Paulo Tabuada

Bio: Paulo Tabuada is an academic researcher from University of California, Los Angeles. The author has contributed to research in topics: Control system & Control theory. The author has an hindex of 60, co-authored 288 publications receiving 20444 citations. Previous affiliations of Paulo Tabuada include University of California, Berkeley & Instituto Superior Técnico.

Symbolic models for linear control systems with disturbances

Abstract: A recent trend in the control systems community is the study of appropriate symbolic abstractions capturing the behavior of continuous and hybrid systems. This approach provides a common mathematical language to describe physical systems as well as software and hardware, and is therefore particularly appealing when dealing with the design of embedded systems. In this paper we address the construction of symbolic models for the class of linear control systems with politopically bounded states and disturbances. We show that under an asymptotic stabilizability assumption, it is always possible to construct a symbolic model that approximates the control system with a precision that is chosen a priori, as a design parameter. While in previous approaches in the existing literature, the construction of symbolic models relied on a (arbitrary) choice of a finite number of control signals, the symbolic model that we propose, captures any (control and disturbance) input. Therefore, the proposed model provides a finer description of the continuous model than the existing ones and this feature translates into a more efficient controller synthesis process. Furthermore, the computation of the symbolic model can be performed by resorting to linear matrix inequalities.

Evrostos: the rLTL verifier

Abstract: Robust Linear Temporal Logic (rLTL) was crafted to incorporate the notion of robustness into Linear-time Temporal Logic (LTL) specifications. Technically, robustness was formalized in the logic rLTL via 5 different truth values and it led to an increase in the time complexity of the associated model checking problem. In general, model checking an rLTL formula relies on constructing a generalized Buchi automaton of size 5 | φ | where | φ | denotes the length of an rLTL formula φ. It was recently shown that the size of this automaton can be reduced to 3 | φ | (and even smaller) when the formulas to be model checked come from a fragment of rLTL. In this paper, we introduce Evrostos, the first tool for model checking formulas in this fragment. We also present several empirical studies, based on models and LTL formulas reported in the literature, confirming that rLTL model checking for the aforementioned fragment incurs in a time overhead that makes the verification of rLTL practical.

Towards the use of Symmetries to Ensure Privacy in Control Over the Cloud

Abstract: With the advent of cloud computing and the increasing connectivity of devices at the edge of the internet, closing feedback control loops over the cloud is becoming a reality. This is especially the case when computationally expensive algorithms, such as model-predictive control for nonlinear plants, are used to optimize performance. In view of this, these algortihms often delegate most of the computations to the cloud. A major roadblock to closing feedback control loops over the cloud, however, is ensuring privacy of the exchanged data. Further exacerbating this difficulty is the need to minimize the computational overhead of enforcing privacy so as not to degrade control performance. In this paper, we propose several methods for enforcing data privacy using symmetry transformations. We address three different scenarios: a) the cloud has no knowledge about the system being controlled; b) the cloud knows what sensors and actuators the system employs but not the system dynamics; c) the cloud knows the system dynamics, its sensors, and actuators. The proposed methods allow us, in all of these three scenarios, to successfully execute control over the cloud without revealing private information (which information is considered private depends on the considered scenario). The advantage of these methods lies in their generality, which makes them applicable to a wide class of systems and with low computational overhead.

Cyclic directed formations of multi-agent systems

Abstract: Formations of multi-agent systems, such as satellites, aircrafts and mobile robots require that individual agents satisfy their kinematic equations while constantly maintaining inter-agent constraints. In previous work we introduced the concept of undirected formation graphs and directed formation graphs to model such formations and presented conditions to determine formation feasibility. However the directed formations were only analyzed in the absence of cycles in the formation graph. In this paper we extend our previous results to accommodate also the presence of cycles in directed formations. Differential geometric and algebraic conditions are presented to determine feasibility of directed formations with possible cycles.

Verifying rLTL formulas: now faster than ever before!

Abstract: Robust Linear Temporal Logic (rLTL) was crafted to incorporate the notion of robustness into Linear-time Temporal Logic specifications. Robustness is ubiquitous in control systems and translates the intuitive notion that “small” violations of environment assumptions should only lead to “small” violations of system guarantees. This notion was formalized in the logic rLTL via 5 different truth values and it led to an increase in the time complexity of the associated model checking problem. In this paper we identify and analyze a fragment of rLTL for which the model checking problem can be solved using generalized Biichi automata with at most $3^{\vert \varphi\vert }$ states where $\vert \varphi \vert$ denotes the length of an rLTL formula $\varphi$ . This is a substantial improvement over the previously known bound of $5^{\vert \varphi \vert}$ and close to the tight upper bound $2^{\vert \varphi\vert }$ for LTL.

I and i

Abstract: 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 …

Information flow and cooperative control of vehicle formations

Abstract: 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.

Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks

Abstract: 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.

Coverage control for mobile sensing networks

Abstract: 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.

Coverage control for mobile sensing networks

Abstract: 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.