Accurate state estimation in nonlinear dynamical systems remains critical for modern energy infrastructure, especially when direct measurements are unavailable or prohibitively expensive. A new framework combining Koopman operator theory with Luenberger observer design offers a practical solution for monitoring systems where internal conditions cannot be directly sensed.
The approach lifts nonlinear dynamics into a higher-dimensional space using physics-informed basis functions, where linear observer techniques can be applied. Extended dynamic mode decomposition with control identifies a linear predictor, and a discrete-time Luenberger observer is then synthesized. The observer gain is computed via dual linear-quadratic regulator formulation to ensure stable and tunable estimation error dynamics.
The research demonstrates this framework on latent thermal energy storage systems based on phase-change materials—increasingly important for grid-scale energy storage and building thermal management. Phase-change materials absorb and release significant heat energy during state transitions, but internal temperature monitoring is difficult in practical deployments. The observer successfully reconstructs these unmeasured internal temperatures from limited external measurements.
Experimental validation under varying operating conditions achieved reconstruction errors below 0.08°C for outlet temperatures and generally under 1.0°C for internal PCM temperatures. This accuracy level is sufficient for effective system control and performance optimization.
The method's computational efficiency and reliance only on external measurements make it deployable across existing thermal storage installations without retrofitting. This has direct applications for demand response strategies, renewable energy integration, and thermal load shifting on modern grids. As thermal energy storage gains prominence alongside battery systems for grid support, reliable state estimation without extensive instrumentation reduces capital costs and operational complexity. The framework could extend to other nonlinear energy systems requiring monitoring under sparse sensing constraints.
