Distributed adaptive tracking control for multi-agent systems with uncertain dynamics

Nonlinear Dynamics - In this paper, we investigate a general integrable three-component coupled nonlocal nonlinear Schrödinger system with the parity-time symmetry. The general Nth Darboux...     

Leader-following second-order consensus in multi-agent systems with sampled data via pinning control

This paper studies the second-order consensus in multi-agent systems with sampled position and velocity data via pinning control. The distributed pinning consensus protocols with second-order dynamics are designed, where both sampled position and velocity data are employed. Necessary and sufficient conditions are derived for reaching second-order consensus by combining the algebraic graph theory and the analytical method. According to the obtained consensus criteria, the second-order leader-following consensus can be reached if and only if the sampling period, the coupling gain, and the pinning gains satisfy some derived algebraic inequalities. Moreover, it is found that second-order consensus in multi-agent systems cannot be reached with only sampled position data in the pinning controllers. Finally, the effectiveness and correctness of our theoretical findings are demonstrated by some numerical examples.     

Distributed cooperative adaptive tracking control for heterogeneous systems with hybrid nonlinear dynamics

Nonlinear Dynamics - The cooperative leader-following tracking for a group of heterogeneous mechanical systems with nonlinear hybrid order dynamics is studied. The controlled systems are considered...     

Design of sampled data state estimator for Markovian jumping neural networks with leakage time-varying delays and discontinuous Lyapunov functional approach

This paper is concerned with the sampled-data state estimation problem for neural networks with both Markovian jumping parameters and leakage time-varying delays. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. In order to make full use of the sawtooth structure characteristic of the sampling input delay, a discontinuous Lyapunov functional is proposed based on the extended Wirtinger inequality. A less conservative delay dependent stability criterion is derived via constructing a new triple-integral Lyapunov–Krasovskii functional and the famous Jenson integral inequality. Based on the Lyapunov–Krasovskii functional approach, a state estimator of the considered neural networks has been achieved by solving some linear matrix inequalities, which can be easily facilitated by using the standard numerical software. Finally, two numerical examples are provided to show the effectiveness of the proposed methods.     

Leader-following formation control for second-order multiagent systems with time-varying delay and nonlinear dynamics

In this paper, the leader-following formation control problem for second-order multiagent systems with time-varying delay and nonlinear dynamics is considered. Two different cases of coupling topologies, fixed topology and switching topology, are analyzed. Based on the Lyapunov theory combined with the linear matrix inequality (LMI) method, sufficient conditions in terms of LMIs are given to ensure the multiagent systems can reach and maintain the desired formation. The simulation results are provided to demonstrate the effectiveness of the obtained theory results.     

Distributed adaptive tracking backstepping control in networked nonidentical Lagrange systems

In this paper, the problem of adaptive tracking control in networked nonidentical Lagrange systems is investigated via backstepping schemes. Two distributed tracking control algorithms are designed for directed network topology graph with a spanning tree, where both the leader’s position and its velocity are assumed to be varying. Some generic criteria for adaptive tracking control algorithms with uncertain external disturbance and parametric uncertainties are presented. It is shown that the proposed algorithms only require a subset of the followers access to leader’s position. Furthermore, the adaptive control algorithm for uncertain external disturbance systems is robust, and it can avoid online measurement for neighbors’ velocities and efficiently eliminate the chattering during tracking. The results show that all followers can track the leader’s dynamics. Two examples and their simulations show the effectiveness of the proposed algorithms.     

Distributed coordinated tracking control for multi-manipulator systems under intermittent communications

Nonlinear Dynamics - The distributed coordinated tracking control problem for multiple robotic manipulators under intermittent communications is researched, respectively, with a stationary leader...     

Distributed average tracking with input saturation

Nonlinear Dynamics - In this paper, the distributed average tracking (DAT) problem of a multi-agent system with input saturation is considered, whose objective is to make each agent track the...     

Robust tracking control method based on composite nonlinear feedback technique for linear systems with time-varying uncertain parameters and disturbances

In this paper, the composite nonlinear feedback control method is considered for robust tracking and model following of uncertain linear systems. The control law guarantees that the tracking error decreases asymptotically to zero in the presence of time varying uncertain parameters and disturbances. For performance improvement of the dynamical system, the proposed robust tracking controller consists of linear and nonlinear feedback parts without any switching element. The linear feedback law is designed to allow the closed loop system have a small damping ratio and a quick response while the nonlinear feedback law increases the damping ratio of the system as the system output approaches the output of the reference model. A new collection of different nonlinear functions used in the control law are offered to improve the reference tracking performance of the system. The proposed robust tracking controller improves the transient performance and steady state accuracy simultaneously. Finally, the simulations are provided to verify the theoretical results.     

Technical stability of nonlinear time-varying systems with small parameters

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Robust synchronization of Rossler systems with mismatched time-varying parameters

This paper presents robust synchronization algorithms for the Rossler systems in the presence of unknown time-varying parameters. First, an adaptive synchronization algorithm based on the Lyapunov theory is introduced for identical Rossler systems with mismatched uncertainties. This method does not require a priori information regarding the bound of uncertainties. In addition, this technique is such that the states of the synchronization error system are uniformly ultimately bounded. Since in practice the parameters of the drive and response systems are not necessarily the same, two synchronization approaches are used for the drive and response systems with different parameters. In the first approach, a simple controller is designed for the nominal error system, as if there is no uncertainty in the system. The stability analysis is then investigated as the uncertainties are reintroduced, and it is shown that the size of the uncertainties directly affects the synchronization performance. To deal with this problem, an H _∞ controller is designed in which the effects of unknown bounded uncertainties can be attenuated at an appropriate level. It is shown that, using these two approaches, the Rossler systems can be synchronized effectively and the synchronization error is uniformly ultimately bounded. Numerical simulations confirm the effectiveness of the proposed methods.     

A study of linear time-varying systems

Some linear time-varying systems that can be solved in closed form and are of practical importance in the problems of mechanics are considered. Several properties of the linear time-varying systems whose matrices belong to different classes simultaneously are studied. The stability analysis is performed using a nontraditional method of matrix decomposition. A number of mechanical problems are discussed to illustrate the efficiency of the proposed method.     

Efficient computation for dynamic responses of systems with time-varying characteristics

Based on Neumman series and epsilon-algorithm, an efficient computation for dynamic responses of systems with arbitrary time-varying characteristics is investigated. Avoiding the calculation for the inverses of the equivalent stiffness matrices in each time step, the computation effort of the proposed method is reduced compared with the full analysis of Newmark method. The validity and applications of the proposed method are illustrated by a 4-DOF spring-mass system with periodical time-varying stiffness properties and a truss structure with arbitrary time-varying lumped mass. It shows that good approximate results can be obtained by the proposed method compared with the responses obtained by the full analysis of Newmark method.     

Robust synchronization of uncertain fractional-order chaotic systems with time-varying delay

This paper presents a new technique using a recurrent non-singleton type-2 sequential fuzzy neural network (RNT2SFNN) for synchronization of the fractional-order chaotic systems with time-varying delay and uncertain dynamics. The consequent parameters of the proposed RNT2SFNN are learned based on the Lyapunov–Krasovskii stability analysis. The proposed control method is used to synchronize two non-identical and identical fractional-order chaotic systems, with time-varying delay. Also, to demonstrate the performance of the proposed control method, in the other practical applications, the proposed controller is applied to synchronize the master–slave bilateral teleoperation problem with time-varying delay. Simulation results show that the proposed control scenario results in good performance in the presence of external disturbance, unknown functions in the dynamics of the system and also time-varying delay in the control signal and the dynamics of system. Finally, the effectiveness of proposed RNT2SFNN is verified by a nonlinear identification problem and its performance is compared with other well-known neural networks.     

Decentralized stabilization of large-scale linear interconnected systems with time-varying delays

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｒｅｃｅｎｔｙｅａｒｓ,ｄｅｃｅｎｔｒａｌｉｚｅｄｓｔａｂｉｌｉｚａｔｉｏｎｏｆｌａｒｇｅ＿ｓｃａｌｅｉｎｔｅｒｃｏｎｎｅｃｔｅｄｓｙｓｔｅｍｓｈａｓｂｅｅｎｗｉｄｅｌｙｓｔｕｄｉｅｄ .ＬｅｅａｎｄＲａｄｏｖｉｃ[1,2 ]ｅｓｔａｂｌｉｓｈｅｄｓｏｍｅｄｅｃｅｎｔｒａｌｉｚｅｄｓｔａｂｉｌｉｚａｔｉｏｎｃｏｎｄｉｔｉｏｎｓｆｏｒｌａｒｇｅ＿ｓｃａｌｅｌｉｎｅａｒｃｏｎｔｉｎｕｏｕｓａｎｄｄｉｓｃｒｅｔｅｔｉｍｅ＿ｄｅｌａｙ .Ｉｎｔｈｉｓｍｅｔｈｏｄ ,ｍｏｒｅｓｔｒｕｃｔｕ…     

Projective-dual synchronization in delay dynamical systems with time-varying coupling delay

The existence of projective-dual-anticipating, projective-dual, and projective-dual-lag synchronization in a coupled time-delayed systems with modulated delay time is investigated via nonlinear observer design approach. Transition from projective-dual-anticipating to projective-dual synchronization and from projective-dual to projective-dual-lag synchronization as a function of variable coupling delay τ _p (t) is discussed. Using Krasovskii–Lyapunov stability theory, a general condition for projective-dual synchronization is derived. Numerical simulations on the chaotic Ikeda and Mackey–Glass systems are given to demonstrate the effectiveness of the theoretical results.     

Recursive identification of discrete-time nonlinear cascade systems with time-varying output hysteresis

Nonlinear Dynamics - A recursive identification method for discrete-time nonlinear cascade systems with a linear dynamic system followed by a time-varying output hysteresis is presented. The...