This dissertation presents a framework for computationally-efficient, health-consciousonline state estimation and control in lithium-ion batteries. The framework buildson three main tools, namely, (i) battery model reformulation and (ii) pseudo-spectral optimization for (iii) differential flatness. All of these tools already existin the literature. However, their application to electrochemical battery estimationand control, both separately and in an integrated manner, represents a significantaddition to the literature. The dissertation shows that these tools, together, providesignificant improvements in computational efficiency for both online moving horizonbattery state estimation and online health-conscious model predictive battery con-trol. These benefits are demonstrated both in simulation and using an experimentalcase study.Two key facts motivate this dissertation. First, lithium-ion batteries are widelyused for different applications due to their low self-discharge rates, lack of memoryeffects, and high power/energy densities compared to traditional lead-acid and nickel-metal hydride batteries. Second, lithium-ion batteries are also vulnerable to agingand degradation mechanisms, such as lithium plating, some of which can lead tosafety issues. Conventional battery management systems (BMS) typically use model-free control strategies and therefore do not explicitly optimize the performance, lifespan, and cost of lithium-ion battery packs. They typically avoid internal damageby constraining externally-measured variables, such as battery voltage, current,and temperature. When pushed to charge a battery quickly without inducingexcessive damage, these systems often follow simple and potentially sub-optimalcharge/discharge trajectories, e.g., the constant-current/constant-voltage (CCCV)charging strategy. While the CCCV charging strategy is simple to implement,it suffers from its poor ability to explicitly control the internal variables causingbattery aging, such as side reaction overpotentials. Another disadvantage is theinability of this strategy to adapt to changes in battery dynamics caused by aging.Model-based control has the potential to alleviate many of the above limitationsof classical battery management systems. A model-based control system can estimate the internal state of a lithium-ion battery and use the estimated stateto adjust battery charging/discharging in a manner that avoids damaging sidereactions. By doing so, model-based control can (i) prolong battery life, (ii) improvebattery safety, (iii) increase battery energy storage capacity, (iv) decrease internaldamage/degradation, and (v) adapt to changes in battery dynamics resulting fromaging. These potential benefits are well-documented in the literature. However,one major challenge remains, namely, the computational complexity associatedwith online model-based battery state estimation and control. The goal of thisdissertation is to address this challenge by making five contributions to the literature.Specifically: Chapter 2 exploits the differential flatness of solid-phase lithium-ion batterydiffusion dynamics, together with pseudo-spectral optimization and diffusionmodel reformulation, to decrease the computational load associated withhealth-conscious battery trajectory optimization significantly. This contribu-tion forms a foundation for much of the subsequent work in this dissertation,but is limited to isothernal single-particle battery models with significanttime scale separation between anode- and cathode-side solid-phase diffusiondynamics. Chapter 3 extends the results of Chapter 2 in two ways. First , it exploitsthe law of conservation of charge to enable flatness-based, health-consciousbattery trajectory optimization for single particle battery models even in theabsence of time scale separation between the negative and positive electrodes.Second, it performs this optimization for a combined thermo-electrochemicalbattery model, thereby relaxing the above assumption of isothermal batterybehavior and highlighting the benefits of flatness-based optimization for anonlinear battery model. Chapter 4 presents a framework for flatness-based pseudo-spectral combinedstate and parameter estimation in lumped-parameter nonlinear systems.This framework enables computationally-efficient total least squares (TLS)estimation for lumped-parameter nonlinear systems. This is quite relevant topractical lithium-ion battery systems, where both battery input and outputmeasurements can be quite noisy. Chapter 5 utilizes the above flatness-based TLS estimation algorithm formoving horizon state estimation using a coupled thermo-electrochemicalequivalent circuit model of lithium-ion battery dynamics. Chapter 6 extends the battery estimation framework from Chapter 5 to enablemoving horizon, flatness-based TLS state estimation in thermo-electrochemical single-particle lithium-ion battery models, and demonstrates this frameworkusing laboratory experiments.The overall outcome of this dissertation is an integrated set of tools, all of themexploiting model reformulation, differential flatness, and pseudo-spectral methods,for computationally efficient online state estimation and health-conscious controlin lithium-ion batteries.