On-The-Fly Control of Unknown Smooth Systems from Limited Data

Djeumou, Franck; Vinod, Abraham P.; Goubault, Éric; Putot, Sylvie; Topcu, Ufuk

doi:10.23919/acc50511.2021.9483367

Cited by 10 publications

(11 citation statements)

References 17 publications

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“…In [15], the authors describe a data-driven algorithm similar to our algorithm. However, the algorithm in [15] works only for control-affine dynamics.…”

Section: Related Workmentioning

confidence: 99%

“…In [15], the authors describe a data-driven algorithm similar to our algorithm. However, the algorithm in [15] works only for control-affine dynamics. Further, most of the considered side information is not tailored for robotic systems, and the authors investigate only one-step optimal control problems.…”

Section: Related Workmentioning

confidence: 99%

“…Furthermore, in their current forms, none of the above approaches can incorporate side information. The authors in [15] empirically demonstrate that a learning algorithm with side information outperforms these approaches in terms of computation time and suboptimality of the control. Thus, our approach is guaranteed to inherit such properties.…”

Section: Related Workmentioning

confidence: 99%

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Learning to Reach, Swim, Walk and Fly in One Trial: Data-Driven Control with Scarce Data and Side Information

Djeumou¹,

Topcu²

2021

Preprint

Self Cite

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We develop a learning-based control algorithm for unknown dynamical systems under very severe data limitations. Specifically, the algorithm has access to streaming data only from a single and ongoing trial. Despite the scarcity of data, we show-through a series of examples-that the algorithm can provide performance comparable to reinforcement learning algorithms trained over millions of environment interactions. It accomplishes such performance by effectively leveraging various forms of side information on the dynamics to reduce the sample complexity. Such side information typically comes from elementary laws of physics and qualitative properties of the system. More precisely, the algorithm approximately solves an optimal control problem encoding the system's desired behavior. To this end, it constructs and refines a differential inclusion that contains the unknown vector field of the dynamics. The differential inclusion, used in an interval Taylor-based method, enables to over-approximate the set of states the system may reach. Theoretically, we establish a bound on the suboptimality of the approximate solution with respect to the case of known dynamics. We show that the longer the trial or the more side information is available, the tighter the bound. Empirically, experiments in a high-fidelity F-16 aircraft simulator and MuJoCo's environments such as the Reacher, Swimmer, and Cheetah illustrate the algorithm's effectiveness.

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“…In [15], the authors describe a data-driven algorithm similar to our algorithm. However, the algorithm in [15] works only for control-affine dynamics.…”

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Learning to Reach, Swim, Walk and Fly in One Trial: Data-Driven Control with Scarce Data and Side Information

Djeumou¹,

Topcu²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

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“…with a priori unknown terms f and g, for which the assumptions we impose are restricted to local Lipschitz continuity. Unlike previous works in the related literature, we do not impose growth conditions [3] or global Lipschitz continuity on the dynamics [4], [5], and we do not assume boundedness of the state [5]. Moreover, we do not restrict g to be in the…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, many of the aforementioned works require large amounts of data in order to provide accurate resutls. Recent methodologies that employ limited data obtained on the fly have been developed in [4], [5], [35], imposing, how-ever, restrictive assumptions on the dynamics, such as global boundedness and Lipschitz continuity with known bounds, or known bounds on the approximation errors. In addition, the aforementioned works resort to online optimization techniques for safety specifications, increasing thus the complexity of the resulting algorithms.…”

Section: Introductionmentioning

confidence: 99%

Safety-Constrained Learning and Control using Scarce Data and Reciprocal Barriers

Verginis,

Djeumou,

Topcu

2021

Preprint

Self Cite

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We develop a control algorithm that ensures the safety, in terms of confinement in a set, of a system with unknown, 2nd-order nonlinear dynamics. The algorithm establishes novel connections between data-driven and robust, nonlinear control. It is based on data obtained online from the current trajectory and the concept of reciprocal barriers. More specifically, it first uses the obtained data to calculate set-valued functions that over-approximate the unknown dynamic terms. For the second step of the algorithm, we design a robust control scheme that uses these functions as well as reciprocal barriers to render the system forward invariant with respect to the safe set. In addition, we provide an extension of the algorithm that tackles issues of controllability loss incurred by the nullspace of the controldirection matrix. The algorithm removes a series of standard, limiting assumptions considered in the related literature since it does not require global boundedness, growth conditions, or a priori approximations of the unknown dynamics' terms.

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Physics‐Informed Neural Networks to Model and Control Robots: A Theoretical and Experimental Investigation

Liu,

Borja,

Della Santina

2024

Advanced Intelligent Systems

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This work concerns the application of physics‐informed neural networks to the modeling and control of complex robotic systems. Achieving this goal requires extending physics‐informed neural networks to handle nonconservative effects. These learned models are proposed to combine with model‐based controllers originally developed with first‐principle models in mind. By combining standard and new techniques, precise control performance can be achieved while proving theoretical stability bounds. These validations include real‐world experiments of motion prediction with a soft robot and trajectory tracking with a Franka Emika Panda manipulator.

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On-The-Fly Control of Unknown Smooth Systems from Limited Data

Cited by 10 publications

References 17 publications

Learning to Reach, Swim, Walk and Fly in One Trial: Data-Driven Control with Scarce Data and Side Information

Learning to Reach, Swim, Walk and Fly in One Trial: Data-Driven Control with Scarce Data and Side Information

Safety-Constrained Learning and Control using Scarce Data and Reciprocal Barriers

Physics‐Informed Neural Networks to Model and Control Robots: A Theoretical and Experimental Investigation

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