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This paper considers the design of sparse actuator schedules for linear time-invariant systems. An actuator schedule selects, for each time instant, which control inputs act on the system in that instant. We address the optimal scheduling of control inputs under a hard constraint on the number of inputs that can be used at each time. For a sparsely controllable system, we characterize sparse actuator schedules that make the system controllable, and then devise a greedy selection algorithm that guarantees controllability while heuristically providing low control effort. We further show how to enhance our greedy algorithm via Markov chain Monte Carlo-based randomized optimization

We consider the control of discrete-time linear dynamical systems using sparse inputs where we limit the number of active actuators at every time step. We develop an algorithm for determining a sparse actuator schedule that ensures the existence of a sparse control input sequence, following the schedule, that takes the system from any given initial state to any desired final state. Since such an actuator schedule is not unique, we look for a schedule that minimizes the energy of sparse inputs. For this, we optimize the trace of the inverse of the resulting controllability Gramian, which is an approximate measure of the average energy of the inputs. We present a greedy algorithm along with its theoretical guarantees. Finally, we empirically show that our greedy algorithm ensures the controllability of the linear system with a small number of active actuators per time step without a significant average energy expenditure compared to the fully actuated system.

Sparsity constraints on the control inputs of a linear dynamical system naturally arise in several practical applications such as networked control, computer vision, seismic signal processing, and cyber-physical systems. In this work, we consider the problem of jointly estimating the states and sparse inputs of such systems from low-dimensional (compressive) measurements. Due to the low-dimensional measurements, conventional Kalman filtering and smoothing algorithms fail to accurately estimate the states and inputs. We present a Bayesian approach that exploits the input sparsity to significantly improve estimation accuracy. Sparsity in the input estimates is promoted by using different prior distributions on the input. We investigate two main approaches: regularizer-based MAP, and Bayesian learning-based estimation. We also extend the approaches to handle control inputs with common support and analyze the time and memory complexities of the presented algorithms. Finally, using numerical simulations, we show that our algorithms outperform the state-of-the-art methods in terms of accuracy and time/memory complexities, especially in the low-dimensional measurement regime.

In this paper, we address the problem of detecting anomalies among a given set of binary processes via learning-based controlled sensing. Each process is parameterized by a binary random variable indicating whether the process is anomalous. To identify the anomalies, the decision-making agent is allowed to observe a subset of the processes at each time instant. Also, probing each process has an associated cost. Our objective is to design a sequential selection policy that dynamically determines which processes to observe at each time with the goal to minimize the delay in making the decision and the total sensing cost. We cast this problem as a sequential hypothesis testing problem within the framework of Markov decision processes. This formulation utilizes both a Bayesian log-likelihood ratio-based reward and an entropy-based reward. The problem is then solved using two approaches: 1) a deep reinforcement learning-based approach where we design both deep Q-learning and policy gradient actor-critic algorithms; and 2) a deep active inference-based approach. Using numerical experiments, we demonstrate the efficacy of our algorithms and show that our algorithms adapt to any unknown statistical dependence pattern of the processes.

This paper studies the problem of modifying the input matrix of a structured system to make the system strongly structurally controllable. We focus on the generalized structured systems that rely on zero/nonzero/arbitrary structure, i.e., some entries of system matrices are zeros, some are nonzero, and the remaining entries can be zero or nonzero (arbitrary). We analyze the feasibility of the problem, and if it is feasible, we reformulate it into another equivalent problem. This new formulation leads to a greedy heuristic algorithm. However, we also show that the greedy algorithm can give arbitrarily poor solutions for some special systems. Our alternative approach is a randomized Markov chain Monte Carlo-based algorithm. Unlike the greedy algorithm, this algorithm is guaranteed to converge to an optimal solution with high probability. Finally, we numerically evaluate the algorithms on random graphs to show that the algorithms perform well.

Neuromorphic computing shows promise for advancing computing efficiency and capabilities of AI applications using brain-inspired principles. However, the neuromorphic research field currently lacks standardized benchmarks, making it difficult to accurately measure technological advancements, compare performance with conventional methods, and identify promising future research directions. Prior neuromorphic computing benchmark efforts have not seen widespread adoption due to a lack of inclusive, actionable, and iterative benchmark design and guidelines. To address these shortcomings, we present NeuroBench: a benchmark framework for neuromorphic computing algorithms and systems. NeuroBench is a collaboratively-designed effort from an open community of nearly 100 co-authors across over 50 institutions in industry and academia, aiming to provide a representative structure for standardizing the evaluation of neuromorphic approaches. The NeuroBench framework introduces a common set of tools and systematic methodology for inclusive benchmark measurement, delivering an objective reference framework for quantifying neuromorphic approaches in both hardware-independent (algorithm track) and hardware-dependent (system track) settings. In this article, we present initial performance baselines across various model architectures on the algorithm track and outline the system track benchmark tasks and guidelines. NeuroBench is intended to continually expand its benchmarks and features to foster and track the progress made by the research community.

Phased arrays in near-field communication allow the transmitter to focus wireless signals in a small region around the receiver. Proper focusing is achieved by carefully tuning the phase shifts and the polarization of the signals transmitted from the phased array. In this paper, we study the impact of polarization on near-field focusing and investigate the use of dynamic polarization control (DPC) phased arrays in this context. Our studies indicate that the optimal polarization configuration for near-field focusing varies spatially across the antenna array. Such a spatial variation motivates the need for DPC phased arrays which allow independent polarization control across different antennas. We show using simulations that DPC phased arrays in the near-field achieve a higher received signal-to-noise ratio than conventional switched- or dual-polarization phased arrays.

Stock price prediction is a challenging task and a lot of propositions exist in the literature in this area. Portfolio construction is a process of choosing a group of stocks and investing in them optimally to maximize the return while minimizing the risk. Since the time when Markowitz proposed the Modern Portfolio Theory, several advancements have happened in the area of building efficient portfolios. An investor can get the best benefit out of the stock market if the investor invests in an efficient portfolio and could take the buy or sell decision in advance, by estimating the future asset value of the portfolio with a high level of precision. In this project, we have built an efficient portfolio and to predict the future asset value by means of individual stock price prediction of the stocks in the portfolio. As part of building an efficient portfolio we have studied multiple portfolio optimization methods beginning with the Modern Portfolio theory. We have built the minimum variance portfolio and optimal risk portfolio for all the five chosen sectors by using past daily stock prices over the past five years as the training data, and have also conducted back testing to check the performance of the portfolio. A comparative study of minimum variance portfolio and optimal risk portfolio with equal weight portfolio is done by backtesting.

We address the problem of monitoring a set of binary stochastic processes and generating an alert when the number of anomalies among them exceeds a threshold. For this, the decision-maker selects and probes a subset of the processes to obtain noisy estimates of their states (normal or anomalous). Based on the received observations, the decisionmaker first determines whether to declare that the number of anomalies has exceeded the threshold or to continue taking observations. When the decision is to continue, it then decides whether to collect observations at the next time instant or defer it to a later time. If it chooses to collect observations, it further determines the subset of processes to be probed. To devise this three-step sequential decision-making process, we use a Bayesian formulation wherein we learn the posterior probability on the states of the processes. Using the posterior probability, we construct a Markov decision process and solve it using deep actor-critic reinforcement learning. Via numerical experiments, we demonstrate the superior performance of our algorithm compared to the traditional model-based algorithms.

We address the problem of sequentially selecting and observing processes from a given set to find the anomalies among them. The decision-maker observes a subset of the processes at any given time instant and obtains a noisy binary indicator of whether or not the corresponding process is anomalous. In this setting, we develop an anomaly detection algorithm that chooses the processes to be observed at a given time instant, decides when to stop taking observations, and declares the decision on anomalous processes. The objective of the detection algorithm is to identify the anomalies with an accuracy exceeding the desired value while minimizing the delay in decision making. We devise a centralized algorithm where the processes are jointly selected by a common agent as well as a decentralized algorithm where the decision of whether to select a process is made independently for each process. Our algorithms rely on a Markov decision process defined using the marginal probability of each process being normal or anomalous, conditioned on the observations. We implement the detection algorithms using the deep actor-critic reinforcement learning framework. Unlike prior work on this topic that has exponential complexity in the number of processes, our algorithms have computational and memory requirements that are both polynomial in the number of processes. We demonstrate the efficacy of these algorithms using numerical experiments by comparing them with state-of-the-art methods.

In this paper, we address the anomaly detection problem where the objective is to find the anomalous processes among a given set of processes. To this end, the decision-making agent probes a subset of processes at every time instant and obtains a potentially erroneous estimate of the binary variable which indicates whether or not the corresponding process is anomalous. The agent continues to probe the processes until it obtains a sufficient number of measurements to reliably identify the anomalous processes. In this context, we develop a sequential selection algorithm that decides which processes to be probed at every instant to detect the anomalies with an accuracy exceeding a desired value while minimizing the delay in making the decision and the total number of measurements taken. Our algorithm is based on active inference which is a general framework to make sequential decisions in order to maximize the notion of free energy. We define the free energy using the objectives of the selection policy and implement the active inference framework using a deep neural network approximation. Using numerical experiments, we compare our algorithm with the state-of-the-art method based on deep actor-critic reinforcement learning and demonstrate the superior performance of our algorithm.

We address the problem of sequentially selecting and observing processes from a given set to find the anomalies among them. The decision-maker observes one process at a time and obtains a noisy binary indicator of whether or not the corresponding process is anomalous. In this setting, we develop an anomaly detection algorithm that chooses the process to be observed at a given time instant, decides when to stop taking observations, and makes a decision regarding the anomalous processes. The objective of the detection algorithm is to arrive at a decision with an accuracy exceeding a desired value while minimizing the delay in decision making. Our algorithm relies on a Markov decision process defined using the marginal probability of each process being normal or anomalous, conditioned on the observations. We implement the detection algorithm using the deep actor-critic reinforcement learning framework. Unlike prior work on this topic that has exponential complexity in the number of processes, our algorithm has computational and memory requirements that are both polynomial in the number of processes. We demonstrate the efficacy of our algorithm using numerical experiments by comparing it with the state-of-the-art methods.

In this paper, we study the conditions to be satisfied by a discrete-time linear system to ensure output controllability using sparse control inputs. A set of necessary and sufficient conditions can be directly obtained by extending the Kalman rank test for output controllability. However, the verification of these conditions is computationally heavy due to their combinatorial nature. Therefore, we derive non-combinatorial conditions for output sparse controllability which can be verified with polynomial time complexity. Our results also provide bounds on the minimum sparsity level required to ensure output controllability of the system. This additional insight is useful for designing sparse control input that drives the system to any desired output.

This paper considers a social network modeled as an Erdos Renyi random graph. Each individual in the network updates her opinion using the weighted average of the opinions of her neighbors. We explore how an external manipulative agent can drive the opinions of these individuals to a desired state with a limited additive influence on their innate opinions. We show that the manipulative agent can steer the network opinion to any arbitrary value in finite time (i.e., the system is controllable) almost surely when there is no restriction on her influence. However, when the control input is sparsity constrained, the network opinion is controllable with some probability. We lower bound this probability using the concentration properties of random vectors based on the Levy concentration function and small ball probabilities. Further, through numerical simulations, we compare the probability of controllability in Erdos Renyi graphs with that of power-law graphs to illustrate the key differences between the two models in terms of controllability. Our theoretical and numerical results shed light on how controllability of the network opinion depends on the parameters such as the size and the connectivity of the network, and the sparsity constraints faced by the manipulative agent.

This paper studies controllability of a discrete-time linear dynamical system using nonnegative and sparse inputs. These constraints on the control input arise naturally in many real-life systems where the external influence on the system is unidirectional, and activating each input node adds to the cost of control. We derive the necessary and sufficient conditions for controllability of the system, without imposing any constraints on the system matrices. Unlike the well-known Kalman rank based controllability criteria, the conditions presented in this paper can be verified in polynomial time, and the verification complexity is independent of the sparsity level. The proof of the result is based on the analytical tools concerning the properties of a convex cone. Our results also provide a closed-form expression for the minimum number of control nodes to be activated at every time instant to ensure controllability of the system using positive controls.

In this work, we consider the controllability of a discrete-time linear dynamical system with sparse control inputs. Sparsity constraints on the input arises naturally in networked systems, where activating each input variable adds to the cost of control. We derive algebraic necessary and sufficient conditions for ensuring controllability of a system with an arbitrary transfer matrix. The derived conditions can be verified in polynomial time complexity, unlike the more traditional Kalman-type rank tests. Further, we characterize the minimum number of input vectors required to satisfy the derived conditions for controllability. Finally, we present a generalized Kalman decomposition-like procedure that separates the state-space into subspaces corresponding to sparse-controllable and sparse-uncontrollable parts. These results form a theoretical basis for designing networked linear control systems with sparse inputs.