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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. 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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3. Improving Input-Output Linearizing Controllers for Bipedal Robots via Reinforcement Learning

   Castañeda, Fernando; Wulfman, Mathias; Agrawal, Ayush; Westenbroek, Tyler; Tomlin, Claire J.; Sastry, S. Shankar; Sreenath, Koushil (June 2020, Learning for Dynamics and Control (L4DC))

   The main drawbacks of input-output linearizing controllers are the need for precise dynamics models and not being able to account for input constraints. Model uncertainty is common in almost every robotic application and input saturation is present in every real world system. In this paper, we address both challenges for the specific case of bipedal robot control by the use of reinforcement learning techniques. Taking the structure of a standard input-output linearizing controller, we use an additive learned term that compensates for model uncertainty. Moreover, by adding constraints to the learning problem we manage to boost the performance of the final controller when input limits are present. We demonstrate the effectiveness of the designed framework for different levels of uncertainty on the five-link planar walking robot RABBIT. 

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4. Nonlinear System Identification via Tensor Completion

   https://doi.org/10.1609/aaai.v34i04.5868  

   Kargas, Nikos; Sidiropoulos, Nicholas D. (June 2020, Proceedings of the AAAI Conference on Artificial Intelligence)

   Function approximation from input and output data pairs constitutes a fundamental problem in supervised learning. Deep neural networks are currently the most popular method for learning to mimic the input-output relationship of a general nonlinear system, as they have proven to be very effective in approximating complex highly nonlinear functions. In this work, we show that identifying a general nonlinear function y = ƒ(x1,…,xN) from input-output examples can be formulated as a tensor completion problem and under certain conditions provably correct nonlinear system identification is possible. Specifically, we model the interactions between the N input variables and the scalar output of a system by a single N-way tensor, and setup a weighted low-rank tensor completion problem with smoothness regularization which we tackle using a block coordinate descent algorithm. We extend our method to the multi-output setting and the case of partially observed data, which cannot be readily handled by neural networks. Finally, we demonstrate the effectiveness of the approach using several regression tasks including some standard benchmarks and a challenging student grade prediction task. 

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5. Stabilization via Distributed Control

   https://doi.org/10.1109/TAC.2025.3614507  

   Iwasaki, Tetsuya; Taneja, Laqshya (September 2025, IEEE Transactions on Automatic Control)

   We consider the linear plant with multiple pairs of input and output channels, and solve the problem of designing a stabilizing controller consisting of a set of control stations, one for each channel pair, connected with an arbitrarily fixed network topology and communication dynamics. It is shown that such stabilizing distributed controller exists if and only if the fixed modes of the plant, augmented with the network communication, are stable; this leverages and extends the classical fixed mode result for decentralized control. Moreover, a condition is given to reveal exactly what connections are needed between control stations to achieve stabilizability via a distributed control. Thus, the feasibility of optimal distributed control synthesis can readily be checked or enforced before applying computationally expensive optimization methods. Stabilizing distributed controllers, if feasible, can be designed using decentralized control theories. 

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