Distributed Control of Spatially Reversible Interconnected Systems with Boundary Conditions

We present a class of spatially interconnected systems with boundary conditions that have close links with their spatially invariant extensions. In particular, well-posedness, stability, and performance of the extension imply the same characteristics for the actual, finite extent system. In turn, existing synthesis methods for control of spatially invariant systems can be extended to this class. The relation between the two kinds of systems is proved using ideas based on the "method of images" of partial differential equations theory and uses symmetry properties of the interconnection as a key tool

A Faithful Distributed Implementation of Dual Decomposition and Average Consensus Algorithms

We consider large scale cost allocation problems and consensus seeking problems for multiple agents, in which agents are suggested to collaborate in a distributed algorithm to find a solution. If agents are strategic to minimize their own individual cost rather than the global social cost, they are endowed with an incentive not to follow the intended algorithm, unless the tax/subsidy mechanism is carefully designed. Inspired by the classical Vickrey-Clarke-Groves mechanism and more recent algorithmic mechanism design theory, we propose a tax mechanism that incentivises agents to faithfully implement the intended algorithm. In particular, a new notion of asymptotic incentive compatibility is introduced to characterize a desirable property of such class of mechanisms. The proposed class of tax mechanisms provides a sequence of mechanisms that gives agents a diminishing incentive to deviate from suggested algorithm.Comment: 8 page

Task Release Control for Decision Making Queues

We consider the optimal duration allocation in a decision making queue. Decision making tasks arrive at a given rate to a human operator. The correctness of the decision made by human evolves as a sigmoidal function of the duration allocated to the task. Each task in the queue loses its value continuously. We elucidate on this trade-off and determine optimal policies for the human operator. We show the optimal policy requires the human to drop some tasks. We present a receding horizon optimization strategy, and compare it with the greedy policy.Comment: 8 pages, Submitted to American Controls Conference, San Francisco, CA, June 201

Misinformation Regulation in the Presence of Competition between Social Media Platforms (Extended Version)

Social media platforms have diverse content moderation policies, with many prominent actors hesitant to impose strict regulations. A key reason for this reluctance could be the competitive advantage that comes with lax regulation. A popular platform that starts enforcing content moderation rules may fear that it could lose users to less-regulated alternative platforms. Moreover, if users continue harmful activities on other platforms, regulation ends up being futile. This article examines the competitive aspect of content moderation by considering the motivations of all involved players (platformer, news source, and social media users), identifying the regulation policies sustained in equilibrium, and evaluating the information quality available on each platform. Applied to simple yet relevant social networks such as stochastic block models, our model reveals the conditions for a popular platform to enforce strict regulation without losing users. Effectiveness of regulation depends on the diffusive property of news posts, friend interaction qualities in social media, the sizes and cohesiveness of communities, and how much sympathizers appreciate surprising news from influencers.Comment: This version extends the article submitted to the IEEE Transactions on Control of Network System

Almost-Bayesian Quadratic Persuasion (Extended Version)

In this article, we relax the Bayesianity assumption in the now-traditional model of Bayesian Persuasion introduced by Kamenica & Gentzkow. Unlike preexisting approaches -- which have tackled the possibility of the receiver (Bob) being non-Bayesian by considering that his thought process is not Bayesian yet known to the sender (Alice), possibly up to a parameter -- we let Alice merely assume that Bob behaves 'almost like' a Bayesian agent, in some sense, without resorting to any specific model. Under this assumption, we study Alice's strategy when both utilities are quadratic and the prior is isotropic. We show that, contrary to the Bayesian case, Alice's optimal response may not be linear anymore. This fact is unfortunate as linear policies remain the only ones for which the induced belief distribution is known. What is more, evaluating linear policies proves difficult except in particular cases, let alone finding an optimal one. Nonetheless, we derive bounds that prove linear policies are near-optimal and allow Alice to compute a near-optimal linear policy numerically. With this solution in hand, we show that Alice shares less information with Bob as he departs more from Bayesianity, much to his detriment.Comment: This version extends the article submitted to the IEEE Transactions on Automatic Contro

Learn and Control while Switching: with Guaranteed Stability and Sublinear Regret

Over-actuated systems often make it possible to achieve specific performances by switching between different subsets of actuators. However, when the system parameters are unknown, transferring authority to different subsets of actuators is challenging due to stability and performance efficiency concerns. This paper presents an efficient algorithm to tackle the so-called "learn and control while switching between different actuating modes" problem in the Linear Quadratic (LQ) setting. Our proposed strategy is constructed upon Optimism in the Face of Uncertainty (OFU) based algorithm equipped with a projection toolbox to keep the algorithm efficient, regret-wise. Along the way, we derive an optimum duration for the warm-up phase, thanks to the existence of a stabilizing neighborhood. The stability of the switched system is also guaranteed by designing a minimum average dwell time. The proposed strategy is proved to have a regret bound of $\mathcal{\bar{O}}\big(\sqrt{T}\big)+\mathcal{O}\big(ns\sqrt{T}\big)$ in horizon $T$ with $(ns)$ number of switches, provably outperforming naively applying the basic OFU algorithm

The Price of Distributed Design in Optimal Control

We study control design strategies which, when presented with a plant made of interconnected subsystems, construct a sub-controller for each one of them using only a model of this particular subsystem. We prove that, for a class of linear time-invariant, discrete-time systems, any such distributed control strategy must have a worst-case performance at least twice the optimal. The best distributed design strategy is one that results in a deadbeat controller for every plant