shown by the Lyapunov method and initialization technique. Numerical and experiment examples are performed to illustrate our proposed control scheme with satisfactory results. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of self-triggered state-feedback control for linear plants under bounded disturbances. In a self-triggered scenario, the controller is allowed to choose when the next sampling time should occur and does so based on the current sampled state and on a priori knowledge about the plant. Besides comparing some existing approaches to self-triggered control available in the literature, we propose a new self-triggered control strategy that allows for the consideration of model-based controllers, a class of controllers that includes as a special case static controllers with a zero-order hold of the last state measurement. We show that our proposed control strategy renders the solutions of the closed-loop system globally uniformly ultimately bounded. We further show that there exists a minimum time interval between sampling times and provide a method for computing a lower bound for it. An illustrative example with numerical results is included in order to compare the existing strategies and the proposed one. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]