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.

/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.

Time-delay systems are an important class of dynamical systems which provide a solid mathematical framework to deal with many application domains of interest ranging from biology, chemical, electrical, and mechanical engineering, to economics. However, the inherent complexity of such systems poses serious difficulties to control design, when control objectives depart from the standard ones investigated in the current literature, e.g. stabilization, regulation, and etc. In this paper we propose one approach to control design, which is based on the construction of symbolic models, where each symbolic state and each symbolic label correspond to an aggregate of continuous states and to an aggregate of input signals in the original system. The use of symbolic models offers a systematic methodology for control design in which constraints coming from software and hardware, interacting with the physical world, can be integrated. The main contribution of this paper is in showing that incrementally input-to-state stable time-delay systems do admit symbolic models that are approximately bisimilar to the original system, with a precision that can be rendered as small as desired. An algorithm is also presented which computes the proposed symbolic models. When the state and input spaces of time-delay systems are bounded, which is the case in many realistic situations, the proposed algorithm is shown to terminate in a finite number of steps.

Symbolic models for nonlinear time-delay systems using approximate bisimulations

Stability is arguably one of the core concepts upon which our understanding of dynamical and control systems has been built. The related notion of incremental stability, however, has received much less attention until recently, when it was successfully used as a tool for the analysis and design of intrinsic observers, output regulation of nonlinear systems, frequency estimators, synchronization of coupled identical dynamical systems, symbolic models for nonlinear control systems, and bio-molecular systems. However, most of the existing controller design techniques provide controllers enforcing stability rather than incremental stability. Hence, there is a growing need to extend existing methods or develop new ones for the purpose of designing incrementally stabilizing controllers. In this technical note, we develop a backstepping design approach for incremental stability.

Backstepping Design for Incremental Stability

We consider the problem of estimation and control of a linear system when some of the sensors or actuators are attacked by a malicious agent. In our previous work [1] we studied systems with no control inputs and we formulated the estimation problem as a dynamic error correction problem with sparse attack vectors. In this paper we extend our study and look at the role of inputs and control. We first show that it is possible to increase the resilience of the system to attacks by changing the dynamics of the system using state-feedback while having (almost) total freedom in placing the new poles of the system. We then look at the problem of stabilizing a plant using output-feedback despite attacks on sensors, and we show that a principle of separation of estimation and control holds. Finally we look at the effect of attacks on actuators in addition to attacks on sensors: we characterize the resilience of the system with respect to actuator and sensor attacks and we formulate an efficient optimization-based decoder to estimate the state of the system despite attacks on actuators and sensors.

Security for control systems under sensor and actuator attacks

Bisimilar control affine systems

In this paper we present and analyze a novel algorithm to synthesize controllers enforcing linear temporal logic specifications on discrete-time linear systems. The central step within this approach is the computation of the maximal controlled invariant set contained in a possibly non-convex safe set. Although it is known how to compute approximations of maximal controlled invariant sets, its exact computation remains an open problem. We provide an algorithm which computes a controlled invariant set that is guaranteed to be an under-approximation of the maximal controlled invariant set. Moreover, we guarantee that our approximation is at least as good as any invariant set whose distance to the boundary of the safe set is lower bounded. The proposed algorithm is founded on the notion of sets adapted to the dynamics and binary decision diagrams. Contrary to most controller synthesis schemes enforcing temporal logic specifications, we do not compute a discrete abstraction of the continuous dynamics. Instead, we abstract only the part of the continuous dynamics that is relevant for the computation of the maximal controlled invariant set. For this reason we call our approach specification guided. We describe the theoretical foundations and technical underpinnings of a preliminary implementation and report on several experiments including the synthesis of an automatic cruise controller. Our preliminary implementation handles up to five continuous dimensions and specifications containing up to 160 predicates defined as polytopes in about 30 minutes with less than 1 GB memory.

Paulo Tabuada

Papers

Symbolic models for nonlinear time-delay systems using approximate bisimulations

Backstepping Design for Incremental Stability

Security for control systems under sensor and actuator attacks

Bisimilar control affine systems

Specification-guided controller synthesis for linear systems and safe linear-time temporal logic