Propagation of projective synchronization in a series connection of chaotic systems

Projective synchronization is a type of chaos synchronization where the response system states are scaled replicas of the drive system states. This paper deals with the propagation of projective synchronization in a series connection of N chaotic discrete-time drive systems and N response systems. By exploiting an observer-based approach, the paper demonstrates that dead-beat projective synchronization (i.e., exact synchronization in finite time for any scaling factor) is achieved between the nth drive and nth response systems. In particular, it is shown that projective synchronization starts from the innermost (Nth) drive-response system pair and propagates toward the outermost (first) drive-response system pair. Only a single scalar synchronizing signal connects the cascaded drive and response systems. Finally, an example illustrates the propagation of different types of chaos synchronization in a series connection consisting of a Gingerbreadman map, a third order hyperchaotic Henon map and a Lozi map.     

Chaotic synchronization between different fractional-order chaotic systems

Based on the idea of tracking control and stability theory of fractional-order systems, a novel synchronization approach for fractional order chaotic systems is proposed. We prove that the synchronization between drive system and response system with different fractional order q can be achieved, and the synchronization between different fractional-order chaotic systems with different fractional order q can be achieved. Two examples are used to illustrate the effectiveness of the proposed synchronization method. Numerical simulations coincide with the theoretical analysis.     

Adaptive synchronization of uncertain chaotic systems with adaptive scaling function

The problem of adaptive synchronization for the uncertain chaotic systems with adaptive scaling function is investigated in this paper. In comparison to those of the existing scaling function synchronization, such as the presetting scaling function, the aim of this paper is focused not only on the scaling function but also on the identification of parameters of the chaotic system. Finally, to illustrate the implementation of the proposed method, some numerical simulations are given.     

Decentralized adaptive synchronization with bounded identification errors for discrete-time nonlinear multi-agent systems with unknown parameters and unknown high-frequency gains

This paper addresses the challenging problem of decentralized adaptive control for a class of coupled hidden leader-follower multi-agent systems, in which each agent is described by a nonlinearly parameterized uncertain model in discrete time and can interact with its neighbors via the history information from its neighbors. One of the agents is a leader, who knows the desired reference trajectory, while other agents cannot receive the desired reference signal or are unaware of existence of the leader. In order to tackle unknown internal parameters and unknown high-frequency gains, a projection-type parameter estimation algorithm is proposed. Based on the certainty equivalence principle and neighborhood history information, the decentralized adaptive control is designed, under which, the boundedness of identification error is guaranteed with the help of the Lyapunov theory. Under some conditions, it is shown that the multi-agent system eventually achieves synchronization in the presence of strong couplings. Finally, a simulation example is given to support the results of the proposed scheme.     

Command filtered adaptive neural network synchronization control of fractional-order chaotic systems subject to unknown dead zones

Command filters are essential for alleviating the inherent computational complexity (ICC) of the standard backstepping control method. This paper addresses the synchronization control scheme for an uncertain fractional-order chaotic system (FOCS) subject to unknown dead zone input (DZI) based on a fractional-order command filter (FCF). A virtual control function (VCF) and its fractional-order derivative are approximated by the output of the FCF. In order to handle filtering errors and obtain good control performance, an error compensation mechanism (ECM) is developed. A radial basis function neural network (RBFNN) is introduced to relax the requirement of the uncertain function must be linear in the standard backstepping control method. The construction of a VCF in each step satisfies the Lyapunov function to ensure the stability of the corresponding subsystem. By using the bounded information to cope with the unknown DZI, the stability of the synchronization error system is guaranteed. Finally, simulation results verify the effectiveness of our methods.     

Adaptive anti-lag synchronization of two identical or non-identical hyperchaotic complex nonlinear systems with uncertain parameters

In this paper we present the adaptive anti-lag synchronization (ALS) of two identical or non-identical hyperchaotic complex nonlinear systems with uncertain parameters. The concept of ALS is not detected yet in the literature. Based on the Lyapunov function a scheme is designed to achieve ALS of hyperchaotic attractors of these systems. The ALS of two identical complex Lü systems and two different hyperchaotic complex Lorenz and Lü systems are taken as two examples to verify the feasibility of the presented scheme. These hyperchaotic complex systems appear in several applications in physics, engineering and other applied sciences. Numerical simulations are calculated to demonstrate the effectiveness of the proposed synchronization scheme and verify the theoretical results.     

Finite-time multi-switching synchronization behavior for multiple chaotic systems with network transmission mode

By considering network transmission mode, this paper addresses the finite-time multi-switching synchronization problem for two kinds of multiple chaotic systems. For multiple same-order chaotic systems, we construct the general switching rules and analyze the existence of switching cases. The presented schemes guarantee the states of each derive system to be finite-timely synchronized with the desired states of every respond system in the different transmission paths and switching sequences. For multiple different order chaotic systems, we analyze a special multi-switching hybrid synchronization behavior, where part of the states are completely synchronized and the others belong to combination synchronization. Moveover, the easily verifiable criterion is derived for such synchronization. Finally, numerical examples are given to show the effectiveness of the presented theoretical results.     

Optimal LQG controller for linear stochastic systems with unknown parameters

This paper presents the optimal LQG controller for linear systems with unknown parameters. The optimal controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. Performance of the obtained optimal controller is verified in the illustrative example against the conventional LQG controller that is optimal for linear systems with known parameters. Simulation graphs verifying overall performance and computational accuracy of the designed optimal controller are included.     

Robust adaptive visual tracking control for uncertain robotic systems with unknown dead-zone inputs

This paper is concerned with the image-based visual servoing (IBVS) control for uncalibrated camera-robot system with unknown dead-zone constraint, where the uncertain kinematics and dynamics are also considered. The control implementation is achieved by constructing a smooth inverse model for dead-zone-input to eliminate the nonlinear effect resulting from the actuator constraint. A novel adaptive algorithm, which does not require a priori knowledge of the parameter intervals of dead-zone model, is proposed to update the parameter values online, and the dead-zone slopes are not required the same. Furthermore, to accommodate the uncertainties of uncalibrated camera-robot system, adaptation laws are developed to estimate the uncertain parameters, simultaneously avoiding singularity of the image Jacobian matrix. With the full consideration of unknown dead-zone constraint and system uncertainties, an adaptive robust visual tracking control scheme together with dead-zone compensation is subsequently established such that the image tracking error converges to the origin. Based on a 3-DOF manipulator, simulations are conducted to verify the tracking performance of the proposed controller.     

On aperiodic event-triggered master-slave synchronization of chaotic Lur'e systems

This paper is concerned with master-slave synchronization for chaotic Lur'e systems subject to aperiodic sampled-data. To reduce the communication burden, an aperiodic event-triggered (APET) transmission scheme is introduced to determine the transmission of the latest sampling synchronization data. In order to reduce the design conservatism, a novel time-dependent Lyapunov functional (TDLF) is constructed to fully use the characteristics about sampling behavior, triggering error, and nonlinear part of the system, simultaneously. A more relaxed constraint criterion is then presented to ensure the positivity of the whole functional between two sampling instants. By partially resorting to the TDLF, the APET-based synchronization criterion depending on the upper and lower bounds of the uncertain sampling period is presented. The synchronization criterion based on aperiodic-sampling mechanism is also provided. Finally, a typical example about neural networks is offered to illustrate the benefit and validity of obtained synchronization methodologies.     

Robust synchronization of different coupled oscillators: Application to antenna arrays

This paper deals with the synchronization of a chain of nonlinear and uncertain models of nonidentical oscillators. Using Lyapunov's theory of stability, a dynamical controller guaranteeing the synchronization of the oscillators is determined. The problem of synchronization is transformed into a problem of asymptotic stabilization for a nonlinear system and then is formulated as a system of linear matrix inequalities where the parameter variations of the two oscillators and their differences are modeled by polytopic matrices. The theoretical result is successfully applied to an array of transistor-based oscillators used in “smart antenna” systems.     

One input control for exponential synchronization in generalized Lorenz systems with uncertain parameters

By taking account of uncertain slave system parameters, the main goal of this paper is to investigate exponential master–slave synchronization between two nearly identical generalized Lorenz systems via one control input, which including a single state proportional feedback, associated with system parameter estimated laws, which not including states of the master system. Sufficient conditions are provided for the guaranteed exponential stability of both synchronized errors and system parameter errors. Meanwhile, numerical studies are also performed to verify the effectiveness of presented schemes.     

Robust stability analysis for a class of fractional order systems with uncertain parameters

The research of robust stability for fractional order linear time-invariant (FO-LTI) interval systems with uncertain parameters has become a hot issue. In this paper, it is the first time to consider robust stability of uncertain parameters FO-LTI interval systems, which have deterministic linear coupling relationship between fractional order and other model parameters. Linear matrix inequalities (LMI) methods are used, and a criterion for checking asymptotical stability of this class of systems is presented. One numerical illustrative example is given to verify the correctness of the conclusions.     

Generalized matrix projective synchronization of general colored networks with different-dimensional node dynamics

This paper investigates the generalized matrix projective synchronization problem of general colored networks with different-dimensional node dynamics. A general colored network consists of colored nodes and edges, where the dimensions of colored node dynamics can be different in addition to the difference of the inner coupling matrices between any pair of nodes. For synchronizing a colored network onto a desired orbit with respect to the given matrices, open-plus-closed-loop controllers are designed. The closed-loop controllers are chosen as adaptive feedback and intermittent controllers, respectively. Based on the Lyapunov stability theory and mathematical induction, corresponding synchronization criteria are derived. Noticeably, many existing synchronization settings can be regarded as special cases of the present synchronization framework. Numerical simulations are provided to verify the theoretical results.     

Finite-time synchronization of Markovian jump complex networks with partially unknown transition rates

In this paper, finite-time synchronization problem is considered for a class of Markovian jump complex networks (MJCNs) with partially unknown transition rates. By constructing the suitable stochastic Lyapunov–Krasovskii functional, using finite-time stability theorem, inequality techniques and the pinning control technique, several sufficient criteria have been proposed to ensure the finite-time synchronization for the MJCNs with or without time delays. Since finite-time synchronization means the optimality in convergence time and has better robustness and disturbance rejection properties, this paper has important theory significance and practical application value. Finally, numerical simulations illustrated by mode jumping from one mode to another according to a Markovian chain with partially unknown transition probability verify the effectiveness of the proposed results.     

Robust stable pole-placement-based adaptive control of continuous linear systems with two parametrical estimation schemes

This paper deals with the pole-placement-type robust adaptive control of continuous linear systems in the presence of bounded noise and a common class of unmodeled dynamics provided that two estimation schemes are used in parallel. Both estimation schemes are introduced in order to minimize the plant identification error by selecting, as plant parameter estimates, a convex combination of both parameter estimates which leads to the selection of one of the estimation schemes, via a switching rule, on time intervals of at least a minimum prefixed residence duration. The weights of the individual parameter vector estimates are provided at each time by an optimization or suboptimization scheme for a quadratic loss function of the possibly filtered tracking error and/or control input. The robust stability of the overall adaptive scheme is ensured by an adaptation relative dead zone which takes into account the contribution of the unmodeled dynamics and bounded noise. The basic results are derived for two different estimation strategies which have either a shared regressor with the plant or individual regressors for the input contribution and its contributed derivatives. In this second case, the plant input is obtained from a similar convex combination rule as the one used for the estimators in the first approach. An extension of the basic strategies is also pointed out including a combined use of the (sub) optimization scheme with a supervisor of past measures for the on-line calculation of the estimator weights in the convex combination. Finally, the extension of the scheme for the use of any number of parametrical estimators is focused on.     

Optimal filtering over linear observations with unknown parameters

This paper presents the optimal filtering and parameter identification problem for linear stochastic systems over linear observations with unknown parameters, where the unknown parameters are considered Wiener processes. The original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states. The resulting filtering system is bilinear in state and linear in observations. The obtained optimal filter for the extended state vector also serves as the optimal identifier for the unknown parameters. Performance of the designed optimal state filter and parameter identifier is verified for both, positive and negative, parameter values.     

Optimal synchronization controller design for complex dynamical networks with unknown system dynamics

In this paper, the optimal synchronization controller design problem for complex dynamical networks with unknown system internal dynamics is studied. A necessary and sufficient condition on the existence of the optimal control minimizing a quadratic performance index is given. The optimal control law consists of a feedback control and a compensated feedforward control, and the feedback control gain can be obtained by solving the well-known Algebraic Riccati Equation (ARE). Especially, in the presence of unknown system dynamics, a novel adaptive iterative algorithm using the information of system states and inputs is proposed to solve the ARE to get the optimal feedback control gain. Finally, a simulation example shows the effectiveness of the theoretical results.     

Finite-time lag synchronization of master-slave complex dynamical networks with unknown signal propagation delays

This paper studies the finite-time lag synchronization issue of master-slave complex networks with unknown signal propagation delays by the linear and adaptive error state feedback approaches. The unknown signal propagation delays are fully considered and estimated by adaptive laws. By designing new Lyapunov functional and discontinuous feedback controllers, which involves the estimated error rather than the general synchronization error, sufficient conditions are derived to ensure lag synchronization of the networks within a setting time. It is interesting to discover that the setting time is related to initial values of both the estimated error and the estimated unknown signal propagation delays. Finally, two numerical examples are given to illustrate the effectiveness and correctness of the proposed finite-time lag synchronization criteria.     

Lr-synchronization and adaptive synchronization of a class of chaotic Lurie systems under perturbations

The synchronous control of a class of disturbed chaotic Lurie systems is probed in. The conception of L_r-synchronization of drive-respond systems is presented. Via Lyapunov function analysis and comparison principle, L_r synchronous controller of the drive-respond systems under perturbation is given and its robustness is also discussed. Barbalat lemma is further used to derive the adaptively synchronous controller for the unknown disturbance situation and the globally asymptotical synchronization is realized. All designed controllers are verified by the simulations and the given controllers are linear, which are convenient and can produce rapid convergence speed of the error systems.