In response to the challenges encountered in high-throughput resilience assessment of zonal ship central cooling systems, including numerical stiffness in physics-based dynamic models, abnormal solver termination, and insufficient continuity in batch simulation campaigns, a physics-informed co-simulation framework for resilience-oriented assessment is proposed. With control–physics orthogonal decoupling as its core, the framework separates the control-scheduling layer from the thermo-hydraulic solver at the software-execution level, while retaining information exchange through standardized interfaces. In addition, physics constraint-based pre-filtering, process-level fault isolation, and automatic recovery mechanisms are integrated to improve the robustness and continuity of automated batch assessment. A hierarchical reduced-order thermo-hydraulic model of the zonal ship central cooling system is established. Subsequently, the numerical stiffness characteristics of the fluid network and heat-transfer units under valve topology switching conditions are analyzed. A standalone C++ solver kernel is generated from a Simulink prototype model, and a Java/Web-based collaborative scheduling platform is constructed. Cross-environment consistency tests show that the C++ solver reproduces the Simulink prototype results under representative fast hydraulic and slow thermal scenarios, with steady-state and transient discrepancies below 0.05% and 1.08%, respectively. Physics constraint-based pre-filtering intercepted 42.6% of infeasible samples and reduced the total wall-clock runtime of the tested optimization task by approximately 38%. In 1000 fault-injection tests, the process-isolation mechanism isolated 12 abnormal solver terminations, while the main scheduling process remained alive and the remaining batch tasks were completed under the tested conditions. Finally, an abrupt pulse thermal-load increase in the forward zone was used as a representative scenario to demonstrate automatic extraction of temperature trajectories and quantitative evaluation using the cumulative temperature-exceedance severity (CTS) index. The results indicate that the proposed framework can support offline resilience-oriented assessment, reconfiguration-strategy screening, and batch evaluation of shipboard fluid–thermal systems under the tested conditions.

Extended state observers (ESOs) are usually tuned in continuous time and then transferred to sampled implementations, where the poles that the running code actually places, and the resulting noise sensitivity, can differ from the values the design intended. This paper examines a third-order ESO that combines exact zero-order-hold state prediction with a bandwidth-parameterized innovation gain vector. Its characteristic polynomial differs from the intended triple-pole polynomial by a defect proportional to the third gain, and the resulting spectral radius returns toward 1 as the requested bandwidth increases, although the observer remains Schur stable at every positive bandwidth. Matching the characteristic polynomial term by term gives a corrected gain vector that places all three poles at the intended location for the same update timing. When the disturbance varies from sample to sample, its increment enters the extended state through a specific input channel, and the resulting estimation lag depends on bandwidth. We then separate three noise measures that are often used interchangeably: the white-noise variance factor, the unit-impulse peak, and the induced gain for bounded input. A closed-loop simulation confirms that the spectral-radius rebound is a genuine disturbance rejection penalty: at high bandwidth the examined estimate alternates in sign from sample to sample, whereas the corrected design stays monotone. Finally, a JONSWAP (Joint North Sea Wave Project) case study uses the physically consistent spectral moment and log-uniform importance weights, and the corrected estimator is unbiased for the band-limited spectral moment that carries almost all of the physical spectral mass in the band used here. All numerical results are produced by a documented Python workflow that is released as an open repository.

This paper studies three computational kernels of a digital-twin prototype for USV formations—a cyclic Jacobi routine for algebraic connectivity, a connectivity-driven formation-gain scheduler, and a hysteretic topology selector—verified through kernel-level spectral checks, frozen-topology linear consensus, and graph-level switching and fault analysis. First, the Jacobi routine’s ${45}^{\circ }$ equal-diagonal rotation matches symmetric eigensolutions on star, complete, and implementation-specific graphs of order 3–13 to $1.60\times {10}^{-14}$. Second, for a frozen connected graph of m vessels, the scheduled gain $k\left({\lambda }_2\right)=\mathrm{clamp}(m/{\lambda }_2,0.5,4)$ yields $k{\lambda }_2=\min \{m,4{\lambda }_2\}$, hence $m/8\le k{\lambda }_2\le m$ on ${\lambda }_2\in [m/32,m]$. Third, with M constant-utility candidates and bounded observation noise, $2\sigma <\Delta U$ makes every accepted switch a strict ascent, permitting at most $M-1$ switches. Fourth, an isolation fault, via distinct full-diagnostic and online graphs, leaves a seven-vessel complete graph with ${\lambda }_2=0$, while a re-elected star on six online vessels recovers ${\lambda }_2=1$ and $1.667$ versus $5.000$ messages per agent. Finally, a scalar ADRC stress test and its multi-agent extension show estimation-based rejection (∼$7.5\times$) and gain re-scheduling (∼$4.1\times$) act independently for a combined ∼$31\times$ reduction in steady-state disagreement, with a switched-loop corollary bounding disagreement under finitely many switches at the frozen-topology rate. New experiments close the loop end-to-end: an integrated hysteresis–scheduling–ADRC loop holds the observer factor near $8\times$ across a star → mesh → star reconfiguration, hub-fault recovery gives a $10\times$ lower peak and $1.6\times$ faster settling than PD, and the rejection advantage holds at matched feedback authority, with the accuracy–effort trade-off against PD and LQR baselines quantified explicitly; the switched-loop corollary is stated for the full state (disagreement, relative velocities, observer errors) at rate $\min \{\mu ,{\omega }_0\}$ consistent with the observer’s response speed.

Distributed model predictive control (MPC) coordinates constrained multi-agent systems while preserving computational locality, yet an implementation can cease to represent its stated convex program. We study a minimal linear plant so communication denial is a modeled source of uncertainty, and treat centralized equivalence as a hard gate: an edge-splitting consensus alternating direction method of multipliers (ADMM) formulation of the formation-tracking quadratic program is built so every distributed update can be audited against a centralized solver. Against a Lagrangian dual-decomposition baseline, ADMM attains the same accuracy without step-size tuning. Across topologies, horizons, penalties, budgets, and denial windows, the exact branch matches the centralized optimum to numerical precision, the equivalence gate and saturation signature survive scaling to eight agents, and the saturation signature also survives measurement noise. For communication denial, we prove a bounded-error result separating the summable-error regime, which recovers the optimum exactly, from the merely-bounded regime, whose limit points remain O(ε)-optimal. Coupling each edge weight to message age through an exponentially decaying confidence factor contracts the distributed problem to uncoupled local MPC, so formation error saturates as outages lengthen; a fixed-weight ablation isolates this decay as the causal mechanism. We contribute a reproducible baseline and two honest mechanisms—centralized-equivalence gating and confidence-decayed coupling—for distributed formation MPC.