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1. The Role of Strategic Load Participants in Two-Stage Settlement Electricity Markets

   https://doi.org/10.1109/CDC40024.2019.9029514  

   You, Pengcheng; Gayme, Dennice F.; Mallada, Enrique (December 2019, Conference on Decision and Control)

   We consider the problem of designing a feedback controller that guides the input and output of a linear time-invariant system to a minimizer of a convex optimization problem. The system is subject to an unknown disturbance, piecewise constant in time, which shifts the feasible set defined by the system equilibrium constraints. Our proposed design combines proportional-integral control with gradient feedback, and enforces the Karush-Kuhn-Tucker optimality conditions in steady-state without incorporating dual variables into the controller. We prove that the input and output variables achieve optimality in steady-state, and provide a stability criterion based on absolute stability theory. The effectiveness of our approach is illustrated on a simple example system. 

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2. Using Deep Learning to Bootstrap Abstractions for Robot Planning

   Shah, Naman; Srivastava, Siddharth (May 2022, Proceedings of the International Conference on Autonomous Agents)

   This paper addresses the problem of learning abstractions that boost robot planning performance while providing strong guarantees of reliability. Although state-of-the-art hierarchical robot planning algorithms allow robots to efficiently compute long-horizon motion plans for achieving user desired tasks, these methods typically rely upon environment-dependent state and action abstractions that need to be hand-designed by experts. We present a new approach for bootstrapping the entire hierarchical planning process. This allows us to compute abstract states and actions for new environments automatically using the critical regions predicted by a deep neural network with an auto-generated robot-specific architecture. We show that the learned abstractions can be used with a novel multi-source bi-directional hierarchical robot planning algorithm that is sound and probabilistically complete. An extensive empirical evaluation on twenty different settings using holonomic and non-holonomic robots shows that (a) our learned abstractions provide the information necessary for efficient multi-source hierarchical planning; and that (b) this approach of learning, abstractions, and planning outperforms state-of-the-art baselines by nearly a factor of ten in terms of planning time on test environments not seen during training. 

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3. Using Deep Learning to Bootstrap Abstractions for Hierarchical Robot Planning

   Shah, Naman; Srivastava, Siddharth (May 2022, International Conference on Autonomous Agents and Multiagent Systems)

   Pelachaud, Catherine; Taylor, Matthew E.; Mascardi, Viviana (Ed.)

   This paper addresses the problem of learning abstractions that boost robot planning performance while providing strong guarantees of reliability. Although state-of-the-art hierarchical robot planning algorithms allow robots to efficiently compute long-horizon motion plans for achieving user desired tasks, these methods typically rely upon environment-dependent state and action abstractions that need to be hand-designed by experts. We present a new approach for bootstrapping the entire hierarchical planning process. This allows us to compute abstract states and actions for new environments automatically using the critical regions predicted by a deep neural network with an auto-generated robot-specific architecture. We show that the learned abstractions can be used with a novel multi-source bi-directional hierarchical robot planning algorithm that is sound and probabilistically complete. An extensive empirical evaluation on twenty different settings using holonomic and non-holonomic robots shows that (a) our learned abstractions provide the information necessary for efficient multi-source hierarchical planning; and that (b) this approach of learning, abstractions, and planning outperforms state-of-the-art baselines by nearly a factor of ten in terms of planning time on test environments not seen during training. 

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4. Optimal Steady-State Control for Linear Time-Invariant Systems

   https://doi.org/10.1109/CDC.2018.8619812  

   Lawrence, Liam S.; Nelson, Zachary E.; Mallada, Enrique; Simpson-Porco, John W. (December 2018, 2018 IEEE Conference on Decision and Control (CDC))

   We consider the problem of designing a feedback controller that guides the input and output of a linear time-invariant system to a minimizer of a convex optimization problem. The system is subject to an unknown disturbance that determines the feasible set defined by the system equilibrium constraints. Our proposed design enforces the Karush-Kuhn-Tucker optimality conditions in steady-state without incorporating dual variables into the controller. We prove that the input and output variables achieve optimality in equilibrium and outline two procedures for designing controllers that stabilize the closed-loop system. We explore key ideas through simple examples and simulations. 

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5. An integral quadratic constraint framework for real-time steady-state optimization of linear time-invariant systems

   https://doi.org/10.23919/ACC.2018.8431231  

   Nelson, Zachary E.; Mallada, Enrique (June 2018, 2018 Annual American Control Conference (ACC))

   Achieving optimal steady-state performance in real-time is an increasingly necessary requirement of many critical infrastructure systems. In pursuit of this goal, this paper builds a systematic design framework of feedback controllers for Linear Time-Invariant (LTI) systems that continuously track the optimal solution of some predefined optimization problem. We logically divide the proposed solution into three components. The first component estimates the system state from the output measurements. The second component uses the estimated state and computes a drift direction based on an optimization algorithm. The third component calculates an input to the LTI system that aims to drive the system toward the optimal steady-state. We analyze the equilibrium characteristics of the closed-loop system and provide conditions for optimality and stability. Our analysis shows that the proposed solution guarantees optimal steady-state performance, even in the presence of constant disturbances. Furthermore, by leveraging recent results on the analysis of optimization algorithms using Integral Quadratic Constraints (IQCs), the proposed framework can translate input-output properties of our optimization component into sufficient conditions, based on linear matrix inequalities (LMIs), for global exponential asymptotic stability of the closed-loop system. We illustrate several resulting controller designs using a numerical example. 

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