Online Feedback Optimization is a method used to steer the operation of a process plant to its optimal operating point without explicitly solving a nonlinear constrained optimization problem. This is achieved by leveraging a linear plant model and feedback from measurements. However the presence of plant-model mismatch leads to suboptimal results when using this approach. Learning the plant-model mismatch enables Online Feedback Optimization to overcome this shortcoming. In this work we present a novel application of Online Feedback Optimization with online model adaptation using Gaussian process regression. We demonstrate our approach with a realistic load sharing problem in a compressor station with parametric and structural plant-model mismatch. We assume imperfect knowledge of the compressor maps and design an Online Feedback Optimization controller that minimizes the compressor station power consumption. In the evaluated scenario, imperfect knowledge of the plant leads to a 5% increase in power consumption compared to the case with perfect knowledge. We demonstrate that Online Feedback Optimization with model adaptation reduces this increase to only 0.8%, closely approximating the case of perfect knowledge of the plant, regardless of the type of mismatch.

The morning commute bottleneck congestion problem has classically been modelled as a static game in which commuters act strategically based on their immediate Value of Time (VOT). This has restricted existing congestion mitigation techniques to rely on essentially monetary incentives to affect the static costs of the commuters. In contrast, a dynamic model enables characterizing the strategic tradeoff between immediate and future resource access rights and inspires the design of new classes of fair, non-monetary congestion mitigation schemes. In this paper, we show how the recently proposed Dynamic Population Game (DPG) framework can be leveraged to study a non-monetary economy for bottleneck congestion management based on karma, a non-tradable mobility credit. Our DPG model allows to consider an elastic demand of commuters that only travel if congestion is reduced, and we show that a Stationary Nash Equilibrium (SNE) is guaranteed to exist despite of the dynamic participation of these commuters. Through numerical case studies we illustrate how our tools can assist policy makers in taking informed decisions about complex policy outcomes. In particular, we show how the dynamic karma scheme is robust to a potentially detrimental rebound effect that would manifest in a static monetary scheme.

The electric power system is currently undergoing a period of unprecedented changes. Environmental and sustainability concerns lead to replacement of a significant share of conventional fossil fuel-based power plants with renewable energy sources. As a result of this energy transition, centralized bulk generation based on fossil fuel and interfaced with synchronous machines is substituted by distributed generation based on renewables and interfaced with power electronic converters. Accordingly, the entire operation of power systems is undergoing several major paradigm shifts: from decentralized device-level control, over distributed coordination of energy sources, to real-time system-level optimization, and open markets involving demand response and energy storage. In this article, we give a tutorial introduction to new and emerging thrusts in analysis, control, and optimization of future, smart, and cyber-enabled power systems. The solutions that we present tap into some recent methodological advances in control and optimization, with a focus on the analysis of multiagent decision scenarios and on the design of decentralized and networked control strategies. We cover the topics of decentralized control of power converters in low-inertia power systems, real-time control of distribution grids, optimal and distributed frequency control of transmission grids, and coordination of energy supply and demand. Throughout the article we also present worthwhile open directions for future research.