Electric distribution grid operations typically rely on both centralized optimization and local non-optimal control techniques. As an alternative, distribution system operational practices can consider distributed optimization techniques that leverage communications among various neighboring agents to achieve optimal operation. With the rapidly increasing integration of distributed energy resources (DERs), distributed optimization algorithms are growing in importance due to their potential advantages in scalability, flexibility, privacy, and robustness relative to centralized optimization. Implementation of distributed optimization offers multiple challenges and also opportunities. This paper provides a comprehensive review of the recent advancements in distributed optimization for electric distribution systems and classifications using key attributes. Problem formulations and distributed optimization algorithms are provided for example use cases, including volt/var control, market clearing process, loss minimization, and conservation voltage reduction. Finally, this paper also presents future research needs for the applicability of distributed optimization algorithms in the distribution system.

The world faces some of the greatest challenges of modern times. How we address them will have a dramatic impact on society at large for generations to come. The field of control systems pertains to specific methods and principles to control dynamic systems and produce desired outcomes despite uncertainties in the system and in the environment. The development of these principles and methods has been both broad and deep, from aerospace systems and wireless networks to bioengineering and traffic control. These methods are deeply embedded in many sectors, including energy, transportation, health care, manufacturing, and robotics. With their advanced toolbox for understanding and designing feedback, robustness, dynamics, and decision making in complex systems, control systems have an opportunity to play a central role in the development of technologies and solutions for many of the key challenges that society faces.

The control of physical systems in the presence of time-delays becomes particularly challenging when parametric uncertainties are present. To cope with these ubiquitous uncertainties, we propose an adaptive controller in this paper that can accommodate both a time-delay and parametric uncertainties. The controller includes a) a control architecture that is based on the plant relative degree rather than the plant order, b) an integral implementation of the well known Posicast Controller so as to accommodate unstable plants, c) high-order tuners for parameter adaptation, and d) a Lyapunov-Krasvoskii functional that allows adaptive stabilization. The controller is shown to be semi-global in the time-delay τ and to result in asymptotic tracking. The implications of the adaptive controller are explored in the context of combustion control through simulation studies. Robustness properties of the controller are briefly discussed.