Myopic Control of Systems with Unknown Dynamics

Ornik, Melkior; Carr, Steven; Israel, Arie; Topcu, Ufuk

doi:10.23919/acc.2019.8814482

Cited by 4 publications

(20 citation statements)

References 33 publications

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“…We assume that dynamics given by (10) still evolve on X . Because of the time-varying element of N , (10) does not automatically fall within the class of systems in (1). However, by appending an additional variable x n+1 given by the dynamics dx n+1 /dt = 1 and x n+1 (0) = 0, and with an obvious slight abuse of notation, we obtain dynamicṡ…”

Section: Robustness To Disturbancesmentioning

confidence: 99%

“…All values are in feet, seconds and centiradians. The limits on control inputs are set to u 1 = δ e ∈ [− 30,30] and 1], roughly informed by the descriptions in [41], [42].…”

Section: A Damaged Aircraft Examplementioning

confidence: 99%

“…For the sake of narrative, we will usually omit a formal distinction between a control law u and a control input u ∈ U when such a distinction is obvious from the context. Additionally, while the notion of a solution to (1), and hence to (3) as well, is questionable in the case of general measurable functions u * , in the remainder of the paper we will be working with piecewise-continuous control laws, and in that sense we will not have any issues.…”

mentioning

confidence: 99%

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Control-Oriented Learning on the Fly

Ornik

Carr

Israel

et al. 2020

IEEE Trans. Automat. Contr.

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This paper focuses on developing a strategy for control of systems whose dynamics are almost entirely unknown.This situation arises naturally in a scenario where a system undergoes a critical failure. In that case, it is imperative to retain the ability to satisfy basic control objectives in order to avert an imminent catastrophe. A prime example of such an objective is the reach-avoid problem, where a system needs to move to a certain state in a constrained state space. To deal with limitations on our knowledge of system dynamics, we develop a theory of myopic control.The primary goal of myopic control is to, at any given time, optimize the current direction of the system trajectory, given solely the information obtained about the system until that time. We propose an algorithm that uses small perturbations in the control effort to learn local dynamics while simultaneously ensuring that the system moves in a direction that appears to be nearly optimal, and provide hard bounds for its suboptimality. We additionally verify the usefulness of the algorithm on a simulation of a damaged aircraft seeking to avoid a crash, as well as on an example of a Van der Pol oscillator.

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Section: Robustness To Disturbancesmentioning

confidence: 99%

“…All values are in feet, seconds and centiradians. The limits on control inputs are set to u 1 = δ e ∈ [− 30,30] and 1], roughly informed by the descriptions in [41], [42].…”

Section: A Damaged Aircraft Examplementioning

confidence: 99%

mentioning

confidence: 99%

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Control-Oriented Learning on the Fly

Ornik

Carr

Israel

et al. 2020

IEEE Trans. Automat. Contr.

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“…The assumptions and objectives of this work come from the context of online learning and control of a nonlinear system with unknown dynamics. Such a framework, described by Ornik et al [2017Ornik et al [ , 2019, is motivated by the desire to successfully control a system with entirely unknown dynamics by learning as much as possible about the dynamics "on the fly", i.e., solely from the system's behavior during a single system run; it differs from classical work on adaptive or robust control [Ioannou andSun, 1996, Dullerud andPaganini, 2000] by not assuming almost any knowledge about the magnitude or the structure of uncertainty about the system dynamics, and from work on datadriven learning and control synthesis by not allowing collection of information on system dynamics by way of repeated system runs [Brunton et al, 2016, Chen et al, 2018.…”

Section: Motivation and Overviewmentioning

confidence: 99%

“…While previous work has considered computation of reachable sets under uncertainties in dynamics such as those given by bounded unknown disturbances [Mitchell et al, 2005] or a finite number of uncertain parameters [Althoff et al, 2008], the framework that we are considering contains substantially fewer information. Namely, motivated by the work of Ornik et al [2017Ornik et al [ , 2019 that determines local controlled dynamics of a nonlinear system at a given state using solely the information from a single trajectory until the time that the system reached that state, we assume that the only available knowledge at the time of computing the reachable set consists of (i) local dynamics at a single point and (ii) Lipschitz bounds on the rate of change of system dynamics in the state space. As we do not know anything else about the system dynamics, we wish to determine the set of states that are guaranteed to be reachable from that single point regardless of the true system dynamics, as long as they are consistent with the above knowledge.…”

Section: Introductionmentioning

confidence: 99%

Guaranteed Reachability for Systems with Unknown Dynamics

Ornik¹

2019

Preprint

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The problem of computing the reachable set for a given system is a quintessential question in nonlinear control theory. While previous work has yielded a plethora of approximate and analytical methods for determining such a set, these methods naturally require the knowledge of the controlled system dynamics throughout the state space. In contrast to such classical methods, this paper considers the question of estimating the reachable set of a control system using only the knowledge of local system dynamics at a single point and a bound on the rate of change of dynamics. Namely, motivated by the need for safety-critical planning for systems with unknown dynamics, we consider the problem of describing the guaranteed reachability set: the set of all states that are guaranteed to be reachable regardless of the true system dynamics, given the current knowledge about the system. We show that such a set can be underapproximated by a reachable set of a related known system whose dynamics at every state depend on the velocity vectors that are guaranteed to all control systems consistent with the assumed knowledge. Complementing the theory, numerical examples of a singledimensional control system and a simple model of an aircraft in distress verify that such an underapproximation is meaningful in practice, and may indeed equal the desired guaranteed reachability set.

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On-the-Fly Control of Unknown Nonlinear Systems With Sublinear Regret

Vinod

Israel

Topcu

2023

IEEE Trans. Automat. Contr.

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We study the problem of data-driven, constrained control of unknown nonlinear dynamics from a single ongoing and finite-horizon trajectory. We consider a one-step optimal control problem with a smooth, black-box objective, typically a composition of a known cost function and the unknown dynamics. We investigate an on-the-fly control paradigm, i.e., at each time step, the evolution of the dynamics and the first-order information of the cost are provided only for the executed control action. We propose an optimization-based control algorithm that iteratively minimizes a data-driven surrogate function for the unknown objective. We prove that the proposed approach incurs sublinear cumulative regret (step-wise suboptimality with respect to an optimal one-step controller) and is worst-case optimal among a broad class of data-driven control algorithms. We also present tractable reformulations of the approach that can leverage offthe-shelf solvers for efficient implementations.

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Myopic Control of Systems with Unknown Dynamics

Cited by 4 publications

References 33 publications

Control-Oriented Learning on the Fly

Control-Oriented Learning on the Fly

Guaranteed Reachability for Systems with Unknown Dynamics

On-the-Fly Control of Unknown Nonlinear Systems With Sublinear Regret

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