arXiv subjects

Yonatan Mintz

Publications and source records attributed to Yonatan Mintz.

23 records · Page 2Linked to original sources

arXiv2017

Designing Real-Time Prices to Reduce Load Variability with HVAC

Utilities use demand response to shift or reduce electricity usage of flexible loads, to better match electricity demand to power generation. A common mechanism is peak pricing (PP), where consumers pay reduced (increased) prices for electricity during periods of low (high) demand, and its simplicity allows consumers to understand how their consumption affects costs. However, new consumer technologies like internet-connected smart thermostats simplify real-time pricing (RP), because such devices can automate the tradeoff between costs and consumption. These devices enable consumer choice under RP by abstracting this tradeoff into a question of quality of service (e.g., comfort) versus price. This paper uses a principal-agent framework to design PP and RP rates for heating, ventilation, and air-conditioning (HVAC) to address adverse selection due to variations in consumer comfort preferences. We formulate the pricing problem as a stochastic bilevel program, and numerically solve it by reformulation as a mixed integer program (MIP). Last, we compare the effectiveness of different pricing schemes on reductions of peak load or load variability. We find that PP pricing induces HVAC consumption to spike high (before), spike low (during), and spike high (after) the PP event, whereas RP achieves reductions in peak loads and load variability while preventing large spikes in electricity usage.

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arXiv2017

Polynomial-Time Approximation for Nonconvex Optimization Problems with an L1-Constraint

Nonconvex optimization problems with an L1-constraint are ubiquitous, and are found in many application domains including: optimal control of hybrid systems, machine learning and statistics, and operations research. This paper shows that nonconvex optimization problems with an L1-constraint can be approximately solved in polynomial time. We first show that nonlinear integer programs with an L1-constraint can be solved in a number of oracle steps that is polynomial in the dimension of the decision variable, for each fixed radius of the L1-constraint. When specialized to polynomial integer programs, our result shows that such problems have a time complexity that is polynomial in simultaneously both the dimension of the decision variables and number of constraints, for each fixed radius of the L1-constraint. We prove this result using a geometric argument that leverages ideas from stochastic process theory and from the theory of convex bodies in high-dimensional spaces. We conclude by providing an additive polynomial time approximation scheme (PTAS) for continuous optimization of Lipschitz functions subject to Lipschitz constraints intersected with an L1-constraint, and we sketch a generalization to mixed-integer optimization.

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arXiv2017

Control Synthesis for Bilevel Linear Model Predictive Control

Distributed model predictive control (MPC) is either cooperative or competitive, and control-theoretic properties have been less studied in the competitive (e.g., game theory) setting. This paper studies MPC with linear dynamics and a Stackelberg game structure: Given a fixed lower-level linear MPC (LoMPC) controller, the bilevel linear MPC (BiMPC) controller chooses inputs to steer LoMPC knowing that LoMPC is optimizing with respect to a different cost function. After defining LoMPC and BiMPC, we give examples to demonstrate how interconnections in a dynamic Stackelberg game can lead to loss/gain (as compared to the same system being centrally controlled) of controllability or stability. Then, we give sufficient conditions under an arbitrary finite MPC horizon for stabilizability of BiMPC, and develop an approach to synthesize a stabilizing BiMPC controller. Next, we define two (a duality-based technique and an integer-programming-based technique) reformulations to numerically solve the optimization problem associated with BiMPC, prove equivalence of these reformulations to BiMPC, and demonstrate their useful by simulations of a synthetic system and a case study of an electric utility changing electricity prices to perform demand response of a home's air conditioner controlled by a linear MPC.

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arXiv2017

Local Water Storage Control for the Developing World

Most cities in India do not have water distribution networks that provide water throughout the entire day. As a result, it is common for homes and apartment buildings to utilize water storage systems that are filled during a small window of time in the day when the water distribution network is active. However, these water storage systems do not have disinfection capabilities, and so long durations of storage (i.e., as few as four days) of the same water leads to substantial increases in the amount of bacteria and viruses in that water. This paper considers the stochastic control problem of deciding how much water to store each day in the system, as well as deciding when to completely empty the water system, in order to tradeoff: the financial costs of the water, the health costs implicit in long durations of storing the same water, the potential for a shortfall in the quantity of stored versus demanded water, and water wastage from emptying the system. To solve this problem, we develop a new Binary Dynamic Search (BiDS) algorithm that is able to use binary search in one dimension to compute the value function of stochastic optimal control problems with controlled resets to a single state and with constraints on the maximum time span in between resets of the system.

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arXiv2017

Behavioral Analytics for Myopic Agents

Many multi-agent systems have the structure of a single coordinator providing behavioral or financial incentives to a large number of agents. Two challenges faced by the coordinator are a finite budget from which to allocate incentives, and an initial lack of knowledge about the utility function of the agents. Here, we present a behavioral analytics approach to solve the coordinator's problem when agents make decisions by maximizing utility functions that depend on prior system states, inputs, and other parameters that are initially unknown and subject to temporal dynamics. Our behavioral analytics framework involves three steps: first, we develop a behavioral model that describes the decision-making process of an agent; second, we use data to estimate behavioral model parameters for each agent and then use these estimates to predict future decisions of each agent; and third, we use the estimated behavioral model parameters to optimize a set of costly incentives to provide to each agent. In this paper, we describe a specific set of tools, models, and approaches that fit into this framework, and that adapt models and incentives as new information is collected by repeating the second and third steps of this framework. Furthermore, we prove that incentives computed by this adaptive approach are asymptotically optimal with respect to a given loss function that describes the coordinator's objective. We optimize incentives using a decomposition scheme, where each sub-problem solves the coordinator's problem for a single agent, and the master problem is a pure integer program. We conclude with a simulation study to evaluate the effectiveness of our behavioral analytics approach in designing personalized treatment plans for a weight loss program. The results show our approach maintains efficacy of the program while reducing costs by up to 60%, while adaptive heuristics provide less savings.

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