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1. Predictive Runtime Monitoring for Linear Stochastic Systems and Applications to Geofence Enforcement for UAVs

   https://doi.org/10.1007/978-3-030-32079-9_20  

   Yoon, Hansol; Chou, Yi; Chen, Xin; Frew, Eric; Sankaranarayanan, Sriram (October 2019, Lecture notes in computer science)

   We propose a predictive runtime monitoring approach for linear systems with stochastic disturbances. The goal of the monitor is to decide if there exists a possible sequence of control inputs over a given time horizon to ensure that a safety property is maintained with a sufficiently high probability. We derive an efficient algorithm for performing the predictive monitoring in real time, specifically for linear time invariant (LTI) systems driven by stochastic disturbances. The algorithm implicitly defines a control envelope set such that if the current control input to the system lies in this set, there exists a future strategy over a time horizon consisting of the next N steps to guarantee the safety property of interest. As a result, the proposed monitor is oblivious of the actual controller, and therefore, applicable even in the presence of complex control systems including highly adaptive controllers. Furthermore, we apply our proposed approach to monitor whether a UAV will respect a “geofence” defined by a geographical region over which the vehicle may operate. To achieve this, we construct a data-driven linear model of the UAVs dynamics, while carefully modeling the uncertainties due to wind, GPS errors and modeling errors as time-varying disturbances. Using realistic data obtained from flight tests, we demonstrate the advantages and drawbacks of the predictive monitoring approach. 

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2. A Fixed-Time Stable Adaptation Law for Safety-Critical Control under Parametric Uncertainty

   Black, Mitchell; Arabi, Ehsan; Panagou, Dimitra (January 2021, 2021 European Control Conference)

   We present a novel technique for solving the problem of safe control for a general class of nonlinear, control-affine systems subject to parametric model uncertainty. Invoking Lyapunov analysis and the notion of fixed-time stability (FxTS), we introduce a parameter adaptation law which guarantees convergence of the estimates of unknown parameters in the system dynamics to their true values within a fixed-time independent of the initial parameter estimation error. We then synthesize the adaptation law with a robust, adaptive control barrier function (RaCBF) based quadratic program to compute safe control inputs despite the considered model uncertainty. To corroborate our results, we undertake a comparative case study on the efficacy of this result versus other recent approaches in the literature to safe control under uncertainty, and close by highlighting the value of our method in the context of an automobile overtake scenario. 

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3. Scalable Robust Adaptive Control from the System Level Perspective

   https://doi.org/10.23919/ACC.2019.8814896  

   Ho, Dimitar; Doyle, John C. (July 2019, 2019 American Control Conference (ACC))

   We will present a new general framework for robust and adaptive control that allows for distributed and scalable learning and control of large systems of interconnected linear subsystems. The control method is demonstrated for a linear time-invariant system with bounded parameter uncertainties, disturbances and noise. The presented scheme continuously collects measurements to reduce the uncertainty about the system parameters and adapts dynamic robust controllers online in a stable and performance-improving way. A key enabler for our approach is choosing a time-varying dynamic controller implementation, inspired by recent work on System Level Synthesis [1]. We leverage a new robustness result for this implementation to propose a general robust adaptive control algorithm. In particular, the algorithm allows us to impose communication and delay constraints on the controller implementation and is formulated as a sequence of robust optimization problems that can be solved in a distributed manner. The proposed control methodology performs particularly well when the interconnection between systems is sparse and the dynamics of local regions of subsystems depend only on a small number of parameters. As we will show on a five-dimensional exemplary chain-system, the algorithm can utilize system structure to efficiently learn and control the entire system while respecting communication and implementation constraints. Moreover, although current theoretical results require the assumption of small initial uncertainties to guarantee robustness, we will present simulations that show good closed-loop performance even in the case of large uncertainties, which suggests that this assumption is not critical for the presented technique and future work will focus on providing less conservative guarantees. 

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4. Robust-RRT: Probabilistically-Complete Motion Planning for Uncertain Nonlinear Systems

   Wu, Albert; Lew, Thomas; Solovey, Kiril; Schmerling, Edward; Pavone, Marco (September 2022, International Symposium on Robotics Research)

   Robust motion planning entails computing a global motion plan that is safe under all possible uncertainty realizations, be it in the system dynamics, the robot’s initial position, or with respect to external disturbances. Current approaches for robust motion planning either lack theoretical guarantees, or make restrictive assumptions on the system dynamics and uncertainty distributions. In this paper, we address these limitations by proposing the robust rapidly-exploring random-tree (Robust-RRT) algorithm, which integrates forward reachability analysis directly into sampling-based control trajectory synthesis. We prove that Robust-RRT is probabilistically complete (PC) for nonlinear Lipschitz continuous dynamical systems with bounded uncertainty. In other words, Robust-RRT eventually finds a robust motion plan that is feasible under all possible uncertainty realizations assuming such a plan exists. Our analysis applies even to unstable systems that admit only short-horizon feasible plans; this is because we explicitly consider the time evolution of reachable sets along control trajectories. Thanks to the explicit consideration of time dependency in our analysis, PC applies to unstabilizable systems. To the best of our knowledge, this is the most general PC proof for robust sampling-based motion planning, in terms of the types of uncertainties and dynamical systems it can handle. Considering that an exact computation of reachable sets can be computationally expensive for some dynamical systems, we incorporate sampling-based reachability analysis into Robust-RRT and demonstrate our robust planner on nonlinear, underactuated, and hybrid systems. 

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5. Autonomous Spacecraft Attitude Reorientation Using Robust Sampled-Data Control Barrier Functions

   https://doi.org/10.2514/1.G007456  

   Breeden, Joseph; Panagou, Dimitra (October 2023, Journal of Guidance, Control, and Dynamics)

   This paper presents a provably safe method for constrained reorientation of a spacecraft in the presence of input constraints, bounded disturbances, and fixed frequency zero-order-hold (ZOH) control inputs. The set of states satisfying all pointing and rate constraints, herein called the safe set, is expressed as the intersection of the sublevel sets of several constraint functions, which are subsequently converted into control barrier functions (CBFs). The method then extends prior results on utilizing CBFs with ZOH controllers to the case of relative-degree-2 constraint functions, as occurs in the constrained attitude reorientation problem. The developed sampled-data controller is also shown to remain provably safe in the presence of input constraints and bounded disturbances. Finally, the method is validated and compared to three prior approaches via both low-fidelity and mid-fidelity simulations. 

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