This article investigates the practically predefined-time stabilization issue of fuzzy memristive neural networks (FMNNs) in the presence of stochastic disturbances and random deception attacks (RDAs). First, in this article, the concept of practically predefined-time stabilization in probability (PPDTSP) of FMNNs is introduced, and a novel Lyapunov-type criterion for PPDTSP is proposed. The novel criterion eases the restrictions on the differential operator of the Lyapunov function and can be reduced to the existing criterion of predefined-time stabilization in probability (PDTSP). Then, a simplified, practically predefined-time control scheme is constructed to ensure PPDTSP of FMNNs under the interference of stochastic disturbances and RDAs. Furthermore, by employing the simplified control scheme and in the absence of RDAs, some PDTSP results are presented as special instances of the PPDTSP conclusions given in this article. Finally, numerical simulations are conducted to validate the accuracy of the theoretical results.

This work is concerned with mean-square bipartite containment of second-order multileader multiagent systems (MASs), contaminating compound noise, and antagonistic information under a fixed or Markovian switching signed topology. A new class of bipartite containment control protocols based on absolute velocity and relative position information is designed using signed graphs, and a time-varying control gain is introduced to eliminate the combined effect of additive and multiplicative noises. For the case under fixed topology, sufficient conditions for achieving bipartite containment are derived by using the Lyapunov function method. Then, it is extended to the case of nonlinear dynamics. Specific convergence values for all leaders and followers are obtained. For the case under Markovian switching topology, the boundedness of the agents' states and noise intensity is proved by employing the extended second-moment method. By utilizing properties of stochastic matrices and the ergodicity of Markov chains, the second moments of the bipartite containment errors are estimated to obtain mean-square bipartite containment conditions. In addition, the corresponding convergence rates of mean-square errors are explicitly expressed. The effectiveness of the theoretical results is finally verified through numerical simulations.

The existing group formation-containment (GFC) studies for multi-agent systems (MASs) depend on system model information and generally neglect input saturation constraint, thereby limiting their applicability to MASs with unknown system model and input saturation. This paper investigates the data-driven GFC control problem of nonlinear MASs with asymmetric input saturation. First, a novel communication topology selection algorithm with relaxed topology conditions is proposed. Then, to tackle the challenge posed by asymmetric input saturation, a novel nonquadratic performance index function with a simplified formulation is designed and the corresponding Hamilton-Jacobi-Bellman equation is derived. On this basis, an effective value iteration algorithm is proposed to determine the optimal GFC control policy, accompanied by the rigorous mathematical analysis. By establishing the critic-actor framework based on generalized fuzzy hyperbolic model, a novel data-driven algorithm is proposed to achieve GFC under asymmetric input saturation, which overcomes the dependence on system model. Finally, some simulation results are provided to verify the effectiveness and superiority of the proposed data-driven GFC algorithm.

Industrial circuit systems are subject to significant information uncertainties, such as noise, incomplete state measurements, unknown loads, and lumped disturbances, which can jeopardize stability and safety. This article addresses these challenges in stochastic port-Hamiltonian systems (SPHSs) through novel control strategies. A reduced-order observer, formulated via linear matrix inequalities, is developed to observe system states when complete measurements are unavailable. We prove that the observation error converges to zero both in almost sure and mean square senses. For SPHS with lumped disturbances, a disturbance observer enables feedforward compensation by observing unknown disturbances. In addition, tunable estimators are proposed to identify constant but unknown loads, with performance optimized through function selection. Furthermore, based on stochastic versions of LaSalle’s invariance principle and Barbalat’s lemma, we prove that a SPHS which is passive under constant control is also stabilizable via proportional–integral control. The efficacy of the proposed methods is demonstrated through circuit simulation examples, confirming their applicability in mitigating information uncertainties in industrial environments.

This article explores the optimal containment control of discrete-time multiagent systems (MASs) with the digraph and unknown dynamics under process disturbances. We first demonstrate, through a model transformation, that the mean square bounded containment of MASs can be achieved by guaranteeing the mean square boundedness of the containment error systems. Hence, we can transform the optimal stochastic containment control problem of MASs into a stochastic optimal control problem for containment error systems. Subsequently, utilizing the Bellman optimality principle and the stochastic Lyapunov equation (SLE), we design a model-based policy iteration (PI) algorithm for the optimal stochastic containment control of MASs. This model-based algorithm, by minimizing the cost function in linear quadratic form, enables MASs to achieve mean square bounded containment with the least possible energy input. To circumvent the dependency on the model information, we introduce an online model-free algorithm for the stochastic optimal control problem. The model-free algorithm is developed based on the Q-learning algorithm. Specifically, it uses a historical MAS trajectory to estimate the kernel matrixHof theQfunction, enabling the resolution of the optimal stochastic containment control problem without model information. To realize the model-free algorithm, the LSTD estimator with bounded bias is employed in the policy evaluation step. We prove the equivalence between the model-free algorithm and the model-based algorithm. Finally, a numerical case is presented to demonstrate the efficacy of the proposed algorithms in achieving the optimal stochastic containment control of MASs.

This article investigates the tracking control problem of heterogeneous multiagent systems (MASs) with intrinsic nonlinear dynamics in noisy and time-delayed environments. First, a stability criterion for nonlinear stochastic delay systems with multiplicative noise and time-varying delay is proposed by applying the appropriate Lyapunov-Krasovskii functional. Then, based on the proposed stability criterion, sufficient conditions are derived for mean square (m.s.) and almost sure (a.s.) tracking of heterogeneous MASs with intrinsic nonlinear dynamics. Afterward, the above sufficient conditions further degenerate to integrator heterogeneous MASs. In particular, when the time-delay vanishes, the explicit conditions are obtained for the integrator heterogeneous MASs in the form of scalar inequalities, which can intuitively reflect the relationship between noise intensity and control gains. Finally, simulation results validate the effectiveness of the proposed control protocol.

This paper is concerned with the mean square and almost sure bipartite containment of multi-leader multi-agent systems with antagonistic information and measurement noise. By designing the modified time-varying bipartite containment protocol, the weak conditions are investigated under signed graph. For the case with additive noise, the sufficient and necessary conditions for stochastic bipartite containment are obtained by employing the semidecoupled method, the law of the iterated logarithm for martingales, and the variation of constants formula. For the case with multiplicative noise, a Lyapunov-based method and semimartingale convergence theorem are used to obtain the sufficient conditions for stochastic bipartite containment. This paper shows that the states of followers will finally converge to the deterministic constant formed by leaders’ states. The effectiveness of the theoretical results is verified through numerical simulations.

The classical results of fixed-time stabilization (FxTS) are generally achieved via nonintermittent control, as well as cannot be employed to deal with discontinuous systems and strictly intermittent control. In this article, we establish a novel FxTS method for analyzing fixed-time convergence and newly develop a strictly intermittent control scheme to stabilize discontinuous systems within a fixed time based on it. The presented method can also be used to effectively estimate the settling time and to simultaneously reveal how the control period, control width, and control gain affect the convergence time of the controlled system. Additionally, we also extend the proposed FxTS method and use it to design a new strictly intermittent control scheme for achieving the preassigned-time stabilization (PaTS) of discontinuous systems. Finally, an example of Chua’s circuit is provided to illustrate the feasibility and applicability of the established FxTS and PaTS methods.

The online small-signal stability assessment of electrical power grids is typically a challenging problem due to uncertainties and parameter variations of power system dynamics as well as the incurred high computational complexity. This paper proposes a novel theoretical framework for dynamic small-signal stability assessment of power grids by estimating the region of attraction (ROA) for operating states in real time. By analyzing the latest sampling data of power grids in a fixed time window, an up-to-date training set is constructed with the aid of converse Lyapunov function, which enables us to develop an online learning approach based on Gaussian Process (GP) to assess the stability level of power grids. As a result, an iteration algorithm is designed to update the assessment parameters by learning the input-output pairs in the training set. Theoretical analysis is conducted to ensure the existence of converse Lyapunov function for differential-algebraic system that serves to describe power system dynamics, as well as to estimate the region of attraction for operating states with a given confidence level. In particular, a practical method is proposed to leverage time series of phasor measurement unit (PMU) measurements including voltage/current magnitude, phase and frequency (i.e., PMU data) of real power grids for validating the online GP approach. Moreover, validations are taken to substantiate the proposed approach by using PMU data of real smart-grid infrastructure and IEEE test cases. The proposed assessment approach contributes to situational awareness of human operators in the control station, thereby taking proactive remedial actions prior to emergencies. Note to Practitioners—This paper was motivated by the problem of online assessment of power systems security but it also applies to other industrial control systems that have stable state trajectories. Existing approaches to security assessment of power systems generally focus on the adoption of various machine-learning algorithms by treating power grid as a “black box,” which ignores the intrinsic characteristics of power systems and thus restricts the inference performance. This paper proposes a new approach using limited sampling data and system dynamics to construct a domain of stability for power grids, which can reflect the evolution of security zones and provide more accurate predictions. In this work, we mathematically characterize the domain of stability for a practical power grid by analyzing and learning its state trajectories. Then we show how the proposed approach can be efficiently implemented online, which can timely alert human operators to abnormalities. Preliminary validations suggest that this approach is feasible and effective. In future research, we will incorporate it into an energy management system and test it in other industrial processes.