We study optimal proportional feedback controllers for spatially invariant systems when the controller has access to delayed state measurements received from different spatial locations. We analyze how delays affect the spatial locality of the optimal feedback gain leveraging the problem decoupling in the spatial frequency domain. For the cases of expensive control and small delay, we provide exact expressions of the optimal controllers in the limit for infinite control weight and vanishing delay, respectively. In the expensive control regime, the optimal feedback control law decomposes into a delay-aware filtering of the delayed state and the optimal controller in the delay-free setting. Under small delays, the optimal controller is a perturbation of the delay-free one which depends linearly on the delay. We illustrate our analytical findings with a reaction-diffusion process over the real line and a multi-agent system coupled through circulant matrices, showing that delays reduce the effectiveness of optimal feedback control and may require each subsystem within a distributed implementation to communicate with farther-away locations.

In this paper, we address two practical challenges of distributed learning in multi-agent network systems, namely personalization and resilience. Personalization is the need of heterogeneous agents to learn local models tailored to their own data and tasks, while still generalizing well; on the other hand, the learning process must be resilient to cyberattacks or anomalous training data to avoid disruption. Motivated by a conceptual affinity between these two requirements, we devise a distributed learning algorithm that combines distributed gradient descent and the Friedkin-Johnsen model of opinion dynamics to fulfill both of them. We quantify its convergence speed and the neighborhood that contains the final learned models, which can be easily controlled by tuning the algorithm parameters to enforce a more personalized/resilient behavior. We numerically showcase the effectiveness of our algorithm on synthetic and real-world distributed learning tasks, where it achieves high global accuracy both for personalized models and with malicious agents compared to standard strategies.

Over-actuated systems, namely systems with more inputs than outputs, can increase control performance, yet are susceptible to model-based undetectable attacks if the actuator channel is compromised. In this paper, we show how implementing a sparse actuator schedule can introduce security by rendering these attacks ineffective. We formulate a novel methodology whereby a periodic sparse schedule, implemented at the actuators, secures the system by ensuring that a malicious adversary cannot exploit actuator redundancy to deploy undetectable attacks. The schedule is designed offline and repeats periodically at the actuators, so that the adversary is constrained to only tamper with the active actuators. We devise a degeneracyaware greedy selection procedure with low computational complexity to design an actuator schedule that renders undetectable attacks ineffective, whilst simultaneously providing relatively small performance degradation. We illustrate the effectiveness of our approach using a reference tracking model predictive controller on the IEEE-39 bus power network employing the designed sparse schedule.

Model-based fault detection identifies anomalies by comparing a system's output with the prediction from a model. Although such a technique can be very powerful, it may suffer from the computational complexity of its underlying models, especially for large systems. An alternative approach that circumvents this cost increase uses barrier functions, which abstract the system's behaviour into a single value. In this paper, we propose a fault detection mechanism via output-based barrier functions, that does not require to estimate the full state, copes with noisy processes, and is tailored to safety-critical faults as given by a user-defined safe region. We leverage such a mechanism by introducing so-called p-fault tolerant sets, which guarantee that a faulty system requires at least p time steps before reaching any unsafe state. Our approach is validated through numerical experiments on two systems with linear and nonlinear dynamics, along with the classic three-tank model.

The Friedkin-Johnsen (FJ) model describes how agents adjust their opinions through repeated interactions while accounting for the influence of agents who are partially stubborn. In this work, we demonstrate that the FJ model is stepwise equivalent to solving the average consensus problem via distributed gradient descent. This perspective provides a unifying framework that bridges opinion dynamics and optimization, enabling the application of well-established results from the optimization literature. To illustrate this, we examine the recently proposed FJ model with diminishing stubbornness and extend prior results that were concerned with fixed communication graphs to time-varying and jointly connected communication graphs. We derive convergence guarantees and analyze convergence rates under these relaxed assumptions. Finally, we present numerical experiments on random graphs to showcase the impact of diminishing stubbornness dynamics on convergence in both static and time-varying settings.

Assisted and autonomous driving are rapidly gaining momentum and will soon become a reality. Artificial intelligence and machine learning are regarded as key enablers thanks to the massive amount of data that smart vehicles will collect from onboard sensors. Federated learning is one of the most promising techniques for training global machine learning models while preserving data privacy of vehicles and optimizing communications resource usage. In this article, we propose vehicular radio environment map federated learning (VREM-FL), a computation-scheduling co-design for vehicular federated learning that combines mobility of vehicles with 5G radio environment maps. VREM-FL jointly optimizes learning performance of the global model and wisely allocates communication and computation resources. This is achieved by orchestrating local computations at the vehicles in conjunction with transmission of their local models in an adaptive and predictive fashion, by exploiting radio channel maps. The proposed algorithm can be tuned to trade training time for radio resource usage. Experimental results demonstrate that VREM-FL outperforms literature benchmarks for both a linear regression model (learning time reduced by 28%) and a deep neural network for semantic image segmentation (doubling the number of model updates within the same time window).

Safe operation of multi-robot systems is critical, especially in communication-degraded environments such as underwater for seabed mapping, underground caves for navigation, and in extraterrestrial missions for assembly and construction. We address safety of networked autonomous systems where the information exchanged between robots incurs communication delays. We formalize a notion of distributed control barrier function for multi-robot systems, a safety certificate amenable to a distributed implementation, which provides formal ground to using graph neural networks to learn safe distributed controllers. Further, we observe that learning a distributed controller ignoring delays can severely degrade safety. We finally propose a predictor-based framework to train a safe distributed controller under communication delays, where the current state of nearby robots is predicted from received data and age-of-information. Numerical experiments on multi-robot collision avoidance show that our predictor-based approach can significantly improve the safety of a learned distributed controller under communication delays. A video abstract is available at https://youtu.be/Hcu1Ri32Spk.

We consider a multi-agent system where agents aim to achieve a consensus despite interactions with malicious agents that communicate misleading information. Physical channels supporting communication in cyberphysical systems offer attractive opportunities to detect malicious agents, nevertheless, trustworthiness indications coming from the channel are subject to uncertainty and need to be treated with this in mind. We propose a resilient consensus protocol that incorporates trust observations from the channel and weighs them with a parameter that accounts for how confident an agent is regarding its understanding of the legitimacy of other agents in the network, with no need for the initial observation window T0 that has been utilized in previous works. Analytical and numerical results show that (i) our protocol achieves a resilient consensus in the presence of malicious agents and (ii) the steady-state deviation from nominal consensus can be minimized by a suitable choice of the confidence parameter that depends on the statistics of trust observations.

This letter 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.

This letter studies the Friedkin-Johnsen (FJ) model with diminishing competition, or stubbornness. The original FJ model assumes that each agent assigns a constant competition weight to its initial opinion. In contrast, we investigate the effect of diminishing competition on the convergence point and speed of the FJ dynamics. We prove that, if the competition is uniform across agents and vanishes asymptotically, the convergence point coincides with the nominal consensus reached with no competition. However, the diminishing competition slows down convergence according to its own rate of decay. We study this phenomenon analytically and provide upper and lower bounds on the convergence rate. Further, if competition is not uniform across agents, we show that the convergence point may not coincide with the nominal consensus point. Finally, we evaluate our analytical insights numerically.

In this paper we investigate the design of optimal spatially distributed controllers for a linear and spatially invariant reaction-diffusion process over the real line. The controller receives state measurements from different spatial locations with non-negligible delays. In this set-up and for the class of proportional spatially invariant state feedback controllers, the optimal control synthesis problem is equivalent to a feedback gain optimization for a spatially distributed delay system. We show that the spatial locality of optimal feedback gains is affected not only by diffusion and reaction coefficients, but also by the parameter representing communication time-delay that causes a sharp flattening of the control gains. In the expensive control regime, the optimal controller is solved analytically, yielding some practical design guidelines.