Passivity analysis of coupled neural networks with reaction–diffusion terms and mixed delays

In this paper, we intend to discuss the passivity of coupled neural networks (NNs) with reaction–diffusion terms and mixed delays. By constructing appropriate Lyapunov functional, and with the help of liner matrix inequalities, some inequality techniques, several sufficient conditions are derived to guarantee the output strictly passive, input strictly passive, passive of the proposed neural network model. Then, a stability criterion is presented according to the obtained passivity results. Moreover, the proposed neural network model herein is more general than some recent studies, which can improve and enrich the previous research results. Finally, a numerical example is presented to show the effectiveness of the theoretical criteria.     

Synergetic governing controller design for the hydraulic turbine governing system with complex conduit system

The hydraulic turbine governing system plays an indispensable role in maintaining the stability of electrical power system. In this paper, synergetic control theory is introduced to enhance the regulating ability of the hydraulic turbine governing system. For the purpose of describing the characteristics of objective system and deducing the synergetic control rule, a nonlinear mathematic model of a hydraulic turbine governing system with long tail race and two surge tanks is established. Furthermore, the nonlinear characteristic of the hydraulic turbine is described by six variable partial derivatives. For further investigation, the hydraulic turbine governing system is conducted to running under load condition when its coaxial generator connects to an infinite bus. Simulation experiments have been made under both load disturbance and three-phase short circuit fault conditions to compare the dynamic performances of proposed synergetic governing controller and classic PID controller. The results indicate that the proposed synergetic governing controller is an effective alternative in normal condition and a superior one in emergency. Moreover, the robustness of synergetic governing controller has also been discussed at the end of this paper.     

Optimal control and pattern formation for a haptotaxis model of solid tumor invasion

This paper deal with an optimal control problem for a haptotaxis model of solid tumor invasion by considering the multiple treatments of cancer (a combination of radiotherapy and chemotherapy). Firstly, we obtain the existence and uniqueness of weak solution for the controlled system with spatial dimensions $N=1,2,3$ by applying the Leray–Schauder fixed point theorem and developing adapted a priori estimates. Subsequently, the existence of optimal pair are proved by means of the technique of minimizing sequence. Furthermore, we verify the Lipschitz continuity of control-to-state mapping based on some a priori estimates, hence derive the first-order necessary optimality condition and establish the optimality systems. Finally, the ringlike diffusion and aggregation patterns and the dynamics of tumor invasion as well as the optimal control strategies are presented numerically, which demonstrate that the optimal treatment strategies are capable of breaking the pattern formation, and preventing the tumor invading and metastasizing, even eliminating the tumor possibly. The results of this work improved and extended previous results partially.     

Stochastic consensus of discrete-time second-order multi-agent systems with measurement noises and time delays

We study the consensus control of discrete-time second-order multi-agents systems with time delays and multiplicative noises, where the consensus protocol is designed by both the local relative position measurements and each agent’s absolute velocity. Due to the existence of time delays and multiplicative noises, the classical methods for deterministic models with time delays cannot work. In this paper, we apply stochastic stability theorem of discrete-time stochastic delay equations to find some explicit sufficient conditions for both mean square and almost sure consensus. It is proven that for any given noise intensities and time delays, the second-order multi-agent consensus can be achieved by choosing appropriate control gains in the relative position measurement and absolute velocity, respectively. Numerical simulation is given to demonstrate the effectiveness of the proposed protocols as well as the theoretical results.     

Intermittent control strategy for synchronization of fractional-order neural networks via piecewise Lyapunov function method

In this paper, the synchronization problem of fractional-order neural networks (FNNs) with chaotic dynamics is investigated via the intermittent control strategy. Two types of intermittent control methods, the aperiodic one and the periodic one, are applied to achieve the synchronization of the considered systems. Based on the dynamic characteristics of the intermittent control systems, the piecewise Lyapunov function method is employed to derive the synchronization criteria with less conservatism. The results under the aperiodically intermittent control show more generality than the ones via the periodically intermittent control. For each of the aperiodic and periodic cases, a simple controller design process is presented to show how to design the corresponding intermittent controller. Finally, two numerical examples are provided to demonstrate the effectiveness of the obtained theoretical results.     

Finite-time stabilization of memristor-based inertial neural networks with discontinuous activations and distributed delays

In this paper, the finite-time stabilization problem for memristor-based inertial neural networks (MINNs) with discontinuous activations (DAs) and distributed delays is investigated. To deal with the discontinuous property of the MINNs, the nonsmooth analysis theory is invoked. Furthermore, to simplify the MINNs with second-order state derivative, an order-reduced method is adopted. Then the second-order MINNs is transformed into a simpler first-order differential system. Moreover, the verifiable algebraic criteria are derived for the finite-time stabilization of MINNs with DAs and distributed delays under the designed control approach. Finally, the effectiveness of the obtained results are illustrated via numerical simulations.     

Stability analysis of systems with two additive time-varying delay components via an improved delay interconnection Lyapunov–Krasovskii functional

This paper is concerned with the stability analysis of systems with two additive time-varying delay components in an improved delay interconnection Lyapunov–Krasovskii framework. At first, an augmented vector and some integral terms considering the additive delays information in a new way are introduced to the Lyapunov–Krasovskii functional (LKF), in which the information of the two upper bounds and the relationship between the two upper bounds and the upper bound of the total delay are both fully considered. Then, the obtained stability criterion shows advantage over the existing ones since not only an improved delay interconnection LKF is constructed but also some advanced techniques such as the free-matrix-based integral inequality and extended reciprocally convex matrix inequality are used to estimate the upper bound of the derivative of the proposed LKF. Finally, a numerical example is given to demonstrate the effectiveness and to show the superiority of the proposed method over existing results.     

Chaotification of a class of linear switching systems based on a Shilnikov criterion

This paper proposes an approach for constructing and generating chaos from a class of three-dimensional linear switching systems via a heteroclinic loop based on the Shilnikov criterion. First, the existence of a switching rule for the system is derived by utilizing the Shilnikov heteroclinic criterion. Then a general design philosophy and its procedure of switching rule are provided to ensure that the proposed approach is applicable to engineering. Two numerical examples are presented to validate the main principle and the implementability of the scheme. Theoretical analysis and numerical simulation are used to demonstrate the feasibility and effectiveness of developed techniques.     

Adaptive robust control for planar n-link underactuated manipulator based on radial basis function neural network and online iterative correction method

This paper presents an adaptive robust control strategy based on a radial basis function neural network (RBFNN) and an online iterative correction method (OICM) for a planar n-link underactuated manipulator with a passive first joint to realize its position control objective. An uncertain model of the planar n-link underactuated manipulator is built, which contains the parameter perturbation and the external disturbance. The adaptive robust controllers based on the RBFNN are designed to realize the model reduction, which makes the system reduce to a planar virtual three-link underactuated manipulator (PVTUM) and simplifies the complexity of the system control. An online differential evolution (DE) algorithm is used to calculate the target angles of the PVTUM based on the nominal model parameters. The control of the PVTUM is divided into two stages, and the adaptive robust controllers are still employed to realize the control objective of each stage. Then, the OICM is used to correct the deviations of all link angles of the PVTUM caused by the parameter perturbation, which makes the end-point of the system gradually approach to its target position. Finally, simulation results of a planar four-link underactuated manipulator demonstrate the effectiveness of the proposed adaptive robust control strategy.     

Static group synchronization of second-order multi-agent systems via pinning control

This paper investigates the expected static group synchronization problem of the second-order multi-agent systems via pinning control. For directed communication topology with spanning tree, based on Gershgorin disk theorem and the matrix property, a static pinning control protocol with fixed gains is first introduced and some sufficient and necessary static group synchronization criteria are also established. It is worth mentioning that a rigorous proof is also given that only one pinning node is needed to guarantee static group synchronization, which could be inferred that our protocol might be more economical and effective in large scale of multi-agent systems. Then, for weakly connected directed communication topology with nodes of zero in-degree, an adaptive pinning control applied to the node with zero in-degree is also proposed to achieve static group synchronization. Finally, the efficiency of the proposed protocols is verified by two simulation examples.     

Output feedback based simultaneous stabilization of two Port-controlled Hamiltonian systems with disturbances

In motor system control design, a single controller is usually employed to simultaneously control two or more motors for saving costs, which also achieves the computational simplification of control. In practical Hamiltonian systems control, more systems also need to be stabilized by a single controller under some working conditions. Thus, this paper studies simultaneous stabilization problem of two nonlinear Port-controlled Hamiltonian (PCH) systems with disturbances by a composite controller. Based on the Hamiltonian structure properties, two PCH systems are combined together to generate an augmented PCH system by utilizing output feedbacks firstly. Then, to estimate disturbances effectively, it is essential to design a nonlinear disturbance observer (NDOB) and the estimate is employed to feedforward compensate the effects of disturbances. Next, combining the output feedback part and the disturbance compensation part together, a simultaneous stabilization controller is developed. Subsequently, it is proved that the closed-loop system under the proposed controller is asymptotically stable. Finally, an example with simulations reveals that the proposed method is effective.     

Switching position and range-domain carrier-smoothing-code filtering for GNSS positioning in harsh environments with intermittent satellite deficiencies

Carrier-smoothing-code filtering (CSCF) is widely used in GNSS signal processing to combine code pseudoranges and carrier phases. Position-domain (PD) CSCF is generally more accurate and less sensitive to visible satellite changes than range-domain (RD) CSCF. However, PD-CSCF necessitates at least four visible satellites. Intermittent satellite deficiency with less than four visible satellites is not uncommon in harsh environments like urban canyons. At such deficiency epochs, the PD-CSCF convergence has to break off. This study aims to bridge intermittent deficiency epochs in PD-CSCF without introducing any external information. The proposed solution is called switching RD and PD CSCF in which PD filter is replaced by RD filter at deficiency epochs. Besides detailing the seamless switching algorithms from PD/RD to RD/PD filters, a global RD filter, different from the conventional one, is developed to preserve the correlations among smoothed pseudoranges corresponding to different satellites. Compared to the conventional PD and RD CSCF algorithms, smoother results can be expected from the proposed switching filter, especially after the intermittent deficiency epochs. Experiments are conducted using real BDS signals. Cases with different kinds of deficiency are considered. Superiority of the proposed method is clearly observed from the results.     

Rapid Lyapunov control for decoherence-free subspaces of Markovian open quantum systems

A Lyapunov-based rapid control scheme is proposed to drive a Markovian open quantum system to a decoherence-free subspace by constructing the control Hamiltonians of the system. Based on Lyapunov theory, we design a general form of control laws, which includes the standard Lyapunov control law. The convergence of the control system to the decoherence-free subspace is strictly proved. By analyzing the relationship between the LaSalle invariant set and the decoherence-free subspace, we propose a construction method for the control Hamiltonians to further speed up the control process. Simulation experiments on a three-level quantum system demonstrate that the rapid Lyapunov control scheme proposed in this paper has a good control performance.     

Finite-time control for periodic systems with Markov jump sensor nonlinearities and random input gains

Finite-time control for periodic systems with sensor nonlinearities and random input gains is addressed in this work. The variation of sensor nonlinearities is modeled by a Markov chain, and a stochastic variable is used to describe the influence of the actuator. A mode- and sensor nonlinearity-dependent non-fragile controller is designed to improve the performance and the non-fragility of the controller. The finite-time boundedness of the closed-loop system is ensured by a sufficient condition, the corresponding controller is then designed. Finally, the effectiveness of the developed results is illustrated by a numerical example.     

Synchronization of coupled heterogeneous complex networks

By only designing the internal coupling, quasi synchronization of heterogeneous complex networks coupled by N nonidentical Duffing-type oscillators without any external controller is investigated in this paper. To achieve quasi synchronization, the average of states of all nodes is designed as the virtual target. Heterogeneous complex networks with two kinds of nonlinear node dynamics are analyzed firstly. Some sufficient conditions on quasi synchronization are obtained without designing any external controller. Quasi synchronization means that the states of all nonidentical nodes will keep a bounded error with the virtual target. Then the heterogeneous complex network with impulsive coupling which means the network only has coupling at some discrete impulsive instants, is further discussed. Some sufficient conditions on heterogeneous complex network with impulsive coupling are derived. Based on these results, heterogeneous complex network can still reach quasi synchronization even if its nodes are only coupled at discrete impulsive instants. Finally, two examples are provided to verify the theoretical results.     

Consensus analysis for multi-agent systems via periodic event-triggered algorithms with quantized information

In this article, a novel distributed event-triggered control protocol for the consensus of second-order multi-agent systems with undirected topology is studied. Based on the proposed control protocol, the event-triggered condition is evaluated only at every sampling instant. The control input for each agent will be updated with local information if and only if its condition is violated. Both ideal and quantized relative state measurements are considered under this framework. Some sufficient conditions for achieving consensus are derived using spectral properties of edge Laplacian matrix and the discrete-time Lyapunov function method. Finally, numerical examples are given to demonstrate the effectiveness of our theoretical results.     

Non-fragile control of positive Markovian jump systems

This paper investigates the non-fragile control for positive Markovian jump systems both in continuous-time and discrete-time cases with actuator uncertainty. It is assumed that the coefficient matrices of the non-fragile controller is unknown and bounded. The state-feedback controller gain consists of nominal controller gain and gain perturbation. First, a set of state-feedback controllers for the considered system are designed by using a stochastic co-positive Lyapunov function integrated with linear programming approach. Under the designed controllers, the resulting closed-loop systems are positive and stochastically stable. Then, the proposed controller design approach is extended to discrete-time systems. Through comparisons, it is shown that existing results are special cases of the presented ones in the paper. Finally, two examples are given to illustrate the effectiveness of the proposed design.     

Distributed sensor fault diagnosis for a formation of multi-vehicle systems

In the paper, a distributed sensor fault detection and isolation scheme is presented for a network of second-order integrators. A new distributed control law is developed to achieve formation of the system. By using the integration information of distributed formation errors, the control law improves the robustness of the formation. A distributed observer is then designed in each vehicle based on the closed-loop dynamic model of the vehicle. Each vehicle updates the states of the distributed observer by employing the measurements of itself and the transmitted state estimations from its neighbors. Based on the distributed observer, a distributed fault detection observer and a distributed fault isolation observer are designed. The presented distributed fault detection observer in each vehicle is able to be sensitive to the faults of all vehicles in the system. By using the distributed fault isolation observers, each vehicle is able to be sensitive to the faults of itself, its neighbors and its neighbors’ neighbors and to be robust to the faults of other vehicles. Although the fault isolation of the proposed scheme is simple, computation loads of the scheme are lower than the current ones since only the model of the individual vehicle is used. Finally, the effectiveness of the control law and the fault diagnosis scheme is demonstrated by simulations and real-time experiments carried out based on a formation of three quadrotors.     

Mechanical analysis and ultimate boundary estimation of the chaotic permanent magnet synchronous motor

In this paper, we present the dimensionless form of a chaotic permanent magnet synchronous motor (PMSM). Its Kolmogorov formalism, which can be used to describe dissipative-forced dynamical systems, shows that there exist four types of torques, i.e., inertial torque, internal torque, dissipative torque and external torque. The mechanical analysis of the dimensionless PMSM is given for five different combinations of these torques. Numerical simulations show that the occurrence of chaos depends on these four types of torques. Moreover, the ultimate boundary estimation of the dimensionless chaotic PMSM is also investigated theoretically and numerically.     

Necessary conditions of exponential stability for a class of linear uncertain systems with a single constant delay

In this paper, we will investigate the necessary conditions, described by the Lyapunov matrix, for the robust exponential stability for a class of linear uncertain systems with a single constant delay and time-invariant parametric uncertainties, which are some generalizations of the existing results on uncertain linear time-delay systems. As a medium step, several pivotal properties of parameter-dependent Lyapunov matrix are proposed, which set up the relationships between fundamental matrix and Lyapunov matrix for the considered system. In addition, to calculate the parameter-dependent Lyapunov matrix, we introduce the differential equation method and the Lagrange interpolation method, respectively. Furthermore, it is noted that the proposed necessary conditions can be used to estimate the range of time delay, when the linear uncertain time-delay system is robust exponential stability. Finally, the validity of the obtained theoretical results is illustrated via numerical examples.