Optimizing Average Controllability of Networked Systems
In this paper, we consider the controllability of a networked system where each node in the network has higher order linear time-invariant (LTI) dynamics. We employ a quantitative measure for controllability based on average controllability. We relate this metric to the network topology and the dynamics of individual subsystems that constitute each node of the networked system. Using this, we show that, under certain assumptions, the average controllability increases with increased interactions across subsystems in the network. Next, we consider the problem of identifying an appropriate network topology when there are constraints on the number of links that exist in the network. This problem is formulated as a set function optimization problem. We show that for our problem, this set function is a monotone increasing supermodular function. Since maximization of such a function with cardinality constraints is a hard problem, we implement a greedy heuristic to obtain a sub-optimal solution.
On the interaction between personal comfort systems and centralized HVAC systems in office buildings
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.
Scheduling for Stabilization over Capacity-Constrained Channels
We address the problem of stabilizing a set of discrete-time systems over a communication network. The network consists of capacity-constrained discrete-time Additive White Gaussian Noise (AWGN) channels. We consider the case when the number of channels is limited and propose a dynamic scheduling scheme that, at a given time, determines which subset of systems get access to the channel for feedback control. This problem is addressed by considering two separate problems - scheduling systems over noiseless channels and stabilizing a system over an AWGN channel. The scheduling problem is addressed in the switched system framework by making use of a min-type Lyapunov function. We provide a sufficient condition in the form of Linear Matrix Inequalities (LMIs) to schedule a subset of systems while achieving stability of all systems. We also explicitly determine the scheduling scheme. Next, we provide a novel LMI-based necessary and sufficient condition for stabilization of a discrete-time system over a discrete-time AWGN channel. Finally, we appropriately combine the two results to obtain an LMI-based sufficient condition for the join scheduling-stabilization problem.
An Almost Sure Convergence Analysis of Zeroth-Order Mirror Descent Algorithm
In this paper, we show almost sure convergence of zeroth-order mirror descent algorithm. The algorithm admits non-smooth convex functions and assumes only an estimate of the gradient is available, obtained using Nesterov's Gausssian Approximation technique (NGA). We establish that under suitable condition of step-size, the function value of the iterates of the algorithm converge to a neighborhood of the optimal function value almost surely. We extend the analysis to the distributed implementation of the zeroth-order mirror descent algorithm.
Robust Analysis of Almost Sure Convergence of Zeroth-Order Mirror Descent Algorithm
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.
Distributed Estimation over Directed Graphs Resilient to Sensor Spoofing
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.
Distributed Online Mirror Descent Algorithm with Event Triggered Communication
The paper proposes an algorithm that uses distributed online mirror descent algorithm for solving constrained online optimization problem with event triggered communication. The optimization is over a time horizon and the future objective functions are not apriori known to each agent. In the proposed algorithm, the communication between the agents, that happens in a distributed optimization framework, occurs only when the difference between the current state and the state when the last event has been triggered exceeds a threshold. The performance of the algorithm is analysed using a regret function. We establish a bound on the regret and provide sufficient conditions on the step-size and thresholding error such that the regret is sublinear. We demonstrate the reduction in the number of inter-agent communications using our proposed algorithm for an estimation problem in a dynamic environment.
Reinforcement Learning based Multi-objective Optimization for Broadband Newtonian Noise Cancellation in GW Detectors
The sensitivity of terrestrial Gravitational-Wave detectors can be improved in the low-frequency region by sub-Tracting Newtonian Noise at the mirrors of the interferometer. An estimate of the Newtonian Noise is obtained by gathering information from an array of sensors monitoring the sources of noise. Efficient and maximal subtraction of Newtonian Noise is possible when the position of the sensors is optimized for a wide range of frequencies. This constitutes a multi-objective optimization problem which is solved by generating a Pareto optimal solution. Generally, multiple Pareto optimal solutions are generated, and further analysis is done to select the most suitable Pareto point for implementation. This paper proposes a method to obtain a smart Pareto optimal point by modifying the Normal Boundary Intersection method using reinforcement learning techniques. The proposed method will directly generate the smart Pareto point to be implemented in the Newtonian Noise cancellation system. The performance of our algorithm is compared with existing literature.
Optimizing Driver Nodes for Structural Controllability of Temporal Networks
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.
Optimization of Sensor Placement for Broadband Newtonian Noise Cancellation in GW Detectors
The sensitivity of second-generation interferometric Gravitational-Wave detectors is limited in the low frequency region by Newtonian Noise from seismic fields. Fluctuations in the local gravitational field due to mass density variations results in Newtonian Noise in the interferometer data. To subtract the effects of this noise, an array of seismometers is placed around the mirrors of the interferometer to monitor the noise source. Optimal positioning of these seismometers will result in maximal subtraction of Newtonian Noise. So far the sensor positions were optimized for a single seismic wave frequency. But in reality, the Newtonian Noise at detector site is substantial over the frequency band (8 - 20) Hz. In this paper, the sensor placement optimization problem is formulated as a multi-objective optimization problem, to ensure that the sensor positions are optimized over a broad range of frequencies. The results show a significant improvement from the single objective optimization case currently in use, and is limited only by the seismometer self-noise.