Learning Robustness with Bounded Failure: An Iterative MPC Approach

We propose an approach to design a Model Predictive Controller (MPC) for constrained Linear Time Invariant systems performing an iterative task. The system is subject to an additive disturbance, and the goal is to learn to satisfy state and input constraints robustly. Using disturbance measurements after each iteration, we construct Confidence Support sets, which contain the true support of the disturbance distribution with a given probability. As more data is collected, the Confidence Supports converge to the true support of the disturbance. This enables design of an MPC controller that avoids conservative estimate of the disturbance support, while simultaneously bounding the probability of constraint violation. The efficacy of the proposed approach is then demonstrated with a detailed numerical example.Comment: Added GitHub link to all source code

Regulating TNCs: Should Uber and Lyft Set Their Own Rules?

We evaluate the impact of three proposed regulations of transportation network companies (TNCs) like Uber, Lyft and Didi: (1) a minimum wage for drivers, (2) a cap on the number of drivers or vehicles, and (3) a per-trip congestion tax. The impact is assessed using a queuing theoretic equilibrium model which incorporates the stochastic dynamics of the app-based ride-hailing matching platform, the ride prices and driver wages established by the platform, and the incentives of passengers and drivers. We show that a floor placed under driver earnings pushes the ride-hailing platform to hire more drivers and offer more rides, at the same time that passengers enjoy faster rides and lower total cost, while platform rents are reduced. Contrary to standard economic theory, enforcing a minimum wage for drivers benefits both drivers and passengers, and promotes the efficiency of the entire system. This surprising outcome holds for almost all model parameters, and it occurs because the wage floors curbs TNC labor market power. In contrast to a wage floor, imposing a cap on the number of vehicles hurts drivers, because the platform reaps all the benefits of limiting supply. The congestion tax has the expected impact: fares increase, wages and platform revenue decrease. We also construct variants of the model to briefly discuss platform subsidy, platform competition, and autonomous vehicles

Mechanism Design for Demand Response Programs

Demand Response (DR) programs serve to reduce the consumption of electricity at times when the supply is scarce and expensive. The utility informs the aggregator of an anticipated DR event. The aggregator calls on a subset of its pool of recruited agents to reduce their electricity use. Agents are paid for reducing their energy consumption from contractually established baselines. Baselines are counter-factual consumption estimates of the energy an agent would have consumed if they were not participating in the DR program. Baselines are used to determine payments to agents. This creates an incentive for agents to inflate their baselines. We propose a novel self-reported baseline mechanism (SRBM) where each agent reports its baseline and marginal utility. These reports are strategic and need not be truthful. Based on the reported information, the aggregator selects or calls on agents to meet the load reduction target. Called agents are paid for observed reductions from their self-reported baselines. Agents who are not called face penalties for consumption shortfalls below their baselines. The mechanism is specified by the probability with which agents are called, reward prices for called agents, and penalty prices for agents who are not called. Under SRBM, we show that truthful reporting of baseline consumption and marginal utility is a dominant strategy. Thus, SRBM eliminates the incentive for agents to inflate baselines. SRBM is assured to meet the load reduction target. SRBM is also nearly efficient since it selects agents with the smallest marginal utilities, and each called agent contributes maximally to the load reduction target. Finally, we show that SRBM is almost optimal in the metric of average cost of DR provision faced by the aggregator

Duration-differentiated Energy Services with a Continuum of Loads

As the proportion of total power supplied by renewable sources increases, it gets more costly to use reserve generation to compensate for the variability of renewables like solar and wind. Hence attention has been drawn to exploiting flexibility in demand as a substitute for reserve generation. Flexibility has different attributes. In this paper we consider loads requiring a constant power for a specified duration (within say one day), whose flexibility resides in the fact that power may be delivered at any time so long as the total duration of service equals the load's specified duration. We give conditions under which a variable power supply is adequate to meet these flexible loads, and describe how to allocate the power to the loads. We also characterize the additional power needed when the supply is inadequate. We study the problem of allocating the available power to loads to maximize welfare, and show that the welfare optimum can be sustained as a competitive equilibrium in a forward market in which electricity is sold as service contracts differentiated by the duration of service and power level. We compare this forward market with a spot market in their ability to capture the flexiblity inherent in duration-differentiated loads