The purpose of this paper is twofold. In the first part, we give a review on the current state of nonlinear model predictive control (NMPC). After a brief presentation of the basic principle of predictive control we outline some of the theoretical, computational, and implemen-tational aspects of this control strategy. Most of the theoretical developments in the area of NMPC are based on the assumption that the full state is available for measurement, an assumption that does not hold in the typical practical case. Thus, in the second part of this paper we focus on the output feedback problem in NMPC. After a brief overview on existing output feedback NMPC approaches we derive conditions that guarantee stability of the closed-loop if an NMPC state feedback controller is used together with a full state observer for the recovery of the system state.

Batteries are the key technology for enabling further mobile electrification and energy storage. Accurate prediction of the state of the battery is needed not only for safety reasons, but also for better utilization of the battery. In this work we present a state estimation strategy for a detailed electrochemical model of a lithium-ion battery. The benefit of using a detailed model is the additional information obtained about the battery, such as accurate estimates of the internal temperature, the state of charge within the individual electrodes, overpotential, concentration and current distribution across the electrodes, which can be utilized for safety and optimal operation. Based on physical insight, we propose an output error injection observer based on a reduced set of partial differential-algebraic equations. This reduced model has a less complex structure, while it still captures the main dynamics. The observer is extensively studied in simulations and validated in experiments for actual electric-vehicle drive cycles. Experimental results show the observer to be robust with respect to unmodeled dynamics as well as to noisy and biased voltage and current measurements. The available state estimates can be used for monitoring purposes or incorporated into a model based controller to improve the performance of the battery while guaranteeing safe operation.

This article discusses the options and challenges of dynamic models for the diagnosis and operation of Li-ion batteries. It provides a concise yet understandable overview on models and dynamics, and it discusses future developments needed to progress the field. The diagnosis and operation of batteries require an understanding of the main processes and their dynamics, parameters, and time constants. Processes with large time constants, such as thermal transport are equally important for safe high-performance operation as are processes with shorter time constants such as diffusion. Depending on the specific problem or operating condition, taking all of the scales into account is often unavoidable. Three separate, yet closely connected model classes are reviewed in terms of physical insight and their capabilities and limits: mechanistic models, equivalent circuit models, and data-driven models. We provide guidance for the selection of a suitable model for the particular diagnosis and operation problem of interest. The optimization of battery diagnosis and operation require versatile and simple models that span multiple time scales and allow physical insight and ease of parameterization. Fusing the existing modeling approaches may help to fully exploit their potential while integrating first-principles physical insight and measurement data.