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.

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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.

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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.

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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.

In this paper we revisit the construction of quantized models of control systems. Based on an approximate notion of simulation relation and under a stabilizability assumption we show how we can force a lattice structure on the reachable space of a quantized control system for any finite input quantization. When we are only interested in a compact subset of the state space, as is the case in concrete applications, our results immediately provide a finite model for the quantized control system.

Approximate simulation relations and finite abstractions of quantized control systems

We introduce PESSOA 2.0, a tool that automatically synthesizes controllers for cyber-physical systems based on correct-by-design methodology. PESSOA 2.0 accepts a cyber-physical system represented by a set of smooth differential equations and automata and a specification in a fragment of Linear Temporal Logic that is expressive enough to describe interesting properties but simple enough to avoid Safra's construction. It outputs, if possible, a controller for the system that enforces the specification up to an abstraction parameter. We report on examples illustrating the expressiveness of the fragment and the controllers synthesized by the tool.

Pessoa 2.0: a controller synthesis tool for cyber-physical systems

Robustness as a system property describes the degree to which a system is able to function correctly in the presence of disturbances, i.e., unforeseen or erroneous inputs. In this paper, we introduce a notion of robustness termed input-output dynamical stability for cyber-physical systems (CPS) which merges existing notions of robustness for continuous systems and discrete systems. The notion captures two intuitive aims of robustness: bounded disturbances have bounded effects and the consequences of a sporadic disturbance disappear over time. We present a design methodology for robust CPS which is based on an abstraction and refinement process. We suggest several novel notions of simulation relations to ensure the soundness of the approach. In addition, we show how such simulation relations can be constructed compositionally. The different concepts and results are illustrated throughout the paper with examples.

A Notion of Robustness for Cyber-Physical Systems

Recent developments in computer and communication technologies have led to a new type of large-scale resource-constrained wireless embedded control systems. It is desirable in these systems to limit the sensor and control computation and/or communication to instances when the system needs attention. However, classical sampled-data control is based on performing sensing and actuation periodically rather than when the system needs attention. This article discusses eventand self-triggered control systems where sensing and actuation is performed when needed. Event-triggered control is reactive and generates sensor sampling and control actuation when, for instance, the plant state deviates more than a certain threshold from a desired value. Self-triggered control, on the other hand, is proactive and computes the next sampling or actuation instance ahead of time. The basics of these control strategies are introduced together with references for further reading.

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Event-Triggered and Self-Triggered Control.

The 18 papers in this special issue can be clustered into five areas: abstraction and verification; cyber-physical security; resource-constrained embedded and wireless control; event-based estimation and control; and applications.

Paulo Tabuada

Papers

Approximate simulation relations and finite abstractions of quantized control systems

Pessoa 2.0: a controller synthesis tool for cyber-physical systems

A Notion of Robustness for Cyber-Physical Systems

Event-Triggered and Self-Triggered Control.

Guest Editorial Special Issue on Control of Cyber-Physical Systems