arXiv subjects

Pedro Hespanhol

Publications and source records attributed to Pedro Hespanhol.

14 recordsLinked to original sources

arXiv2021

Resilient Control of Platooning Networked Robotic Systems via Dynamic Watermarking

Networked robotic systems, such as connected vehicle platoons, can improve the safety and efficiency of transportation networks by allowing for high-speed coordination. To enable such coordination, these systems rely on networked communications. This can make them susceptible to cyber attacks. Though security methods such as encryption or specially designed network topologies can increase the difficulty of successfully executing such an attack, these techniques are unable to guarantee secure communication against an attacker. More troublingly, these security methods are unable to ensure that individual agents are able to detect attacks that alter the content of specific messages. To ensure resilient behavior under such attacks, this paper formulates a networked linear time-varying version of dynamic watermarking in which each agent generates and adds a private excitation to the input of its corresponding robotic subsystem. This paper demonstrates that such a method can enable each agent in a networked robotic system to detect cyber attacks. By altering measurements sent between vehicles, this paper illustrates that an attacker can create unstable behavior within a platoon. By utilizing the dynamic watermarking method proposed in this paper, the attack is detected, allowing the vehicles in the platoon to gracefully degrade to a non-communicative control strategy that maintains safety across a variety of scenarios.

math.OC↗

arXiv2020

Statistical Consistency of Set-Membership Estimator for Linear Systems

Suppose we can choose from a set of linear autonomous systems with bounded process noise, the dynamics of each system are unknown, and we would like to design a stabilizing policy. The underlying question is how to estimate the dynamics of each system given that measurements of each system will be nonsequential. Though seemingly straightforward, existing proof techniques for proving statistical consistency of system identification procedures fail when measurements are nonsequential. Here, we prove that the set-membership estimator is statistically consistent even when measurements are nonsequential. We numerically illustrate its strong consistency.

math.OC↗

arXiv2020

Covariance-Robust Dynamic Watermarking

Attack detection and mitigation strategies for cyberphysical systems (CPS) are an active area of research, and researchers have developed a variety of attack-detection tools such as dynamic watermarking. However, such methods often make assumptions that are difficult to guarantee, such as exact knowledge of the distribution of measurement noise. Here, we develop a new dynamic watermarking method that we call covariance-robust dynamic watermarking, which is able to handle uncertainties in the covariance of measurement noise. Specifically, we consider two cases. In the first this covariance is fixed but unknown, and in the second this covariance is slowly-varying. For our tests, we only require knowledge of a set within which the covariance lies. Furthermore, we connect this problem to that of algorithmic fairness and the nascent field of fair hypothesis testing, and we show that our tests satisfy some notions of fairness. Finally, we exhibit the efficacy of our tests on empirical examples chosen to reflect values observed in a standard simulation model of autonomous vehicles.

eess.SY↗

arXiv2020

Hypothesis Testing Approach to Detecting Collusion in Competitive Environments

There is growing concern about tacit collusion using algorithmic pricing, and regulators need tools to help detect the possibility of such collusion. This paper studies how to design a hypothesis testing framework in order to decide whether agents are behaving competitively or not. In our setting, agents are utility-maximizing and compete over prices of items. A regulator, with no knowledge of the agent's utility function, has access only to the agents' strategies (i.e., pricing decisions) and external shock values in order to decide if agents are behaving in competition according to some equilibrium problem. We leverage the formulation of such a problem as an inverse variational inequality and design a hypothesis test under a minimal set of assumptions. We demonstrate our method with computational experiments of the Bertrand competition game (with and without collusion) and show how our method performs.

cs.GT↗

arXiv2020

Detecting Deception Attacks on Autonomous Vehicles via Linear Time-Varying Dynamic Watermarking

Cyber-physical systems (CPS) such as autonomous vehicles rely on both on-board sensors and external communications to estimate their state. Unfortunately, these communications render the system vulnerable to cyber-attacks. While many attack detection methods have begun to address these concerns, they are limited to linear time-invariant (LTI) systems. Though LTI system models provide accurate approximations for CPS such as autonomous vehicles at constant speed and turning radii, they are inaccurate for more complex motions such as lane changes, turns, and changes in velocity. Since these more complex motions are more suitably described by linear time-varying (LTV) system models rather than LTI models, Dynamic Watermarking, which adds a private excitation to the input signal to validate measurements, has recently been extended to LTV systems. However, this extension does not allow for LTV systems that require several steps before the effect of a given control input can be seen in the measurement signal. Additionally, there is no consideration for the time-varying effects of auto-correlation. Furthermore, a proof of concept was only provided using simulations of a simplified model. This paper relaxes the requirement for inputs to be visible in a single step and constructs an auto-correlation normalizing factor to remove the effects of auto-correlation. In addition, Dynamic Watermarking is applied to a high-fidelity vehicle model in carsim and a 1/10 scale autonomous rover to further reinforce the proof of concept for realistic systems. In each case, the vehicle follows a predefined path with time-varying velocity and turning radii. A replay attack, which replays previously recorded measurements, is shown to be detectable using LTV Dynamic Watermarking in a quick and repeatable manner.

math.OC↗

arXiv2019

Detecting Generalized Replay Attacks via Time-Varying Dynamic Watermarking

Cyber-physical systems (CPS) often rely on external communication for supervisory control or sensing. Unfortunately, these communications render the system vulnerable to cyber-attacks. Attacks that alter messages, such as replay attacks that record measurement signals and then play them back to the system, can cause devastating effects. Dynamic Watermarking methods, which inject a private excitation into control inputs to secure resulting measurement signals, have begun addressing the challenges of detecting these attacks, but have been restricted to linear time invariant (LTI) systems. Though LTI models are sufficient for some applications, other CPS, such as autonomous vehicles, require more complex models. This paper develops a linear time-varying (LTV) extension to previous Dynamic Watermarking methods by designing a matrix normalization factor to accommodate the temporal changes in the system. Implementable tests are provided with considerations for real-world systems. The proposed method is then shown to be able to detect generalized replay attacks both in theory and in simulation using a LTV vehicle model.

math.OC↗

arXiv2019

Sensor Switching Control Under Attacks Detectable by Finite Sample Dynamic Watermarking Tests

Control system security is enhanced by the ability to detect malicious attacks on sensor measurements. Dynamic watermarking can detect such attacks on linear time-invariant (LTI) systems. However, existing theory focuses on attack detection and not on the use of watermarking in conjunction with attack mitigation strategies. In this paper, we study the problem of switching between two sets of sensors: One set of sensors has high accuracy but is vulnerable to attack, while the second set of sensors has low accuracy but cannot be attacked. The problem is to design a sensor switching strategy based on attack detection by dynamic watermarking. This requires new theory because existing results are not adequate to control or bound the behavior of sensor switching strategies that use finite data. To overcome this, we develop new finite sample hypothesis tests for dynamic watermarking in the case of bounded disturbances, using the modern theory of concentration of measure for random matrices. Our resulting switching strategy is validated with a simulation analysis in an autonomous driving setting, which demonstrates the strong performance of our proposed policy.

math.OC↗

arXiv2019

A Structure Exploiting Branch-and-Bound Algorithm for Mixed-Integer Model Predictive Control

Mixed-integer model predictive control (MI-MPC) requires the solution of a mixed-integer quadratic program (MIQP) at each sampling instant under strict timing constraints, where part of the state and control variables can only assume a discrete set of values. Several applications in automotive, aerospace and hybrid systems are practical examples of how such discrete-valued variables arise. We utilize the sequential nature and the problem structure of MI-MPC in order to provide a branch-and-bound algorithm that can exploit not only the block-sparse optimal control structure of the problem but that can also be warm started by propagating information from branch-and-bound trees and solution paths at previous time steps. We illustrate the computational performance of the proposed algorithm and compare against current state-of-the-art solvers for multiple MPC case studies, based on a preliminary implementation in MATLAB and C code.

math.OC↗

arXiv2019

Adjoint-based SQP Method with Block-wise quasi-Newton Jacobian Updates for Nonlinear Optimal Control

Nonlinear model predictive control~(NMPC) generally requires the solution of a non-convex optimization problem at each sampling instant under strict timing constraints, based on a set of differential equations that can often be stiff and/or that may include implicit algebraic equations. This paper provides a local convergence analysis for the recently proposed adjoint-based sequential quadratic programming~(SQP) algorithm that is based on a block-structured variant of the two-sided rank-one~(TR1) quasi-Newton update formula to efficiently compute Jacobian matrix approximations in a sparsity preserving fashion. A particularly efficient algorithm implementation is proposed in case an implicit integration scheme is used for discretization of the optimal control problem, in which matrix factorization and matrix-matrix operations can be avoided entirely. The convergence analysis results as well as the computational performance of the proposed optimization algorithm are illustrated for two simulation case studies of nonlinear MPC.

math.OC↗

arXiv2019

Surrogate Optimal Control for Strategic Multi-Agent Systems

This paper studies how to design a platform to optimally control constrained multi-agent systems with a single coordinator and multiple strategic agents. In our setting, the agents cannot apply control inputs and only the coordinator applies control inputs; however, the coordinator does not know the objective functions of the agents, and so must choose control actions based on information provided by the agents. One major challenge is that if the platform is not correctly designed then the agents may provide false information to the coordinator in order to achieve improved outcomes for themselves at the expense of the overall system efficiency. Here, we design an interaction mechanism between the agents and the coordinator such that the mechanism: ensures agents truthfully report their information, has low communication requirements, and leads to a control action that achieves efficiency by achieving a Nash equilibrium. In particular, we design a mechanism in which each agent does not need to posses full knowledge of the system dynamics nor the objective functions of other agents. We illustrate our proposed mechanism in a model predictive control (MPC) application involving heating, ventilation, air-conditioning (HVAC) control by a building manager of an apartment building. Our results showcase how such a mechanism can be potentially used in the context of distributed MPC.

math.OC↗

arXiv2018

Simulation and Real-World Evaluation of Attack Detection Schemes

A variety of anomaly detection schemes have been proposed to detect malicious attacks to Cyber-Physical Systems. Among these schemes, Dynamic Watermarking methods have been proven highly effective at detecting a wide range of attacks. Unfortunately, in contrast to other anomaly detectors, no method has been presented to design a Dynamic Watermarking detector to achieve a user-specified false alarm rate, or subsequently evaluate the capabilities of an attacker under such a selection. This paper describes methods to measure the capability of an attacker, to numerically approximate this metric, and to design a Dynamic Watermarking detector that can achieve a user-specified rate of false alarms. The performance of the Dynamic Watermarking detector is compared to three classical anomaly detectors in simulation and on a real-world platform. These experiments illustrate that the attack capability under the Dynamic Watermarking detector is comparable to those of classic anomaly detectors. Importantly, these experiments also make clear that the Dynamic Watermarking detector is consistently able to detect attacks that the other class of detectors are unable to identify.

eess.SY↗

arXiv2017

Family-Personalized Dietary Planning with Temporal Dynamics

Poor diet and nutrition in the United States has immense financial and health costs, and development of new tools for diet planning could help families better balance their financial and temporal constraints with the quality of their diet and meals. This paper formulates a novel model for dietary planning that incorporates two types of temporal constraints (i.e., dynamics on the perishability of raw ingredients over time, and constraints on the time required to prepare meals) by explicitly incorporating the relationship between raw ingredients and selected food recipes. Our formulation is a diet planning model with integer-valued decision variables, and so we study the problem of designing approximation algorithms (i.e, algorithms with polynomial-time computation and guarantees on the quality of the computed solution) for our dietary model. We develop a deterministic approximation algorithm that is based on a deterministic variant of randomized rounding, and then evaluate our deterministic approximation algorithm with numerical experiments of dietary planning using a database of about 2000 food recipes and 150 raw ingredients.

math.OC↗

arXiv2017

Statistical Watermarking for Networked Control Systems

Watermarking can detect sensor attacks in control systems by injecting a private signal into the control, whereby attacks are identified by checking the statistics of the sensor measurements and private signal. However, past approaches assume full state measurements or a centralized controller, which is not found in networked LTI systems with subcontrollers. Since generally the entire system is neither controllable nor observable by a single subcontroller, communication of sensor measurements is required to ensure closed-loop stability. The possibility of attacking the communication channel has not been explicitly considered by previous watermarking schemes, and requires a new design. In this paper, we derive a statistical watermarking test that can detect both sensor and communication attacks. A unique (compared to the non-networked case) aspect of the implementing this test is the state-feedback controller must be designed so that the closed-loop system is controllable by each sub-controller, and we provide two approaches to design such a controller using Heymann's lemma and a multi-input generalization of Heymann's lemma. The usefulness of our approach is demonstrated with a simulation of detecting attacks in a platoon of autonomous vehicles. Our test allows each vehicle to independently detect attacks on both the communication channel between vehicles and on the sensor measurements.

math.OC↗

arXiv2017

Dynamic Watermarking for General LTI Systems

Detecting attacks in control systems is an important aspect of designing secure and resilient control systems. Recently, a dynamic watermarking approach was proposed for detecting malicious sensor attacks for SISO LTI systems with partial state observations and MIMO LTI systems with a full rank input matrix and full state observations; however, these previous approaches cannot be applied to general LTI systems that are MIMO and have partial state observations. This paper designs a dynamic watermarking approach for detecting malicious sensor attacks for general LTI systems, and we provide a new set of asymptotic and statistical tests. We prove these tests can detect attacks that follow a specified attack model (more general than replay attacks), and we also show that these tests simplify to existing tests when the system is SISO or has full rank input matrix and full state observations. The benefit of our approach is demonstrated with a simulation analysis of detecting sensor attacks in autonomous vehicles. Our approach can distinguish between sensor attacks and wind disturbance (through an internal model principle framework), whereas improperly designed tests cannot distinguish between sensor attacks and wind disturbance.

math.OC↗