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With the pervasiveness of Stochastic Shortest-Path (SSP) problems in high-risk industries, such as last-mile autonomous delivery and supply chain management, robust planning algorithms are crucial for ensuring successful task completion while mitigating hazardous outcomes. Mainstream chance-constrained incremental sampling techniques for solving SSP problems tend to be overly conservative and typically do not consider the likelihood of undesirable tail events. We propose an alternative risk-aware approach inspired by the asymptotically-optimal Rapidly-Exploring Random Trees (RRT*) planning algorithm, which selects nodes along path segments with minimal Conditional Value-at-Risk (CVaR). Our motivation rests on the step-wise coherence of the CVaR risk measure and the optimal substructure of the SSP problem. Thus, optimizing with respect to the CVaR at each sampling iteration necessarily leads to an optimal path in the limit of the sample size. We validate our approach via numerical path planning experiments in a two-dimensional grid world with obstacles and stochastic path-segment lengths. Our simulation results show that incorporating risk into the tree growth process yields paths with lengths that are significantly less sensitive to variations in the noise parameter, or equivalently, paths that are more robust to environmental uncertainty. Algorithmic analyses reveal similar query time and memory space complexity to the baseline RRT* procedure, with only a marginal increase in processing time. This increase is offset by significantly lower noise sensitivity and reduced planner failure rates., Comment: Accepted for presentation at the 2024 IEEE Conference on Decision and Control (CDC)

Better fuel efficiency leads to better financial security as well as a cleaner environment. We propose a novel approach for improving fuel efficiency in unstructured and unregulated traffic environments. Existing intelligent transportation solutions for improving fuel efficiency, however, apply only to traffic intersections with sparse traffic or traffic where drivers obey the regulations, or both. We propose GameOpt+, a novel hybrid approach for cooperative intersection control in dynamic, multi-lane, unsignalized intersections. GameOpt+ is a hybrid solution that combines an auction mechanism and an optimization-based trajectory planner. It generates a priority entrance sequence for each agent and computes velocity controls in real-time, taking less than 10 milliseconds even in high-density traffic with over 10,000 vehicles per hour. Compared to fully optimization-based methods, it operates 100 times faster while ensuring fairness, safety, and efficiency. Tested on the SUMO simulator, our algorithm improves throughput by at least 25%, reduces the time to reach the goal by at least 70%, and decreases fuel consumption by 50% compared to auction-based and signaled approaches using traffic lights and stop signs. GameOpt+ is also unaffected by unbalanced traffic inflows, whereas some of the other baselines encountered a decrease in performance in unbalanced traffic inflow environments., Comment: Journal Version

We study feedback control of a dynamical process over a lossy channel equipped with a hybrid automatic repeat request protocol that connects a sensor to an actuator. The dynamical process is modeled by a Gauss-Markov process, and the lossy channel by a packet-erasure channel with ideal feedback. We suppose that data is communicated in the format of packets with negligible quantization error. In such a networked control system, whenever a packet loss occurs, there exists a tradeoff between transmitting new sensory information with a lower success probability and retransmitting previously failed sensory information with a higher success probability. In essence, an inherent tradeoff between freshness and reliability. To address this tradeoff, we consider a linear-quadratic-regulator performance index, which penalizes state deviations and control efforts over a finite horizon, and jointly design optimal policies for an encoder and a decoder, which are collocated with the sensor and the actuator, respectively. Our emphasis here lies specifically on designing switching and control policies, rather than error-correcting codes. We derive the structural properties of the optimal encoding and decoding policies. We show that the former is a threshold switching policy and the latter is a certainty-equivalent control policy. In addition, we specify the iterative equations that the encoder and the decoder need to solve in order to implement the optimal policies.

In network slicing, the network operator needs to satisfy the service level agreements of multiple slices at the same time and on the same physical infrastructure. To do so with reduced provisioned resources, the operator may consider resource sharing mechanisms. However, each slice then becomes susceptible to traffic surges in other slices which degrades performance isolation. To maintain both high efficiency and high isolation, we propose the introduction of hypothesis testing in resource sharing. Our approach comprises two phases. In the trial phase, the operator obtains a stochastic model for each slice that describes its normal behavior, provisions resources and then signs the service level agreements. In the regular phase, whenever there is resource contention, hypothesis testing is conducted to check which slices follow their normal behavior. Slices that fail the test are excluded from resource sharing to protect the well-behaved ones. We test our approach on a mobile traffic dataset. Results show that our approach fortifies the service level agreements against unexpected traffic patterns and achieves high efficiency via resource sharing. Overall, our approach provides an appealing tradeoff between efficiency and isolation.

In this chapter, we study the consistency of the value of information$\unicode{x2014}$a semantic metric that claims to determine the right piece of information in networked control systems tasks$\unicode{x2014}$in a lossy and delayed communication regime. Our analysis begins with a focus on state estimation, and subsequently extends to feedback control. To that end, we make a causal tradeoff between the packet rate and the mean square error. Associated with this tradeoff, we demonstrate the existence of an optimal policy profile, comprising a symmetric threshold scheduling policy based on the value of information for the encoder and a non-Gaussian linear estimation policy for the decoder. Our structural results assert that the scheduling policy is expressible in terms of $3d-1$ variables related to the source and the channel, where $d$ is the time delay, and that the estimation policy incorporates no residual related to signaling. We then construct an optimal control policy by exploiting the separation principle.

In this chapter, we present our recent invention, i.e., the notion of the value of information$\unicode{x2014}$a semantic metric that is fundamental for networked control systems tasks. We begin our analysis by formulating a causal tradeoff between the packet rate and the regulation cost, with an encoder and a decoder as two distributed decision makers, and show that the valuation of information is conceivable and quantifiable grounded on this tradeoff. More precisely, we characterize an equilibrium, and quantify the value of information there as the variation in a value function with respect to a piece of sensory measurement that can be communicated from the encoder to the decoder at each time. We prove that, in feedback control of a dynamical process over a noiseless channel, the value of information is a function of the discrepancy between the state estimates at the encoder and the decoder, and that a data packet containing a sensory measurement at each time should be exchanged only if the value of information at that time is nonnegative. Finally, we prove that the characterized equilibrium is in fact globally optimal.

In this chapter, we investigate the value of information as a more comprehensive instrument than the age of information for optimally shaping the information flow in a networked control system. In particular, we quantify the value of information based on the variation in a value function, and discuss the structural properties of this metric. Through our analysis, we establish the mathematical relation between the value of information and the age of information. We prove that the value of information is in general a function of an estimation discrepancy that depends on the age of information and the primitive variables. In addition, we prove that there exists a condition under which the value of information becomes completely expressible in terms of the age of information. Nonetheless, we show that this condition is not achievable without a degradation in the performance of the system.

Real-world scenarios are characterized by timing uncertainties, e.g., delays, and disturbances. Algorithms with temporal robustness are crucial in guaranteeing the successful execution of tasks and missions in such scenarios. We study time-robust path planning for synthesizing robots' trajectories that adhere to spatial-temporal specifications expressed in Signal Temporal Logic (STL). In contrast to prior approaches that rely on {discretize}d trajectories with fixed time steps, we leverage Piece-Wise Linear (PWL) signals for the synthesis. PWL signals represent a trajectory through a sequence of time-stamped waypoints. This allows us to encode the STL formula into a Mixed-Integer Linear Program (MILP) with fewer variables. This reduction is more pronounced for specifications with a long planning horizon. To that end, we define time-robustness for PWL signals. Subsequently, we propose quantitative semantics for PWL signals according to the recursive syntax of STL and prove their soundness. We then propose an encoding strategy to transform our semantics into a MILP. Our simulations showcase the soundness and the performance of our algorithm.

The need to satisfy the QoS requirements of multiple network slices deployed at the same base station poses a major challenge to network operators. The problem becomes even harder when the desired QoS involves packet delays. In that case, network utility maximization is not directly applicable since the utilities of the slices are unknown. As a result, most related works learn online the utilities of all slices and how to split the resources among them. Unfortunately, this approach does not scale well for many slices. Instead, it is needed to perform learning separately for each slice. To this end, we develop a bandwidth demand estimator; a network function that periodically receives as input the traffic of the slice and outputs the amount of bandwidth that its MAC scheduler needs to deliver the desired QoS. We develop the bandwidth demand estimator for QoS involving packet delay metrics based on a model-based reinforcement learning algorithm. We implement the algorithm on a cellular testbed and conduct experiments with time-varying traffic loads. Results show that the algorithm delivers the desired QoS but with significantly less bandwidth than non-adaptive approaches and other baseline online learning algorithms.

Safe overtaking, especially in a bidirectional mixed-traffic setting, remains a key challenge for Connected Autonomous Vehicles (CAVs). The presence of human-driven vehicles (HDVs), behavior unpredictability, and blind spots resulting from sensor occlusion make this a challenging control problem. To overcome these difficulties, we propose a cooperative communication-based approach that utilizes the information shared between CAVs to reduce the effects of sensor occlusion while benefiting from the local velocity prediction based on past tracking data. Our control framework aims to perform overtaking maneuvers with the objective of maximizing velocity while prioritizing safety and passenger comfort. Our method is also capable of reactively adjusting its plan to dynamic changes in the environment. The performance of the proposed approach is verified using realistic traffic simulations., Comment: Published in: 2022 IEEE 25th International Conference on Intelligent Transportation Systems (ITSC)

We consider the problem of safely coordinating ensembles of identical autonomous agents to conduct complex missions with conflicting safety requirements and under noisy control inputs. Using non-smooth control barrier functions (CBFs) and stochastic model-predictive control as springboards, and by adopting an extrinsic approach where the ensemble is treated as a unified dynamic entity, we devise a method to synthesize safety-aware control inputs for uncertain collectives. Drawing upon stochastic CBF theory and recent developments in Boolean CBF composition, our method proceeds by smoothing a Boolean-composed CBF and solving a stochastic optimization problem where each agent's forcing term is restricted to the affine subspace of control inputs certified by the combined CBF. For the smoothing step, we employ a polynomial approximation scheme, providing evidence for its advantage in generating more conservative yet sufficiently-filtered control inputs than the smoother but more aggressive equivalents produced from an approximation technique based on the log-sum-exp function. To further demonstrate the utility of the proposed method, we present an upper bound for the expected CBF approximation error, along with results from simulations of a single-integrator collective under velocity perturbations. Lastly, we compare these results with those obtained using a naive state-feedback controller lacking safety filters., Comment: Accepted to the 2024 European Control Conference. See Section VI.B (in particular, Theorem 1, Proposition 2, and Remark 2) for updates incorporating new results (from Reference 3) on almost-sure safety of ZCBFs

Humans have the ability to deviate from their natural behavior when necessary, which is a cognitive process called response inhibition. Similar approaches have independently received increasing attention in recent years for ensuring the safety of control. Realized using control barrier functions or predictive safety filters, these approaches can effectively ensure the satisfaction of state constraints through an online adaptation of nominal control laws, e.g., obtained through reinforcement learning. While the focus of these realizations of inhibitory control has been on risk-neutral formulations, human studies have shown a tight link between response inhibition and risk attitude. Inspired by this insight, we propose a flexible, risk-sensitive method for inhibitory control. Our method is based on a risk-aware condition for value functions, which guarantees the satisfaction of state constraints. We propose a method for learning these value functions using common techniques from reinforcement learning and derive sufficient conditions for its success. By enforcing the derived safety conditions online using the learned value function, risk-sensitive inhibitory control is effectively achieved. The effectiveness of the developed control scheme is demonstrated in simulations., Comment: The 62nd IEEE Conference on Decision and Control, Dec. 13-15, 2023, Singapore

We propose a risk-aware crash mitigation system (RCMS), to augment any existing motion planner (MP), that enables an autonomous vehicle to perform evasive maneuvers in high-risk situations and minimize the severity of collision if a crash is inevitable. In order to facilitate a smooth transition between RCMS and MP, we develop a novel activation mechanism that combines instantaneous as well as predictive collision risk evaluation strategies in a unified hysteresis-band approach. For trajectory planning, we deploy a modular receding horizon optimization-based approach that minimizes a smooth situational risk profile, while adhering to the physical road limits as well as vehicular actuator limits. We demonstrate the performance of our approach in a simulation environment., Comment: Presented at the 26th IEEE International Conference on Intelligent Transportation Systems (ITSC) 2023, Bilbao, Bizkaia, Spain

In the typical multiagent formation tracking problem centered on consensus, the prevailing assumption in the literature is that the agents' nonlinear models can be approximated by integrator systems, by their feedback-linearized equivalents, or by dynamics composed of deterministic linear and nonlinear terms. The resulting approaches associated with such assumptions, however, are hardly applicable to general nonlinear systems. To this end, we present consensus-based control laws for multiagent formation tracking in finite-dimensional state space, with the agents represented by a more general class of dynamics: control-affine nonlinear systems. The agents also exchange information via a leader-follower communication topology modeled as an undirected and connected graph with a single leader node. By leveraging standard tools from algebraic graph theory and Lyapunov analysis, we first derive a locally asymptotically stabilizing formation tracking law. Next, to demonstrate the effectiveness of our approach, we present results from numerical simulations of an example in robotics. These results -- together with a comparison of the formation errors obtained with our approach and those realized via an optimization-based method -- further validate our theoretical propositions., Comment: To appear in the proceedings of the 9th International Conference on Control, Decision, and Information Technologies (CoDIT)

The split delivery vehicle routing problem (SDVRP) is a relaxed variant of the capacitated vehicle routing problem (CVRP) where the restriction that each customer is visited precisely once is removed. Compared with CVRP, the SDVRP allows a reduction in the cost of the routes traveled by vehicles. The exact methods to solve the SDVRP are computationally expensive. Moreover, the complexity and difficult implementation of the state-of-the-art heuristic approaches hinder their application in real-life scenarios of the SDVRP. In this paper, we propose an easily understandable and effective approach to solve the SDVPR based on an a priori adaptive splitting algorithm (PASA). The idea of a priori split strategy was first introduced in Chen et al. (2017). In this approach, the demand of the customers is split into smaller values using a fixed splitting rule in advance. Consequently, the original SDVRP instance is converted to a CVRP instance which is solved using an existing CVRP solver. While the proposed a priori splitting rule in Chen et al. (2017) is fixed for all customers regardless of their demand and location, we suggest an adaptive splitting rule that takes into account the distance of the customers to the depot and their demand values. Our experiments show that PASA can generate solutions comparable to the state-of-the-art but much faster. Furthermore, our algorithm outperforms the fixed a priori splitting rule proposed by Chen et al. (2017).

Distributed massive MIMO networks are envisioned to realize cooperative multi-point transmission in next-generation wireless systems. For efficient cooperative hybrid beamforming, the cluster of access points (APs) needs to obtain precise estimates of the uplink channel to perform reliable downlink precoding. However, due to the radio frequency (RF) impairments between the transceivers at the two en-points of the wireless channel, full channel reciprocity does not hold which results in performance degradation in the cooperative hybrid beamforming (CHBF) unless a suitable reciprocity calibration mechanism is in place. We propose a two-step approach to calibrate any two hybrid nodes in the distributed MIMO system. We then present and utilize the novel concept of reciprocal tandem to propose a low-complexity approach for jointly calibrating the cluster of APs and estimating the downlink channel. Finally, we validate our calibration technique's effectiveness through numerical simulation.

Low-complexity estimation and correction of carrier frequency offset (CFO) are essential in orthogonal frequency division multiplexing (OFDM). In this paper, we propose a low-overhead blind CFO estimation technique based on cyclic prefix (CP), in multi-input multi-output (MIMO)-OFDM systems. We propose to use antenna diversity for CFO estimation. Given that the RF chains for all antenna elements at a communication node share the same clock, the carrier frequency offset (CFO) between two points may be estimated by using the combination of the received signal at all antennas. We improve our method by combining the antenna diversity with time diversity by considering the CP for multiple OFDM symbols. We provide a closed-form expression for CFO estimation and present algorithms that can considerably improve the CFO estimation performance at the expense of a linear increase in computational complexity. We validate the effectiveness of our estimation scheme via extensive numerical analysis., Comment: To Appear in Proceedings of IEEE Globecom 2023

In this work, we study the inverse problem of identifying complex flocking dynamics in a domain cluttered with obstacles. We get inspiration from animal flocks moving in complex ways with capabilities far beyond what current robots can do. Owing to the difficulty of observing and recovering the trajectories of the agents, we focus on the dynamics of their probability densities, which are governed by partial differential equations (PDEs), namely compressible Euler equations subject to non-local forces. We formulate the inverse problem of learning interactions as a PDE-constrained optimization problem of minimizing the squared Hellinger distance between the histogram of the flock and the distribution associated to our PDEs. The numerical methods used to efficiently solve the PDE-constrained optimization problem are described. Realistic flocking data are simulated using the Boids model of flocking agents, which differs in nature from the reconstruction models used in our PDEs. Our analysis and simulated experiments show that the behavior of cohesive flocks can be recovered accurately with approximate PDE solutions., Comment: 6 pages, 5 figures, submitted to IEEE CDC 2023

Network slicing enables the deployment of multiple dedicated virtual sub-networks, i.e. slices on a shared physical infrastructure. Unlike traditional one-size-fits-all resource provisioning schemes, each network slice (NS) in 5G is tailored to the specific service requirements of a group of customers. An end-to-end (E2E) mobile NS orchestration requires the simultaneous provisioning of computing, storage, and networking resources across the core network (CN) and the radio access network (RAN). Constant temporospatial changes in mobile user demand profiles further complicate the E2E NSs resource provisioning beyond the limits of the existing best-effort schemes that are only effective under accurate demand forecasts for all slices. This paper proposes a practical two-time-scale resource provisioning framework for E2E network slicing under demand uncertainty. At each macro-scale instance, we assume that only the spatial probability distribution of the NS demands is available. We formulate the NSs resource allocation problem as a stochastic mixed integer program (SMIP) with the objective of minimizing the total resource cost at the CN and the RAN. At each microscale instance, utilizing the exact slice demand profiles, a linear program is solved to jointly minimize the unsupported traffic and the resource cost at the RAN. We verify the effectiveness of our resource allocation scheme through numerical experiments.

We consider the tradeoff between resource efficiency and performance isolation that emerges when multiplexing the resource demands of Network Slices (NSs). On the one hand, multiplexing allows the use of idle resources, which increases resource efficiency. On the other hand, the performance of each NS becomes susceptible to traffic surges in other NSs, which degrades performance isolation. The analysis of this tradeoff enables network operators to determine the effect of performance isolation on the operating cost of each NS. To study the tradeoff, we solve an optimization problem where we find the multiplexing policy that requires the least provisioned resources to honor the Service Level Agreements (SLAs) of all NSs. The SLA of each NS i states that its resource demand should be met for $P^H_i$ fraction of time, and for $P^L_i \leq P^H_i$ fraction of time, it should be met regardless of the demands of other NSs. For resource demands that follow ergodic Markov chains, we show that the well-known Max-Weight scheduler is an optimal multiplexing policy. Since the Max-Weight scheduler does not require any knowledge of the statistics of the resource demands, we also propose its use in non-markovian settings. For resource demands obtained in the LTE module of ns-3, we show that the Max-Weight scheduler reduces the provisioned bandwidth by 36.2% when no performance isolation is required. Lastly, for these non-markovian resource demands, the Max-Weight scheduler maintains its optimality since it requires as much provisioned bandwidth as the best non-causal scheduler.

This paper proposes a hierarchical autonomous vehicle navigation architecture, composed of a high-level speed and lane advisory system (SLAS) coupled with low-level trajectory generation and trajectory following modules. Specifically, we target a multi-lane highway driving scenario where an autonomous ego vehicle navigates in traffic. We propose a novel receding horizon mixed-integer optimization based method for SLAS with the objective to minimize travel time while accounting for passenger comfort. We further incorporate various modifications in the proposed approach to improve the overall computational efficiency and achieve real-time performance. We demonstrate the efficacy of the proposed approach in contrast to the existing methods, when applied in conjunction with state-of-the-art trajectory generation and trajectory following frameworks, in a CARLA simulation environment., Comment: Presented at the IEEE 61st Conference on Decision and Control (CDC), Cancun, Mexico, 2022

Highway vehicular traffic is an inherently multi-agent problem. Traffic jams can appear and disappear mysteriously. We develop a method for traffic flow control that is applied at the vehicular level via mean-field games. We begin this work with a microscopic model of vehicles subject to control input, disturbances, noise, and a speed limit. We formulate a discounted-cost infinite-horizon robust mean-field game on the vehicles, and obtain the associated dynamic programming (DP) PDE system. We then perform approximate dynamic programming (ADP) using these equations to obtain a sub-optimal control for the traffic density adaptively. The sub-optimal controls are subject to an ODE-PDE system. We show that the ADP ODE-PDE system has a unique weak solution in a suitable Hilbert space using semigroup and successive approximation methods. We additionally give a numerical simulation, and interpret the results., Comment: 42 pages, 5 figures

Non-geostationary (NGSO) satellite communications systems have attracted a lot of attention both from industry and academia, over the past several years. Beam placement is among the major resource allocation problems in multi-beam NGSO systems. In this paper, we formulate the beam placement problem as a Euclidean disk cover optimization model. We aim at minimizing the number of placed beams while satisfying the total downlink traffic demand of targeted ground terminals without exceeding the capacity of the placed beams. We present a low-complexity deterministic annealing (DA)-based algorithm to solve the NP-hard optimization model for near-optimal solutions. We further propose an extended variant of the previous model to ensure the traffic assigned to the beams is balanced. We verify the effectiveness of our proposed methods by means of numerical experiments and show that our scheme is superior to the state-of-the-art methods in that it covers the ground users by fewer number of beams on average.

In this paper, we present a distributed optimal multiagent control scheme for quadrotor formation tracking under localization errors. Our control architecture is based on a leader-follower approach, where a single leader quadrotor tracks a desired trajectory while the followers maintain their relative positions in a triangular formation. We begin by modeling the quadrotors as particles in the YZ-plane evolving under dynamics with uncertain state information. Next, by formulating the formation tracking task as an optimization problem -- with a constraint-augmented Lagrangian subject to dynamic constraints -- we solve for the control law that leads to an optimal solution in the control and trajectory error cost-minimizing sense. Results from numerical simulations show that for the planar quadrotor model considered -- with uncertainty in sensor measurements modeled as Gaussian noise -- the resulting optimal control is able to drive each agent to achieve the desired global objective: leader trajectory tracking with formation maintenance. Finally, we evaluate the performance of the control law using the tracking and formation errors of the multiagent system., Comment: 6 pages, 7 figures

While reinforcement learning has shown experimental success in a number of applications, it is known to be sensitive to noise and perturbations in the parameters of the system, leading to high variance in the total reward amongst different episodes in slightly different environments. To introduce robustness, as well as sample efficiency, risk-sensitive reinforcement learning methods are being thoroughly studied. In this work, we provide a definition of robust reinforcement learning policies and formulate a risk-sensitive reinforcement learning problem to approximate them, by solving an optimization problem with respect to a modified objective based on exponential criteria. In particular, we study a model-free risk-sensitive variation of the widely-used Monte Carlo Policy Gradient algorithm and introduce a novel risk-sensitive online Actor-Critic algorithm based on solving a multiplicative Bellman equation using stochastic approximation updates. Analytical results suggest that the use of exponential criteria generalizes commonly used ad-hoc regularization approaches, improves sample efficiency, and introduces robustness with respect to perturbations in the model parameters and the environment. The implementation, performance, and robustness properties of the proposed methods are evaluated in simulated experiments.

Hierarchical learning algorithms that gradually approximate a solution to a data-driven optimization problem are essential to decision-making systems, especially under limitations on time and computational resources. In this study, we introduce a general-purpose hierarchical learning architecture that is based on the progressive partitioning of a possibly multi-resolution data space. The optimal partition is gradually approximated by solving a sequence of optimization sub-problems that yield a sequence of partitions with increasing number of subsets. We show that the solution of each optimization problem can be estimated online using gradient-free stochastic approximation updates. As a consequence, a function approximation problem can be defined within each subset of the partition and solved using the theory of two-timescale stochastic approximation algorithms. This simulates an annealing process and defines a robust and interpretable heuristic method to gradually increase the complexity of the learning architecture in a task-agnostic manner, giving emphasis to regions of the data space that are considered more important according to a predefined criterion. Finally, by imposing a tree structure in the progression of the partitions, we provide a means to incorporate potential multi-resolution structure of the data space into this approach, significantly reducing its complexity, while introducing hierarchical variable-rate feature extraction properties similar to certain classes of deep learning architectures. Asymptotic convergence analysis and experimental results are provided for supervised and unsupervised learning problems.

In this work, we introduce a learning model designed to meet the needs of applications in which computational resources are limited, and robustness and interpretability are prioritized. Learning problems can be formulated as constrained stochastic optimization problems, with the constraints originating mainly from model assumptions that define a trade-off between complexity and performance. This trade-off is closely related to over-fitting, generalization capacity, and robustness to noise and adversarial attacks, and depends on both the structure and complexity of the model, as well as the properties of the optimization methods used. We develop an online prototype-based learning algorithm based on annealing optimization that is formulated as an online gradient-free stochastic approximation algorithm. The learning model can be viewed as an interpretable and progressively growing competitive-learning neural network model to be used for supervised, unsupervised, and reinforcement learning. The annealing nature of the algorithm contributes to minimal hyper-parameter tuning requirements, poor local minima prevention, and robustness with respect to the initial conditions. At the same time, it provides online control over the performance-complexity trade-off by progressively increasing the complexity of the learning model as needed, through an intuitive bifurcation phenomenon. Finally, the use of stochastic approximation enables the study of the convergence of the learning algorithm through mathematical tools from dynamical systems and control, and allows for its integration with reinforcement learning algorithms, constructing an adaptive state-action aggregation scheme., Comment: arXiv admin note: text overlap with arXiv:2102.05836

In this letter, we investigate the problem of actuator scheduling for networked control systems. Given a stochastic linear system with a number of actuators, we consider the case that one actuator is activated at each time. This problem is combinatorial in nature and NP hard to solve. We propose a convex relaxation to the actuator scheduling problem, and use its solution as a reference to design an algorithm for solving the original scheduling problem. Using dynamic programming arguments, we provide a suboptimality bound of our proposed algorithm. Furthermore, we show that our framework can be extended to incorporate multiple actuators scheduling at each time and actuation costs. A simulation example is provided, which shows that our proposed method outperforms a random selection approach and a greedy selection approach., Comment: 8 pages, 4 figures

We propose GameOpt: a novel hybrid approach to cooperative intersection control for dynamic, multi-lane, unsignalized intersections. Safely navigating these complex and accident prone intersections requires simultaneous trajectory planning and negotiation among drivers. GameOpt is a hybrid formulation that first uses an auction mechanism to generate a priority entrance sequence for every agent, followed by an optimization-based trajectory planner that computes velocity controls that satisfy the priority sequence. This coupling operates at real-time speeds of less than 10 milliseconds in high density traffic of more than 10,000 vehicles/hr, 100 times faster than other fully optimization-based methods, while providing guarantees in terms of fairness, safety, and efficiency. Tested on the SUMO simulator, our algorithm improves throughput by at least 25%, time taken to reach the goal by 75%, and fuel consumption by 33% compared to auction-based approaches and signaled approaches using traffic-lights and stop signs., Comment: Submitted to ITSC 2022

To overcome the high path-loss and the intense shadowing in millimeter-wave (mmWave) communications, effective beamforming schemes are required which incorporate narrow beams with high beamforming gains. The mmWave channel consists of a few spatial clusters each associated with an angle of departure (AoD). The narrow beams must be aligned with the channel AoDs to increase the beamforming gain. This is achieved through a procedure called beam alignment (BA). Most of the BA schemes in the literature consider channels with a single dominant path while in practice the channel has a few resolvable paths with different AoDs, hence, such BA schemes may not work correctly in the presence of multi-path or at the least do not exploit such multipath to achieve diversity or increase robustness. In this paper, we propose an efficient BA scheme in presence of multi-path. The proposed BA scheme transmits probing packets using a set of scanning beams and receives feedback for all the scanning beams at the end of the probing phase from each user. We formulate the BA scheme as minimizing the expected value of the average transmission beamwidth under different policies. The policy is defined as a function from the set of received feedback to the set of transmission beams (TB). In order to maximize the number of possible feedback sequences, we prove that the set of scanning beams (SB) has a special form, namely, Tulip Design. Consequently, we rewrite the minimization problem with a set of linear constraints and a reduced number of variables which is solved by using an efficient greedy algorithm., Comment: Accepted IEEE CISS 2022

In pursuance of the unused spectrum in higher frequencies, millimeter wave (mmWave) bands have a pivotal role. However, the high path-loss and poor scattering associated with mmWave communications highlight the necessity of employing effective beamforming techniques. In order to efficiently search for the beam to serve a user and to jointly serve multiple users it is often required to use a composite beam which consists of multiple disjoint lobes. A composite beam covers multiple desired angular coverage intervals (ACIs) and ideally has maximum and uniform gain (smoothness) within each desired ACI, negligible gain (leakage) outside the desired ACIs, and sharp edges. We propose an algorithm for designing such ideal composite codebook by providing an analytical closed-form solution with low computational complexity. There is a fundamental trade-off between the gain, leakage and smoothness of the beams. Our design allows to achieve different values in such trade-off based on changing the design parameters. We highlight the shortcomings of the uniform linear arrays (ULAs) in building arbitrary composite beams. Consequently, we use a recently introduced twin-ULA (TULA) antenna structure to effectively resolve these inefficiencies. Numerical results are used to validate the theoretical findings., Comment: Accepted at IEEE WCNC 2022

We consider the problem of understanding the coordinated movements of biological or artificial swarms. In this regard, we propose a learning scheme to estimate the coordination laws of the interacting agents from observations of the swarm's density over time. We describe the dynamics of the swarm based on pairwise interactions according to a Cucker-Smale flocking model, and express the swarm's density evolution as the solution to a system of mean-field hydrodynamic equations. We propose a new family of parametric functions to model the pairwise interactions, which allows for the mean-field macroscopic system of integro-differential equations to be efficiently solved as an augmented system of PDEs. Finally, we incorporate the augmented system in an iterative optimization scheme to learn the dynamics of the interacting agents from observations of the swarm's density evolution over time. The results of this work can offer an alternative approach to study how animal flocks coordinate, create new control schemes for large networked systems, and serve as a central part of defense mechanisms against adversarial drone attacks.

The existence of a universal learning architecture in human cognition is a widely spread conjecture supported by experimental findings from neuroscience. While no low-level implementation can be specified yet, an abstract outline of human perception and learning is believed to entail three basic properties: (a) hierarchical attention and processing, (b) memory-based knowledge representation, and (c) progressive learning and knowledge compaction. We approach the design of such a learning architecture from a system-theoretic viewpoint, developing a closed-loop system with three main components: (i) a multi-resolution analysis pre-processor, (ii) a group-invariant feature extractor, and (iii) a progressive knowledge-based learning module. Multi-resolution feedback loops are used for learning, i.e., for adapting the system parameters to online observations. To design (i) and (ii), we build upon the established theory of wavelet-based multi-resolution analysis and the properties of group convolution operators. Regarding (iii), we introduce a novel learning algorithm that constructs progressively growing knowledge representations in multiple resolutions. The proposed algorithm is an extension of the Online Deterministic Annealing (ODA) algorithm based on annealing optimization, solved using gradient-free stochastic approximation. ODA has inherent robustness and regularization properties and provides a means to progressively increase the complexity of the learning model i.e. the number of the neurons, as needed, through an intuitive bifurcation phenomenon. The proposed multi-resolution approach is hierarchical, progressive, knowledge-based, and interpretable. We illustrate the properties of the proposed architecture in the context of the state-of-the-art learning algorithms and deep learning methods., Comment: arXiv admin note: text overlap with arXiv:2102.05836

Historically, traffic modelling approaches have taken either a particle-like (microscopic) approach, or a gas-like (meso- or macroscopic) approach. Until recently with the introduction of mean-field games to the controls community, there has not been a rigorous framework to facilitate passage between controls for the microscopic models and the macroscopic models. We begin this work with a particle-based model of autonomous vehicles subject to drag and unknown disturbances, noise, and a speed limit in addition to the control. We formulate a robust stochastic differential game on the particles. We pass formally to the infinite-particle limit to obtain a robust mean-field game PDE system. We solve the mean-field game PDE system numerically and discuss the results. In particular, we obtain an optimal control which increases the bulk velocity of the traffic flow while reducing congestion., Comment: Omission of a line corrected in this version. 6 pages; 3 figures; 1 algorithm; Submitted to ACC 2022

Euler alignment systems appear as hydrodynamic limits of interacting self-propelled particle systems such as the (generalized) Cucker-Smale model. In this work, we study weak solutions to an Euler alignment system on smooth, bounded, connected domains. This particular Euler alignment system includes singular alignment, attraction, and repulsion interaction kernels which correspond to a Yukawa potential. We also include a confinement potential and self-propulsion. We embed the problem into an abstract Euler system to conclude that infinitely many weak solutions exist. We further show that we can construct solutions satisfying bounds on an energy quantity, and that the solutions satisfy a weak-strong uniqueness principle. Finally, we present an addition of leader-agents governed by controlled ODEs, and modification of the interactions to be Bessel potentials of fractional order $s > 2$., Comment: 32 pages

We consider the classical sensor scheduling problem for linear systems where only one sensor is activated at each time. We show that the sensor scheduling problem has a close relation to the sensor design problem and the solution of a sensor schedule problem can be extracted from an equivalent sensor design problem. We propose a convex relaxation to the sensor design problem and a reference covariance trajectory is obtained from solving the relaxed sensor design problem. Afterwards, a covariance tracking algorithm is designed to obtain an approximate solution to the sensor scheduling problem using the reference covariance trajectory obtained from the sensor design problem. While the sensor scheduling problem is NP-hard, the proposed framework circumvents this computational complexity by decomposing this problem into a convex sensor design problem and a covariance tracking problem. We provide theoretical justification and a sub-optimality bound for the proposed method using dynamic programming. The proposed method is validated over several experiments portraying the efficacy of the framework., Comment: To appear in Automatica

SDN-enabled Integrated satellite-terrestrial networks (ISTNs), can provide several advantages including global seamless coverage, high reliability, low latency, etc. and can be a key enabler towards next generation networks. To deal with the complexity of the control and management of the integrated network, leveraging the concept of software-defined networking (SDN) will be helpful. In this regard, the SDN controller placement problem in SDN-enabled ISTNs becomes of paramount importance. In this paper, we formulate an optimization problem for the SDN controller placement with the objective of minimizing the average failure probability of SDN control paths to ensure the SDN switches receive the instructions in the most reliable fashion. Simultaneously, we aim at deploying the SDN controllers close to the satellite gateways to ensure the connection between the two layers occurs with the lowest latency. We first model the problem as a mixed integer linear program (MILP). To reduce the time complexity of the MILP model, we use submodular optimization techniques to generate near-optimal solutions in a time-efficient manner. Finally, we verify the effectiveness of our approach by means of simulation, showing that the approximation method results in a reasonable optimality gap with respect to the exact MILP solution., Comment: Accepted at IEEE Globecom 2021. arXiv admin note: substantial text overlap with arXiv:2103.08735

With the increasing scale, complexity, and heterogeneity of the next generation networked systems, seamless control, management, and security of such systems becomes increasingly challenging. Many diverse applications have driven interest in networked systems, including large-scale distributed learning, multi-agent optimization, 5G service provisioning, and network slicing, etc. In this paper, we propose trust as a measure to evaluate the status of network agents and improve the decision-making process. We interpret trust as a relation among entities that participate in various protocols. Trust relations are based on evidence created by the interactions of entities within a protocol and may be a composite of multiple metrics such as availability, reliability, resilience, etc. depending on application context. We first elaborate on the importance of trust as a metric and then present a mathematical framework for trust computation and aggregation within a network. Then we show in practice, how trust can be integrated into network decision-making processes by presenting two examples. In the first example, we show how utilizing the trust evidence can improve the performance and the security of Federated Learning. Second, we show how a 5G network resource provisioning framework can be improved when augmented with a trust-aware decision-making scheme. We verify the validity of our trust-based approach through simulations. Finally, we explain the challenges associated with aggregating the trust evidence and briefly explain our ideas to tackle them.

In this paper, we study the trade-off between the transmission cost and the control performance of the multi-loop networked control system subject to network-induced delay. Within the linear-quadratic-Gaussian (LQG) framework, the joint design of control policy and networking strategy is decomposed into separation optimization problems. Based on the trade-off analysis, a scalable, delay-dependent Value-of-Information (VoI) based scheduling policy is constructed to quantify the value of transmitting the data packet, and enables the decision-makers embedded in subsystems to determine the transmission policy. The proposed scalable VoI inherits the task criticality of the previous VoI metric meanwhile is sensitive to the system parameters such as information freshness and network delays. The VoI-based scheduling policy is proved to outperform the periodical triggering policy and existing Age-of-Information (AoI) based policy for network control system under transmission delay. The effectiveness of the constructed VoI with arbitrary network delay is validated through numerical simulations., Comment: accepted CDC2021

The rate-regulation tradeoff, defined between two objective functions, one penalizing the packet rate and one the regulation cost, can express the fundamental performance bound of networked control systems. However, the characterization of the set of globally optimal solutions in this tradeoff for multi-dimensional Gauss-Markov processes has been an open problem. In the present article, we characterize a policy profile that belongs to this set without imposing any restrictions on the information structure or the policy structure. We prove that such a policy profile consists of a symmetric threshold triggering policy based on the value of information and a certainty-equivalent control policy based on a non-Gaussian linear estimator. These policies are deterministic and can be designed separately. Besides, we provide a global optimality analysis for the value of information $\text{VoI}_k$, a semantic metric that emerges from the rate-regulation tradeoff as the difference between the benefit and the cost of a data packet. We prove that it is globally optimal that a data packet containing sensory information at time $k$ be transmitted to the controller only if $\text{VoI}_k$ becomes nonnegative. These results have important implications in the areas of communication and control., Comment: arXiv admin note: text overlap with arXiv:1812.07534

Several challenging optimization problems arise while considering the deployment of the space-air-ground integrated networks (SAGINs), among which the optimal satellite gateway deployment problem is of significant importance. Moreover, with the increasing interest in the software-defined integration of 5G networks and satellites, the existence of an effective scheme for optimal placement of SDN controllers is essential. In this paper, we discuss the interrelation between the two problems above and propose suitable methods to solve them under various network design criteria. We first provide a MILP model for solving the joint problem, and then motivate the decomposition of the model into two disjoint MILPs. We then show that the resulting problems can be modeled as the optimization of submodular set functions and can be solved efficiently with provable optimality gaps.

We propose a family of compactly supported parametric interaction functions in the general Cucker-Smale flocking dynamics such that the mean-field macroscopic system of mass and momentum balance equations with non-local damping terms can be converted from a system of partial integro-differential equations to an augmented system of partial differential equations in a compact set. We treat the interaction functions as Green's functions for an operator corresponding to a semi-linear Poisson equation and compute the density and momentum in a translating reference frame, i.e. one that is taken in reference to the flock's centroid. This allows us to consider the dynamics in a fixed, flock-centered compact set without loss of generality. We approach the computation of the non-local damping using the standard finite difference treatment of the chosen differential operator, resulting in a tridiagonal system which can be solved quickly.

Inherent in virtually every iterative machine learning algorithm is the problem of hyper-parameter tuning, which includes three major design parameters: (a) the complexity of the model, e.g., the number of neurons in a neural network, (b) the initial conditions, which heavily affect the behavior of the algorithm, and (c) the dissimilarity measure used to quantify its performance. We introduce an online prototype-based learning algorithm that can be viewed as a progressively growing competitive-learning neural network architecture for classification and clustering. The learning rule of the proposed approach is formulated as an online gradient-free stochastic approximation algorithm that solves a sequence of appropriately defined optimization problems, simulating an annealing process. The annealing nature of the algorithm contributes to avoiding poor local minima, offers robustness with respect to the initial conditions, and provides a means to progressively increase the complexity of the learning model, through an intuitive bifurcation phenomenon. The proposed approach is interpretable, requires minimal hyper-parameter tuning, and allows online control over the performance-complexity trade-off. Finally, we show that Bregman divergences appear naturally as a family of dissimilarity measures that play a central role in both the performance and the computational complexity of the learning algorithm.

A framework for the event-triggered control synthesis under signal temporal logic (STL) tasks is proposed. In our previous work, a continuous-time feedback control law was designed, using the prescribed performance control technique, to satisfy STL tasks. We replace this continuous-time feedback control law by an event-triggered controller. The event-triggering mechanism is based on a maximum triggering interval and on a norm bound on the difference between the value of the current state and the value of the state at the last triggering instance. Simulations of a multi-agent system quantitatively show the efficacy of using an event-triggered controller to reduce communication and computation efforts., Comment: Conference on Decision and Control (2018), 6 pages

Unmanned Aerial Vehicles (UAVs) have been extensively utilized to provide wireless connectivity in rural and under-developed areas, enhance network capacity and provide support for peaks or unexpected surges in user demand, mainly due to their fast deployment, cost-efficiency and superior communication performance resulting from Line of Sight (LoS)-dominated wireless channels. In order to exploit the benefits of UAVs as base stations or relays in a mobile network, a major challenge is to determine the optimal UAV placement and relocation strategy with respect to the mobility and traffic patterns of the ground network nodes. Moreover, considering that the UAVs form a multi-hop aerial network, capacity and connectivity constraints have significant impacts on the end-to-end network performance. To this end, we formulate the joint UAV placement and routing problem as a Mixed Integer Linear Program (MILP) and propose an approximation that leads to a LP rounding algorithm and achieves a balance between time-complexity and optimality., Comment: 15 Pages, Accepted at ADHOCNETS2020

With the emergence of network function virtualization (NFV), and software-defined networking (SDN), the realization and implementation of service function chains (SFCs) have become much easier. An SFC is an ordered set of interconnected virtual network functions (VNFs). NFV allows for decoupling the network functions from proprietary hardware realizing a software-based implementation of VNFs on commodity hardware and SDN decouples the network control from its forwarding logic allowing for a more flexible and programmable traffic routing among the VNFs. The SFC embedding problem (i.e. placement of SFCs on a shared substrate and establishing the corresponding traffic routes between the VNFs), has been extensively studied in the literature. In this paper, we extend a previous work on trust-aware service chain embedding with generalizing the role of trust by incorporating the trustworthiness of the service network links and substrate network paths into the SFC embedding decision process. We first introduce and formulate the path-based trust-aware service chain embedding problem as a mixed integer-linear program (MILP), and then provide an approximate model-based on selecting k-shortest candidate substrate paths for hosting each virtual link, to reduce the complexity of the model. We validate the performance of our methods through simulations and conduct a discussion on evaluating the methods and some operation trade-offs., Comment: 6 pages, Accepted at IEEE NFV-SDN 2020

In the operation of networked control systems, where multiple processes share a resource-limited and time-varying cost-sensitive network, communication delay is inevitable and primarily influenced by, first, the control systems deploying intermittent sensor sampling to reduce the communication cost by restricting non-urgent transmissions, and second, the network performing resource management to minimize excessive traffic and eventually data loss. In a heterogeneous scenario, where control systems may tolerate only specific levels of sensor-to-controller latency, delay sensitivities need to be considered in the design of control and network policies to achieve the desired performance guarantees. We propose a cross-layer optimal co-design of control, sampling and resource management policies for an NCS consisting of multiple stochastic linear time-invariant systems which close their sensor-to-controller loops over a shared network. Aligned with advanced communication technology, we assume that the network offers a range of latency-varying transmission services for given prices. Local samplers decide either to pay higher cost to access a low-latency channel, or to delay sending a state sample at a reduced price. A resource manager residing in the network data-link layer arbitrates channel access and re-allocates resources if link capacities are exceeded. The performance of the local closed-loop systems is measured by a combination of linear-quadratic Gaussian cost and a suitable communication cost, and the overall objective is to minimize a defined social cost by all three policy makers. We derive optimal control, sampling and resource allocation policies under different cross-layer awareness models, including constant and time-varying parameters, and show that higher awareness generally leads to performance enhancement at the expense of higher computational complexity.