A matrix-based approach to verifying stability and synthesizing optimal stabilizing controllers for finite-state automata

In this paper, we develop a matrix-based methodology to investigate the problems of stability and stabilizability for a deterministic finite automaton (DFA) in the framework of the semi-tensor product (STP) of matrices. First, we discuss the equilibrium point stability (resp., set stability) of a DFA, i.e., verifying whether or not all state trajectories starting from a subset of states converge to a specified equilibrium point (resp., subset of states). The necessary and sufficient conditions for verifying both stabilities are given, respectively. Second, equilibrium point stabilizability (resp., set stabilizability) of a DFA is investigated as verifying the issue of whether or not a DFA can be globally or locally stabilized to a specified equilibrium point (resp., subset of states) by a permissible state-feedback controller. Based on the pre-reachability set and invariant-subset defined in this paper, the matrix-based criteria for verifying equilibrium point stabilizability and set stabilizability are derived, respectively. Furthermore, for each type of stabilizability, all permissible state-feedback controllers for the case of minimal length state trajectories, called optimal state-feedback controllers, are characterized by using the proposed polynomial algorithms. Finally, two examples are presented to illustrate the effectiveness of the theoretical results.     

Chaos control of the permanent magnet synchronous motor with time-varying delay by using adaptive sliding mode control based on DSC

This paper focuses on the problem of chaos control for the permanent magnet synchronous motor with chaotic oscillation, unknown dynamics and time-varying delay by using adaptive sliding mode control based on dynamic surface control. To reveal the mechanism of motor system and facilitate controller design, the dynamic behavior of the system is investigated. Nonlinear items of system model, upper bounds of time delays and their derivatives are taken as unknown in the overall process. A RBF neural network with an adaptive law, which eliminates restrictions on accurate model and parameters, is employed to cope with unknown dynamics. In order to solve issues such as chaotic oscillation, ‘explosion of complexity’ of backstepping, and chattering associated with sliding mode control, a sliding mode controller is developed within the framework of dynamic surface control by the hybrid of adaptive technology and RBF neural network. In addition, an appropriate Lyapunov function is employed to demonstrate the system stability. Finally, the feasibility of the proposed scheme is testified by simulation.     

Output formation-containment of coupled heterogeneous linear systems under intermittent communication

This paper investigates the output formation-containment problem of the coupled heterogeneous linear systems under intermittent communication. The systems considered in this paper are more general in the sense that each system, whether a leader or a follower, has different dimension and different dynamic. Besides, each system only communicates with its neighbors intermittently. Based on the intermittent information, both the state-feedback and the output-feedback distributed control protocols are designed and a criterion is derived to calculate the lower bound of the communication ratio. Furthermore, a heuristic algorithm based on the Fireworks Algorithm is developed to obtain an optimized communication ratio, which greatly reduces the communication burden. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical 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.     

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.     

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.     

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.     

Extended evidential cognitive maps and its applications

Evidential cognitive maps (ECMs) are uncertain graph structure for describing causal reasoning through the cognitive maps (CMs) and Dempster–Shafer (D-S) theory, and utilize the basic probability assignments (BPAs) and intervals to denote connections among concepts and the state of concepts, respectively. ECMs have been proved effective and convenient in modeling those systems with both subjective and objective uncertainty. However, ECMs may get unreasonable results in system modeling when facing the problem of combining knowledge. To overcome the drawbacks of ECMs, we present extended evidential cognitive maps (EECMs) based on evidential reasoning (ER) theory, distance measure and convex optimization for the development of ECMs. In contrast with ECMs, in the EECMs, the default connections are redefined, a scheme of combining knowledge is established through the ER theory, and a convex-optimization-based approach is proposed for determining the weights of different EECMs. Both theoretical analysis and numerical examples indicate that EECMs not only develop ECMs, but also can overcome the limitations suffered by ECMs and other high-order cognitive maps including fuzzy grey cognitive maps (FGCMs), interval-valued fuzzy cognitive maps (IVFCMs) and intuitionistic fuzzy cognitive maps (IFCMs).     

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.     

Solving future equation systems using integral-type error function and using twice ZNN formula with disturbances suppressed

In this paper, for solving future equation systems, two novel discrete-time advanced zeroing neural network models are proposed, analyzed and investigated. First of all, by using integral-type error function and twice zeroing neural network (or termed, Zhang neural network) formula, as the preliminaries and bases of future problems solving, two continuous-time advanced zeroing neural network models are presented for solving continuous time-variant equation systems. Secondly, a one-step-ahead numerical differentiation rule termed 5-instant discretization formula is presented for the first-order derivative approximation with higher computational precision. By exploiting the presented 5-instant discretization formula to discretize the continuous-time advanced zeroing neural network models, two novel discrete-time advanced zeroing neural network models are proposed. Theoretical analyses on the convergence and precision of the discrete-time advanced zeroing neural network models are proposed. In addition, in the presence of disturbance, the proposed discrete-time advanced zeroing neural network models still possess excellent performance. Comparative numerical experimental results further substantiate the efficacy and superiority of the proposed discrete-time advanced zeroing neural network models for solving the future equation systems.     

Generalized lag synchronization of multiple weighted complex networks with and without time delay

The generalized lag synchronization of multiple weighted complex dynamical networks with fixed and adaptive couplings is investigated in this paper, respectively. By designing appropriate controller, several synchronization criteria are presented for multiple weighted complex dynamical networks with and without time delay based on the selected Lyapunov functional and inequality techniques. Moreover, an adaptive scheme to update the coupling weights is also developed for ensuring the generalized lag synchronization of multiple weighted complex dynamical networks with and without time delay. Finally, two numerical examples are provided in order to validate effectiveness of the proposed generalized lag synchronization criteria.     

Orbit consensus of quantum networks based on interaction design

For a general quantum network system with a non-zero Hamiltonian H composed of n identical m-level quantum subsystems, any symmetric consensus state in the interaction picture exactly corresponds to an orbit in the Schrödinger picture, which is called the H-orbit of the symmetric consensus state. By using the interaction picture transformation and the tool of the LaSalle invariance principle, this paper analyzes the orbit consensus of this quantum network and designs the corresponding swapping operators such that the system converges to the H-orbit of the target symmetric consensus state that exists in the interaction picture. In particular, we prove the convergence of the quantum network to the H-orbit when the quantum interaction graph is connected and the system Hamiltonian is permutation invariant. The orbit consensuses of a four-qubit network system and a quantum network of three identical three-level subsystems are achieved numerically, which verifies the correctness of our theoretical results and the effectiveness of the designed swapping operators.     

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.     

Multi-lagged-input iterative dynamic linearization based data-driven adaptive iterative learning control

This article presents a multi-lagged-input based data-driven adaptive iterative learning control (M-DDAILC) method for nonlinear multiple-input-multiple-output (MIMO) systems by virtue of multi-lagged-input iterative dynamic linearization (IDL). The original nonlinear and non-affine MIMO system is equivalently transformed into a linear input-output incremental counterpart without loss of dynamics. The proposed learning law utilizes the desired trajectory to cancel the influence from iteration-by-iteration variations, as well as additional multi-lagged inputs to improve control performance. The developed iterative estimation law is more effective and also makes estimation of the unknown parameters easier because the dynamics for each parameter to represent are decreased by dividing the system into multiple components in the multi-lagged-input IDL formulation. Moreover, the proposed M-DDAILC does not need an explicit and accurate model. It is proved to be iteratively convergent with rigorous analysis. Both a numerical example and a practical application to a permanent magnet linear motor are provided to verify the validity and applicability of the proposed method.     

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 jamming attack schedule for remote state estimation with two sensors

In cyber-physical systems (CPS), cyber threats emerge in many ways which can cause significant destruction to the system operation. In wireless CPS, adversaries can block the communications of useful information by channel jamming, incurring the so-called denial of service (DoS) attacks. In this paper, we investigate the problem of optimal jamming attack scheduling against remote state estimation wireless network. Specifically, we consider that two wireless sensors report data to a remote estimator through two wireless communication channels lying in two unoverlapping frequency bands, respectively. Meanwhile, an adversary can select one and only one channel at a time to execute jamming attack. We prove that the optimal attack schedule is continuously launching attack on one channel determined based on the system dynamics matrix. The theoretical results are validated by numerical simulations.     

Quantitative mean square exponential stability and stabilization of stochastic systems with Markovian switching

This paper is concerned with the quantitative mean square exponential stability and stabilization for stochastic systems with Markovian switching. First, the concept of quantitative mean square exponential stability(QMSES) is introduced, and two stability criteria are derived. Then, based on an auxiliary definition of general finite-time mean square stability(GFTMSS), the relations among QMSES, GFTMSS and finite time stochastic stability (FTSS) are obtained. Subsequently, QMSE-stabilization is investigated and several new sufficient conditions for the existence of the state and observer-based controllers are provided by means of linear matrix inequalities. An algorithm is given to achieve the relation between the minimum states’ upper bound and the states’ decay velocity. Finally, a numerical example is utilized to show the merit of the proposed results.