This paper studies the robust stabilization of 2 $\times$ 2 linear hyperbolic partial differential equations (PDEs) with Markov-jumping parameters and boundary input delay. The main challenge arises from the simultaneous presence of stochastic parameter variations and input delay, which complicates both the stability analysis and controller design. To address this issue, a nominal delay-compensating backstepping controller is first designed for a fixed nominal system. Applying the nominal transformation to the stochastic system yields a target system with additional perturbation terms induced by parameter mismatch. A mode-independent Lyapunov functional is then constructed to establish a pathwise exponential estimate, which directly implies mean-square exponential stability under an explicit small-mismatch condition. The proposed analysis provides a direct robustness certificate for nominal delay compensation without using mode-dependent Lyapunov functionals. Finally, we present simulation results and discuss how the conservative small-mismatch condition should be interpreted for the numerical example.
The rapid expansion of offshore wind energy is central to the European Union's climate-neutrality targets, with High Voltage Direct Current-connected offshore wind power plants (HVDC-OWPPs) becoming increasingly important for integrating gigawatt-scale renewable generation over l…
Motion planning algorithms compute control sequences that drive autonomous robots to goal regions while avoiding unsafe states. Existing methods, from sampling-based planning to deep reinforcement learning, typically provide task-completion guarantees only with respect to a nomin…
This letter proposes the Predictive Lightweight Multi-Agent Reinforcement Learning (PL-MARL) framework to ensure resilient coverage in bandwidth-constrained UAV swarms. To counter coordination collapse caused by sparse signaling and information aging, we introduce a Kinematic-Awa…
This paper investigates physics-informed neural networks for modeling the full dynamic behavior of droop-controlled grid-forming converters. The approach is trained on synthetic data generated via numerical solvers and benchmarked against both traditional integration methods and…
This paper introduces a novel multivariate Transformer \emph{StateFormer} that forecasts degradation dynamics of large-scale battery systems. The model learns across time scales, from short-term thermal fluctuations to long-term aging trajectories, enabling accurate prediction of…
We introduce trajectory-regularized stochastic optimal control (TRSOC), which augments standard stochastic optimal control (SOC) with a Kullback--Leibler (KL) divergence between controlled and reference trajectory distributions. Using Girsanov's theorem, the trajectory KL reduces…