This paper develops an adaptive PDE observer for battery state-of-charge (SOC) and state-of-health (SOH) estimation. Real-time state and parameter information enables operation near physical limits without compromising durability, thereby unlocking the full potential of battery energy storage. SOC/SOH estimation is technically challenging because battery dynamics are governed by electrochemical principles, mathematically modeled by partial differential equations (PDEs). Simultaneous state and parameter estimation is extremely challenging in PDE models. Consequently, several new theoretical ideas are developed, integrated together, and tested. These include a backstepping PDE state estimator, a Padé-based parameter identifier, nonlinear parameter sensitivity analysis, and adaptive inversion of nonlinear output functions. The end result is the first combined SOC/SOH battery estimation algorithm that identifies physical system variables via an electrochemical model, from measurements of voltage and current only.

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