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.

/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.

Runtime monitoring is commonly used to detect the violation of desired properties in safety critical cyber-physical systems by observing its executions. Bauer et al. introduced an influential framework for monitoring Linear Temporal Logic (LTL) properties based on a three-valued semantics: the formula is already satisfied by the given prefix, it is already violated, or it is still undetermined, i.e., it can still be satisfied and violated by appropriate extensions. However, a wide range of formulas are not monitorable under this approach, meaning that they have a prefix for which satisfaction and violation will always remain undetermined no matter how it is extended. In particular, Bauer et al. report that 44% of the formulas they consider in their experiments fall into this category. Recently, a robust semantics for LTL was introduced to capture different degrees by wich a property can be violated. In this paper we introduce a robust semantics for finite strings and show its potential in monitoring: every formula considered by Bauer et al. is monitorable under our approach. Furthermore, we discuss which properties that come naturally in LTL monitoring --- such as the realizability of all truth values --- can be transferred to the robust setting. Lastly, we show that LTL formulas with robust semantics can be monitored by deterministic automata and report on a prototype implementation.

From LTL to rLTL monitoring: improved monitorability through robust semantics

While most approaches in formal methods address system correctness, ensuring robustness has remained a challenge. In this paper we introduce the logic rLTL which provides a means to formally reason about both correctness and robustness in system design. Furthermore, we identify a large fragment of rLTL for which the verification problem can be efficiently solved, i.e., verification can be done by using an automaton, recognizing the behaviors described by the rLTL formula $\varphi$, of size at most $\mathcal{O} \left( 3^{ |\varphi|} \right)$, where $|\varphi|$ is the length of $\varphi$. This result improves upon the previously known bound of $\mathcal{O}\left(5^{|\varphi|} \right)$ for rLTL verification and is closer to the LTL bound of $\mathcal{O}\left( 2^{|\varphi|} \right)$. The usefulness of this fragment is demonstrated by a number of case studies showing its practical significance in terms of expressiveness, the ability to describe robustness, and the fine-grained information that rLTL brings to the process of system verification. Moreover, these advantages come at a low computational overhead with respect to LTL verification.

Being correct is not enough: efficient verification using robust linear temporal logic.

1School of Engineering and Applied Science 2 Robotics Institute 3Department of Electrical Engineering University of Pennsylvania Carnegie Mellon University University of California, Los Angeles Philadelphia, PA 19104 Pittsburgh, PA 15213 Los Angeles, CA 90095 {pajic, nicbezzo, weimerj}@seas.upenn.edu nmichael@cmu.edu tabuada@ee.ucla.edu {rahulm, pappasg}@seas.upenn.edu {sokolsky, alur, sweirich, lee}@cis.upenn.edu

Towards synthesis of platform-aware attack-resilient control systems: extended abstract

Sum-of-Squares methods for controlled invariant sets with applications to model-predictive control

In this paper we consider the problem of controlling an unknown system without making use of prior data or training. By relying on a feedback linearizability assumption we show how, based on prior ideas by Fliess and co-workers on model-free control, it is possible to accomplish such objective. The key idea is to learn a model that is only valid at the current state and re-learn this model as time progresses. Since this requires learning two real numbers rather than functions, it results in an approach quite different from: 1) deep learning since it requires no prior data neither large amounts of data; 2) reinforcement learning since it converges much faster and does not suffer from the curse of dimensionality.

Paulo Tabuada

Papers

From LTL to rLTL monitoring: improved monitorability through robust semantics

Being correct is not enough: efficient verification using robust linear temporal logic.

Towards synthesis of platform-aware attack-resilient control systems: extended abstract

Sum-of-Squares methods for controlled invariant sets with applications to model-predictive control

Data-driven control for SISO feedback linearizable systems with unknown control gain