arXiv subjects

Paulo Tabuada

Publications and source records attributed to Paulo Tabuada.

At least 55 records · Page 3Linked to original sources

arXiv2020

Privacy Against Adversarial Classification in Cyber-Physical Systems

For a class of Cyber-Physical Systems (CPSs), we address the problem of performing computations over the cloud without revealing private information about the structure and operation of the system. We model CPSs as a collection of input-output dynamical systems (the system operation modes). Depending on the mode the system is operating on, the output trajectory is generated by one of these systems in response to driving inputs. Output measurements and driving inputs are sent to the cloud for processing purposes. We capture this "processing" through some function (of the input-output trajectory) that we require the cloud to compute accurately - referred here as the trajectory utility. However, for privacy reasons, we would like to keep the mode private, i.e., we do not want the cloud to correctly identify what mode of the CPS produced a given trajectory. To this end, we distort trajectories before transmission and send the corrupted data to the cloud. We provide mathematical tools (based on output-regulation techniques) to properly design distorting mechanisms so that: 1) the original and distorted trajectories lead to the same utility; and the distorted data leads the cloud to misclassify the mode.

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arXiv2020

Control Barrier Function based Quadratic Programs Introduce Undesirable Asymptotically Stable Equilibria

Control Lyapunov functions (CLFs) and control barrier functions (CBFs) have been used to develop provably safe controllers by means of quadratic programs (QPs), guaranteeing safety in the form of trajectory invariance with respect to a given set. In this manuscript, we show that this framework can introduce equilibrium points (particularly at the boundary of the unsafe set) other than the minimum of the Lyapunov function into the closed-loop system. We derive explicit conditions under which these undesired equilibria (which can even appear in the simple case of linear systems with just one convex unsafe set) are asymptotically stable. To address this issue, we propose an extension to the QP-based controller unifying CLFs and CBFs that explicitly avoids undesirable equilibria on the boundary of the safe set. The solution is illustrated in the design of a collision-free controller.

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arXiv2020

Rapid Top-Down Synthesis of Large-Scale IoT Networks

Advances in optimization and constraint satisfaction techniques, together with the availability of elastic computing resources, have spurred interest in large-scale network verification and synthesis. Motivated by this, we consider the top-down synthesis of ad-hoc IoT networks for disaster response and search and rescue operations. This synthesis problem must satisfy complex and competing constraints: sensor coverage, line-of-sight visibility, and network connectivity. The central challenge in our synthesis problem is quickly scaling to large regions while producing cost-effective solutions. We explore two qualitatively different representations of the synthesis problems satisfiability modulo convex optimization (SMC), and mixed-integer linear programming (MILP). The former is more expressive, for our problem, than the latter, but is less well-suited for solving optimization problems like ours. We show how to express our network synthesis in these frameworks, and, to scale to problem sizes beyond what these frameworks are capable of, develop a hierarchical synthesis technique that independently synthesizes networks in sub-regions of the deployment area, then combines these. We find that, while MILP outperforms SMC in some settings for smaller problem sizes, the fact that SMC's expressivity matches our problem ensures that it uniformly generates better quality solutions at larger problem sizes.

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arXiv2019

Cloud-based Quadratic Optimization with Partially Homomorphic Encryption

The development of large-scale distributed control systems has led to the outsourcing of costly computations to cloud-computing platforms, as well as to concerns about privacy of the collected sensitive data. This paper develops a cloud-based protocol for a quadratic optimization problem involving multiple parties, each holding information it seeks to maintain private. The protocol is based on the projected gradient ascent on the Lagrange dual problem and exploits partially homomorphic encryption and secure multi-party computation techniques. Using formal cryptographic definitions of indistinguishability, the protocol is shown to achieve computational privacy, i.e., there is no computationally efficient algorithm that any involved party can employ to obtain private information beyond what can be inferred from the party's inputs and outputs only. In order to reduce the communication complexity of the proposed protocol, we introduced a variant that achieves this objective at the expense of weaker privacy guarantees. We discuss in detail the computational and communication complexity properties of both algorithms theoretically and also through implementations. We conclude the paper with a discussion on computational privacy and other notions of privacy such as the non-unique retrieval of the private information from the protocol outputs.

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arXiv2019

A Note on Data-Driven Control for SISO Feedback Linearizable Systems Without Persistency of Excitation

The paper [TF19] proposes a data-driven control technique for single-input single-output feedback linearizable systems with unknown control gain by relying on a persistency of excitation assumption. This note extends those results by showing that persistency of excitation is not necessary. We refer the readers to the papers [TMGA17, TF19] for more background and motivation for the technical results in this note. Conceptually, the results in this note were greatly inspired by the work of Fliess and Join on intelligent PID controllers, e.g., [FJ09]. Technically, we were inspired by the work of Nesic and co-workers on observer and controller design based on approximate models [AN04, NT04] and by the work of Astolfi and Ortega on Immersion and Invariance [AO03].

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arXiv2019

Symmetries and isomorphisms for privacy in control over the cloud

Cloud computing platforms are being increasingly used for closing feedback control loops, especially when computationally expensive algorithms, such as model-predictive control, are used to optimize performance. Outsourcing of control algorithms entails an exchange of data between the control system and the cloud, and, naturally, raises concerns about the privacy of the control system's data (e.g., state trajectory, control objective). Moreover, any attempt at enforcing privacy needs to add minimal computational overhead to avoid degrading control performance. In this paper, we propose several transformation-based methods for enforcing data privacy. We also quantify the amount of provided privacy and discuss how much privacy is lost when the adversary has access to side knowledge. 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. In all of these three scenarios, the proposed methods allow for the control over the cloud without compromising private information (which information is considered private depends on the considered scenario).

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arXiv2019

Securing State Estimation Under Sensor and Actuator Attacks: Theory and Design

This paper discusses the problem of estimating the state of a linear time-invariant system when some of its sensors and actuators are compromised by an adversarial agent. In the model considered in this paper, the malicious agent attacks an input (output) by manipulating its value arbitrarily, i.e., we impose no constraints (statistical or otherwise) on how control commands (sensor measurements) are changed by the adversary. In the first part of this paper, we introduce the notion of sparse strong observability and we show that is a necessary and sufficient condition for correctly reconstructing the state despite the considered attacks. In the second half of this work, we propose an estimator to harness the complexity of this intrinsically combinatorial problem, by leveraging satisfiability modulo theory solving. Numerical simulations demonstrate the effectiveness and scalability of our estimator.

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arXiv2019

Control Barrier Functions: Theory and Applications

This paper provides an introduction and overview of recent work on control barrier functions and their use to verify and enforce safety properties in the context of (optimization based) safety-critical controllers. We survey the main technical results and discuss applications to several domains including robotic systems.

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arXiv2018

Distorting an Adversary's View in Cyber-Physical 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.

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arXiv2018

Supervisory Control of Discrete-event Systems under Attacks

We consider a multi-adversary version of the supervisory control problem for discrete-event systems, in which an adversary corrupts the observations available to the supervisor. The supervisor's goal is to enforce a specific language in spite of the opponent's actions and without knowing which adversary it is playing against. This problem is motivated by applications to computer security in which a cyber defense system must make decisions based on reports from sensors that may have been tampered with by an attacker. We start by showing that the problem has a solution if and only if the desired language is controllable (in the Discrete event system classical sense) and observable in a (novel) sense that takes the adversaries into account. For the particular case of attacks that insert symbols into or remove symbols from the sequence of sensor outputs, we show that testing the existence of a supervisor and building the supervisor can be done using tools developed for the classical DES supervisory control problem, by considering a family of automata with modified output maps, but without expanding the size of the state space and without incurring on exponential complexity on the number of attacks considered., we construct observers that are robust against attacks and lead to an automaton representation of the supervisor. We also develop a test for observability under such replacement-removal attacks by using the so-called product automata.

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arXiv2018

Data Driven Stability Analysis of Black-box Switched Linear Systems

Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of observations, one can give probabilistic stability guarantees. The probabilistic nature of these guarantees implies a trade-off between their quality and the desired level of confidence. We provide an explicit way of computing the best stability-like guarantee, as a function of both the number of observations and the required level of confidence. Our proof techniques rely on geometrical analysis, chance-constrained optimization, and stability analysis tools for switched systems, including the joint spectral radius.

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arXiv2018

Computing controlled invariant sets for hybrid systems with applications to model-predictive control

In this paper, we develop a method for computing controlled invariant sets using Semidefinite Programming. We apply our method to the controller design problem for switching affine systems with polytopic safe sets. The task is reduced to a semidefinite programming problem by enforcing an invariance relation in the dual space of the geometric problem. The paper ends with an application to safety critical model predictive control.

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arXiv2017

Correctness Guarantees for the Composition of Lane Keeping and Adaptive Cruise Control

This paper develops a control approach with correctness guarantees for the simultaneous operation of lane keeping and adaptive cruise control. The safety specifications for these driver assistance modules are expressed in terms of set invariance. Control barrier functions are used to design a family of control solutions that guarantee the forward invariance of a set, which implies satisfaction of the safety specifications. The control barrier functions are synthesized through a combination of sum-of-squares program and physics-based modeling and optimization. A real-time quadratic program is posed to combine the control barrier functions with the performance-based controllers, which can be either expressed as control Lyapunov function conditions or as black-box legacy controllers. In both cases, the resulting feedback control guarantees the safety of the composed driver assistance modules in a formally correct manner. Importantly, the quadratic program admits a closed-form solution that can be easily implemented. The effectiveness of the control approach is demonstrated by simulations in the industry-standard vehicle simulator Carsim.

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arXiv2017

Computing Robust Controlled Invariant Sets of Linear Systems

We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an arbitrarily precise outer approximation of the maximal robust controlled invariant set, while the second method provides an inner approximation. The outer approximation scheme is $δ$-complete, given that the constraint sets are formulated as finite unions of polytopes.

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arXiv2016

Mode-Target Games: Reactive Synthesis for Control Applications

In this paper we introduce a class of Linear Temporal Logic (LTL) specifications for which the problem of synthesizing controllers can be solved in polynomial time. The new class of specifications is an LTL fragment that we term Mode-Target (MT) and is inspired by numerous control applications where there are modes and corresponding (possibly multiple) targets for each mode. We formulate the problem of synthesizing a controller enforcing an MT specification as a game and provide an algorithm that requires $O(\sum_i t_i n^2)$ symbolic steps, where $n$ is the number of states in the game graph, and $t_i$ is the number of targets corresponding to mode $i$.

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arXiv2016

Robustness of Control Barrier Functions for Safety Critical Control

Barrier functions (also called certificates) have been an important tool for the verification of hybrid systems, and have also played important roles in optimization and multi-objective control. The extension of a barrier function to a controlled system results in a control barrier function. This can be thought of as being analogous to how Sontag extended Lyapunov functions to control Lyapunov functions in order to enable controller synthesis for stabilization tasks. A control barrier function enables controller synthesis for safety requirements specified by forward invariance of a set using a Lyapunov-like condition. This paper develops several important extensions to the notion of a control barrier function. The first involves robustness under perturbations to the vector field defining the system. Input-to-State stability conditions are given that provide for forward invariance, when disturbances are present, of a "relaxation" of set rendered invariant without disturbances. A control barrier function can be combined with a control Lyapunov function in a quadratic program to achieve a control objective subject to safety guarantees. The second result of the paper gives conditions for the control law obtained by solving the quadratic program to be Lipschitz continuous and therefore to gives rise to well-defined solutions of the resulting closed-loop system.

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arXiv2016

Control Barrier Function Based Quadratic Programs for Safety Critical Systems

Safety critical systems involve the tight coupling between potentially conflicting control objectives and safety constraints. As a means of creating a formal framework for controlling systems of this form, and with a view toward automotive applications, this paper develops a methodology that allows safety conditions -- expressed as control barrier functions -- to be unified with performance objectives -- expressed as control Lyapunov functions -- in the context of real-time optimization-based controllers. Safety conditions are specified in terms of forward invariance of a set, and are verified via two novel generalizations of barrier functions; in each case, the existence of a barrier function satisfying Lyapunov-like conditions implies forward invariance of the set, and the relationship between these two classes of barrier functions is characterized. In addition, each of these formulations yields a notion of control barrier function (CBF), providing inequality constraints in the control input that, when satisfied, again imply forward invariance of the set. Through these constructions, CBFs can naturally be unified with control Lyapunov functions (CLFs) in the context of a quadratic program (QP); this allows for the achievement of control objectives (represented by CLFs) subject to conditions on the admissible states of the system (represented by CBFs). The mediation of safety and performance through a QP is demonstrated on adaptive cruise control and lane keeping, two automotive control problems that present both safety and performance considerations coupled with actuator bounds.

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arXiv2016

Dynamics-Based Reactive Synthesis and Automated Revisions for High-Level Robot Control

The aim of this work is to address issues where formal specifications cannot be realized on a given dynamical system subjected to a changing environment. Such failures occur whenever the dynamics of the system restrict the robot in such a way that the environment may prevent the robot from progressing safely to its goals. We provide a framework that automatically synthesizes revisions to such specifications that restrict the assumed behaviors of the environment and the behaviors of the system. We provide a means for explaining such modifications to the user in a concise, easy-to-understand manner. Integral to the framework is a new algorithm for synthesizing controllers for reactive specifications that include a discrete representation of the robot's dynamics. The new approach is demonstrated with a complex task implemented using a unicycle model.

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