Prognostics and health management (PHM) is an emerging engineering discipline that diagnoses and predicts how an engineered system will degrade its performance and when it will lose its partial or whole functionality. With monitored parameters from the system and observations from its operating conditions, PHM can significantly enhance the reliability, availability, and predictability of the system. In this dissertation, contributions have been made to address the challenges of PHM for complex dynamic systems applied to lithium-ion batteries, as outlined in the following three major research thrusts:

• Adaptive Dynamic System Modeling for PHM: in this thrust, a new self-cognizant dynamic system (SCDS) approach has been developed to address the challenge of dynamic system modeling considering the deterioration of system performance over time so that system inherent parameters can be accurately identified and system health states can be assessed. The SCDS approach has been applied to battery health management and also generalized for PHM of general complex dynamics systems.
• Lithium-Plating Diagnosis: In this thrust, a novel internal state variable (SV) mapping approach has been developed to address the challenging of diagnosing lithium-plating with only operational measurements such as voltage and current information.
• Lithium-Plating prognosis: In this thrust, a multi-scale filtering technique is developed based on the ISV mapping approach for the remaining useful life prediction of lithium-plating induced battery system failures. This dissertation consists of four journal articles that have been either published or submitted for publication in chapters two to five, whereas chapter one provides an overview of the research background and chapter six summarizes the dissertation with conclusions and future work.