There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. Tools from algebraic graph theory prove useful in modeling the communication network and relating its topology to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that decomposes formation stability into two components: Stability of this is achieved information flow for the given graph and stability of an individual vehicle for the given controller. The information flow can thus be rendered highly robust to changes in the graph, enabling tight formation control despite limitations in intervehicle communication capability.

/pdf/information-flow-and-cooperative-control-of-vehicle-4ws61wioze.pdf

Information flow and cooperative control of vehicle formations

In this note, we revisit the problem of scheduling stabilizing control tasks on embedded processors. We start from the paradigm that a real-time scheduler could be regarded as a feedback controller that decides which task is executed at any given instant. This controller has for objective guaranteeing that (control unrelated) software tasks meet their deadlines and that stabilizing control tasks asymptotically stabilize the plant. We investigate a simple event-triggered scheduler based on this feedback paradigm and show how it leads to guaranteed performance thus relaxing the more traditional periodic execution requirements.

/pdf/event-triggered-real-time-scheduling-of-stabilizing-control-t1gebqsndp.pdf

Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks

This paper describes decentralized control laws for the coordination of multiple vehicles performing spatially distributed tasks. The control laws are based on a gradient descent scheme applied to a class of decentralized utility functions that encode optimal coverage and sensing policies. These utility functions are studied in geographical optimization problems and they arise naturally in vector quantization and in sensor allocation tasks. The approach exploits the computational geometry of spatial structures such as Voronoi diagrams.

/pdf/coverage-control-for-mobile-sensing-networks-3gs75qafnm.pdf

Coverage control for mobile sensing networks

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Finite-state models of control systems were proposed by several researchers as a convenient mechanism to synthesize controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main drawbacks: either they can only be applied to restrictive classes of systems, or they require the exact computation of reachable sets. In this paper, we propose a new abstraction technique that is applicable to any smooth control system as long as we are only interested in its behavior in a compact set. Moreover, the exact computation of reachable sets is not required. The effectiveness of the proposed results is illustrated by synthesizing a controller to steer a vehicle.

Symbolic models for nonlinear control systems without stability assumptions

This demo abstract presents PrOLoc, a localization system thatcombines partially homomorphic encryption with a new way ofstructuring the localization problem to enable efficient and accurate computation of a target’s location while preserving the privacy of the observers.

http://ieeexplore.ieee.org/iel7/7940187/7944706/07944797.pdf

Demo Abstract: PrOLoc: Resilient Localization with Private Observers Using Partial Homomorphic Encryption

In this paper, we revisit the problem of learning a stabilizing controller from a finite number of demonstrations by an expert. By focusing on feedback linearizable systems, we show how to combine expert demonstrations into a stabilizing controller, provided that demonstrations are sufficiently long and there are at least $n+1$ of them, where $n$ is the number of states of the system being controlled. The results are experimentally demonstrated on a CrazyFlie 2.0 quadrotor.

Watch and Learn: Learning to control feedback linearizable systems from expert demonstrations

Control theory is faced with new paradigms and challenges that fall beyond traditional problems. Nowadays applications tend to be distributed, and require partial synchronization among their various subsystems. We give initial steps towards discrete synchronization problems for systems which are compositions of several, possibly distributed, hybrid systems. Such problems arise frequently in the coordination of multi-agent systems, where each agent is modeled as a hybrid system. This results in control problems where the model is the composition of decoupled subsystems, but the specification is coupled across subsystems. A centralized solution to this problem requires computing the product hybrid system resulting in state explosion. We alternatively consider decentralized solutions to such discrete synchronization problems. Partially decentralized synchronization is achieved if each subsystem is allowed to communicate with the subsystems it needs to partially synchronize with. The required communication between agents is provided by modeling abstractions of the remaining agents. These abstractions. which are property-dependent, are then used to derive local controllers using global, but minimal, observations.

/pdf/discrete-synchronization-of-hybrid-systems-3qsx2g4zlp.pdf

Discrete synchronization of hybrid systems

In Cyber-Physical Systems (CPSs), inference based on communicated data is of critical significance as it can be used to manipulate or damage the control operations by adversaries. This calls for efficient mechanisms for secure transmission of data since control systems are becoming increasingly distributed over larger geographical areas. Distortion based security, recently proposed as one candidate for CPSs security, is not only more appropriate for these applications but also quite frugal in terms of prior requirements on shared keys. In this paper, we propose distortion-based metrics to protect CPSs communication and show that it is possible to confuse adversaries with just a few bits of pre-shared keys.

Paulo Tabuada

Papers

Symbolic models for nonlinear control systems without stability assumptions

Demo Abstract: PrOLoc: Resilient Localization with Private Observers Using Partial Homomorphic Encryption

Watch and Learn: Learning to control feedback linearizable systems from expert demonstrations

Discrete synchronization of hybrid systems

Distorting an Adversary's View in Cyber-Physical Systems