Now showing 1 - 8 of 8
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Robust Analysis of Almost Sure Convergence of Zeroth-Order Mirror Descent Algorithm

01-01-2023, Paul, Anik Kumar, Arun D Mahindrakar, Rachel Kalpana Kalaimani

This letter presents an almost sure convergence of the zeroth-order mirror descent (ZOMD) algorithm. The algorithm admits non-smooth convex functions and a biased oracle which only provides noisy function value at any desired point. We approximate the subgradient of the objective function using Nesterov's Gaussian Approximation (NGA) with certain alternations suggested by some practical applications. We prove an almost sure convergence of the iterates' function value to the neighbourhood of optimal function value, which can not be made arbitrarily small, a manifestation of a biased oracle. This letter ends with a concentration inequality, which is a finite time analysis that predicts the likelihood that the function value of the iterates is in the neighbourhood of the optimal value at any finite iteration.

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Optimizing Driver Nodes for Structural Controllability of Temporal Networks

01-03-2022, Srighakollapu, Manikya Valli, Rachel Kalpana Kalaimani, Ramakrishna Pasumarthy

In this article, we derive conditions for structural controllability of temporal networks that change topology and edge weights with time. The existing results for structural controllability of directed networks assume that all edge weights are chosen independently of each other. The undirected case is challenging due to the constraints on the edge weights. We show that even with this additional restriction, the structural controllability results for the directed case are applicable to the undirected case. We further address two important issues. The first is optimizing the number of driver nodes to ensure the structural controllability of the temporal network. The second is to characterize the maximum reachable subspace when there are constraints on the number of driver nodes. Using the max-flow min-cut theorem, we show that the dimension of the reachable subspace is a submodular function of a set of driver nodes. Hence, we propose greedy algorithms with approximation guarantees to solve the above NP-hard problems. The results of the two case studies illustrate that the proposed greedy algorithm efficiently computes the optimum driver node set for both directed and undirected temporal networks.

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Optimizing network topology for average controllability

01-12-2021, Srighakollapu, Manikya Valli, Rachel Kalpana Kalaimani, Ramakrishna Pasumarthy

We address the problem of identifying a network topology of a networked system for maximizing a controllability measure, the average controllability under constraints on the number of links in the network. We consider networked systems consisting of subsystems with higher-order discrete-time linear time-invariant dynamics. We show that the average controllability is a monotone increasing supermodular function of a set of links in the networked system. Since maximizing such a function with cardinality constraints is an NP-hard problem, we analyze the performance guarantees obtained from the greedy algorithm for maximizing non-submodular set functions in terms of supermodular curvature. We show that the lower bound obtained for the greedy algorithm becomes trivial as the number of subsystems in the networked system increases. Hence, we propose two heuristic algorithms to solve the optimization problem and numerically demonstrate the efficiency of the proposed heuristics in terms of computational complexity and performance improvement in average controllability.

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On the interaction between personal comfort systems and centralized HVAC systems in office buildings

02-01-2020, Kalaimani, Rachel, Jain, Milan, Keshav, Srinivasan, Rosenberg, Catherine

Most modern HVAC systems in office buildings are unable to meet diverse comfort requirements of the occupants and are not energy efficient. We propose to mitigate both issues by using personal comfort systems (PCS). Specifically, we address the question, ‘How should an existing HVAC system modify its operation to benefit from the deployment of PCSs?’ For example, energy use could be reduced during periods of sparse occupancy by choosing appropriate thermal set points, with each PCS providing the additional offset in thermal comfort required by each occupant. We present the design of a PCS-aware HVAC control strategy based on Model Predictive Control (MPC) that employs a bi-linear thermal model. We use extensive simulations to compare the energy use and comfort offered by our PCS-aware HVAC system with that of a state-of-the-art MPC-based central HVAC system. We study different room layouts and scenarios with full or partial deployment of PCSs. Numerical evaluations show that our system yields significant savings in energy use in both summer and winter, compared both with a state-of-the-art system that does not deploy PCSs and with a similar system that deploys PCSs, but is not aware of them.

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Distributed computation of fast consensus weights using ADMM

01-08-2022, Rokade, Kiran, Rachel Kalpana Kalaimani

In time-critical multi-agent tasks, it is important for the agents to reach consensus as fast as possible. In this paper, we consider the problem of computing the weights in the weighted-average consensus protocol that achieve average consensus with an optimal per-step convergence factor. Most of the work in the literature either computes these optimal set of weights in a centralized manner, which requires global information about the network that may not be available, or computes a suboptimal set of weights, which are slow in achieving consensus. We propose an iterative, distributed algorithm to compute a set of weights that achieve an optimal convergence factor. We give theoretical guarantees of the convergence of the algorithm. Through numerical examples, we show that our method performs better than other distributed methods of computing weights for consensus, and it matches the performance of the centralized optimal method.

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On Strong Structural Controllability of Temporal Networks

01-01-2022, Srighakollapu, Manikya Valli, Rachel Kalpana Kalaimani, Ramakrishna Pasumarthy

In this letter, we study strong structural controllability of linear time varying network systems that change network topology and edge weights with time. We derive graph based necessary and sufficient conditions for strong structural controllability of temporal networks. We provide a polynomial time algorithm to compute the dimension of the strong structurally controllable subspace of a temporal network. This allows us to verify whether a given set of inputs leads to a controllable system for all choices of numerical realizations. Next, we show that the problem of finding a minimum size input for strong structural controllability of temporal networks is an NP-hard problem. We propose a greedy heuristic algorithm to optimize the size of the input set for strong structural controllability of temporal networks and compare the performance of the greedy algorithm with the optimum solution through simulations.

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Distributed Estimation over Directed Graphs Resilient to Sensor Spoofing

01-01-2023, Bhattacharyya, Shamik, Rokade, Kiran, Rachel Kalpana Kalaimani

This paper addresses the problem of distributed estimation of an unknown dynamic parameter by a multi-agent system over a directed communication network in the presence of an adversarial attack on the agents' sensors. The mode of attack of the adversaries is to corrupt the sensor measurements of some of the agents, while the communication and information processing capabilities of those agents remain unaffected. To ensure that all the agents, both normal as well as those under attack, are able to correctly estimate the parameter value, the Resilient Estimation through Weight Balancing (REWB) algorithm is introduced. The only condition required for the REWB algorithm to guarantee resilient estimation is that at any given point in time, less than half of the total number of agents are under attack. The paper discusses the development of the REWB algorithm using the concepts of weight balancing of directed graphs, and the consensus+innovations approach for linear estimation. Numerical simulations are presented to illustrate the performance of our algorithm over directed graphs under different conditions of adversarial attacks.

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Using personal environmental comfort systems to mitigate the impact of occupancy prediction errors on HVAC performance

01-12-2018, Jain, Milan, Kalaimani, Rachel K., Keshav, Srinivasan, Rosenberg, Catherine

Heating, Ventilation and Air Conditioning (HVAC) consumes a significant fraction of energy in commercial buildings. Hence, the use of optimization techniques to reduce HVAC energy consumption has been widely studied. Model predictive control (MPC) is one state of the art optimization technique for HVAC control which converts the control problem to a sequence of optimization problems, each over a finite time horizon. In a typical MPC, future system state is estimated from a model using predictions of model inputs, such as building occupancy and outside air temperature. Consequently, as prediction accuracy deteriorates, MPC performance–in terms of occupant comfort and building energy use–degrades. In this work, we use a custom-built building thermal simulator to systematically investigate the impact of occupancy prediction errors on occupant comfort and energy consumption. Our analysis shows that in our test building, as occupancy prediction error increases from 5 to 20% the performance of an MPC-based HVAC controller becomes worse than that of even a simple static schedule. However, when combined with a personal environmental control (PEC) system, HVAC controllers are considerably more robust to prediction errors. Thus, we quantify the effectiveness of PECs in mitigating the impact of forecast errors on MPC control for HVAC systems.