Distributed Feedback Optimisation for Robotic Coordination

Sylvain, Fricker,; Perez, Michel; Badyn, Mathias Hudoba de; Dörfler, Florian

doi:10.48550/arxiv.2109.14486

Cited by 1 publication

(4 citation statements)

References 23 publications

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“…Notably, this assumption is satisfied in, e.g., power systems [13], [14], [16], [34], transportation networks [18], and in neuroscience [44]. Our model clearly subsumes the case where no disturbance w is present, as in the models for, e.g., autonomous driving [1], [2] and robotics [45]. We also emphasize that the dynamics (1) can model both the dynamics of the physical system and of the stabilizing controllers; see, for example, [13], our previous work on LTI systems in [47], and the recent survey [19].…”

Section: Assumption 2 (Properties Of Exogenous Inputs)mentioning

confidence: 76%

“…In this section, we illustrate how to apply the proposed framework to control a unicycle robot to track an optimal equilibrium point and whose position is accessible only through camera images. We consider a robot described by unicycle dynamics with state x = (a, b, θ), where r := (a, b) T ∈ R 2 denotes the position of the robot in a 2dimensional plane, and θ ∈ (−π, π] denotes its orientation with respect to the a−axis [45]. The unicycle dynamics are:…”

Section: Data-based Gradient Flowmentioning

confidence: 99%

“…We have: V (φ) = −kφ sin(φ) − kφ 2 ≤ −kφ 2 = −2kV (φ), with V (φ) = 0 if and only if φ = 0. The proof of exponential stability of ξ follows immediately from [45,Lem. 2.1].…”

Section: Data-based Gradient Flowmentioning

confidence: 99%

“…In conclusion, we highlight that the assumptions and control frameworks outlined in this paper find applications in, for example, power systems [13], [14], [16], [34], traffic flow control in transportation networks [18], epidemic control [43], and in neuroscience [44]. When the dynamical model for the plant does not include exogenous disturbances, our optimization-based controllers can also be utilized in the context of autonomous driving [1], [2] and robotics [45].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Online Optimization of Dynamical Systems With Deep Learning Perception

Cothren

Bianchin

Dall’Anese

2022

IEEE Open J. Control. Syst.

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This paper considers the problem of controlling a dynamical system when the state cannot be directly measured and the control performance metrics are unknown or only partially known. In particular, we focus on the design of data-driven controllers to regulate a dynamical system to the solution of a constrained convex optimization problem where: i) the state must be estimated from nonlinear and possibly high-dimensional data; and ii) the cost of the optimization problem -which models control objectives associated with inputs and states of the system -is not available and must be learned from data. We propose a data-driven feedback controller that is based on adaptations of a projected gradient-flow method; the controller includes neural networks as integral components for the estimation of the unknown functions. Leveraging stability theory for perturbed systems, we derive sufficient conditions to guarantee exponential input-to-state stability (ISS) of the control loop. In particular, we show that the interconnected system is ISS with respect to the approximation errors of the neural network and unknown disturbances affecting the system. The transient bounds combine the universal approximation property of deep neural networks with the ISS characterization. Illustrative numerical results are presented in the context of robotics and control of epidemics.

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