This paper addresses the stabilization problem for neutral bilinear systems with distributed delays in Hilbert spaces. Using the spectral properties of the dynamics operator, we decompose the state space and establish well-posedness for the system. Under a null controllability assumption, we prove stabilizability and derive explicit energy decay estimates. Applications involving hyperbolic and parabolic PDEs with delays are displayed.
Accurate estimation of the state of health (SOH) for lithium-ion batteries is fundamental to ensuring safe operation and performance optimization in battery management systems (BMS). However, the existing SOH estimation methods face significant challenges, including poor generalization, excessive data dependency, and high implementation costs. To address these issues, this paper proposes a novel adaptive moment estimation (Adam) algorithm with a forgetting factor (FF-Adam) for estimating battery SOH. By incorporating an exponential decay mechanism to dynamically adjust the weights of historical gradients, the proposed algorithm enhances noise immunity and convergence rate. Simulation results demonstrate that the FF-Adam algorithm significantly outperforms other optimization algorithms, i.e., batch gradient descent, Adam, and Nesterov-accelerated Adam, providing a more robust solution for intelligent BMS.
The management of mixed traffic flows comprising connected and automated vehicles (CAVs) and human-driven vehicles (HVs) is significantly challenged by their heterogeneous dynamics. This study introduces a novel multilayer complex network framework to address the fixed-time consensus problem in such systems, specifically designed to capture vehicle interactions such as car-following and lane-changing behaviors in multi-lane traffic scenarios. Unlike conventional single-layer models, our approach explicitly structures the traffic into interconnected layers, allowing a more realistic representation of vehicle-to-vehicle influence. We propose a pinning control strategy within this framework and establish a method for estimating the upper bound of the settling time. The efficacy of our approach is rigorously validated using Lyapunov theory and demonstrated through numerical simulations. Results demonstrate the superior performance of our multilayer strategy in accelerating consensus and enhancing traffic flow stability, with greater benefits emerging at higher CAV penetration rates.
This study is devoted to establishing the existence of optimal feedback controls for a class of non-autonomous second-order, damped stochastic neutral impulsive evolution systems formulated within Hilbert spaces. Employing the analytical framework of strongly continuous cosine families in conjunction with Schauder’s fixed-point theorem, stochastic analysis techniques, and the theory of evolution operators, we derive a comprehensive set of sufficient conditions ensuring the existence of mild solutions to the considered class of systems. Building upon these foundational results, we further develop a novel set of structural hypotheses-integrating the Cesari property and Filippov’s theorem to secure the existence of admissible control-state pairs corresponding to the associated Lagrange-type optimal control problem. Finally, a constructed example is provided to demonstrate the practical applicability and robustness of the theoretical findings.
This paper describes a unique approach to the design of a functional H_∞ filter for a class of nonlinear descriptor systems subject to disturbances. To create a broad and applicable framework that encompasses a wide range of systems, this work includes nonlinearities and disturbances in both the state and output equations. Deviating from traditional system regularity assumptions, we adopt a more inclusive approach by considering general descriptor systems that satisfy a rank condition on their coefficient matrices. Within this rank condition framework, we establish sufficient conditions for designing the filter, initially formulated as a bilinear matrix inequality (BMI) and subsequently transformed into a linear matrix inequality (LMI). The resulting filter ensures the asymptotic stability of the estimation error and constrains the ℒ_2 gain from disturbances to errors to a predetermined level. Moreover, the filter is realized in a standard state-space form and can be initialized with arbitrary conditions, significantly simplifying implementation compared with prior descriptor-form filters. Numerical examples are provided to demonstrate the effectiveness of the theoretical results obtained.
