On-the-fly, data-driven reachability analysis and control of unknown systems

Djeumou, Franck; Zutshi, Aditya; Topcu, Ufuk

doi:10.1145/3447928.3457355

Cited by 4 publications

(5 citation statements)

References 3 publications

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“…Lastly, we remark that the approaches described above for discovery of model parameters while simultaneously reconstructing the true state of the system is readily comparable to other data-driven model recovery techniques such as SINDy (see [11], for example, or [12,13] and references therein). One particular benefit of the feedback control mechanism exploited here for the purpose of recovering the unknown forcing function in 2D turbulence, is that the parameter estimation is performed on-the-fly in the fashion of continuous data assimilation and without any need for post-processing.…”

Section: Introductionmentioning

confidence: 84%

“…for some universal non-dimensional constant c 0 > 0 that depends on c 1 , c 2 from (3) and the constants of interpolation; we refer to the Appendix for additional details. Finally, (12) implies…”

Section: Rigorous Convergence Analysismentioning

confidence: 97%

“…Note that when t is sufficiently large, one may assume that R 0 , R 1 , R 2 are independent of the initial velocity; this is a safe assumption in the analysis performed above since we must always wait long enough before the first update to ensure that u(t), ∆u(t) henceforth remain bounded by R 0 and R 2 , respectively. Lastly, the crucial ingredient used to close all of the estimates and arrive at ( 14) is provided by the state error estimates (12). The bound stated for ∇w k was originally proven in [9].…”

Section: Appendixmentioning

confidence: 99%

“…from which (12) follows upon taking t sufficiently large to evaluate g k , and finally an application of Gronwall's inequality.…”

Section: Appendixmentioning

confidence: 99%

See 3 more Smart Citations

Identifying the body force from partial observations of a 2D incompressible velocity field

Farhat¹,

Larios²,

Martinez³

et al. 2023

Preprint

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Using limited observations of the velocity field of the two-dimensional Navier-Stokes equations, we successfully reconstruct the steady body force that drives the flow. The number of observed data points is less than 10% of the number of modes that describes the full flow field, indicating that the method introduced here is capable of identifying complicated forcing mechanisms from very simple observations. In addition to demonstrating the efficacy of this method on turbulent flow data generated by simulations of the two-dimensional Navier-Stokes equations, we also rigorously justify convergence of the derived algorithm. Beyond the practical applicability of such an algorithm, the reliance of this method on the dynamical evolution of the system yields physical insight into the turbulent cascade.

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Section: Introductionmentioning

confidence: 84%

Section: Rigorous Convergence Analysismentioning

confidence: 97%

Section: Appendixmentioning

confidence: 99%

“…from which (12) follows upon taking t sufficiently large to evaluate g k , and finally an application of Gronwall's inequality.…”

Section: Appendixmentioning

confidence: 99%

See 2 more Smart Citations

Identifying the body force from partial observations of a 2D incompressible velocity field

Farhat¹,

Larios²,

Martinez³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Data-driven stochastic optimal control is an active area of research [17,18], and provides a promising avenue for controls problems which suffer from high model complexity or system uncertainty, such as robotic motion planning [25,30] and model predictive control [39,40]. Recently, approaches using Gaussian processes [16,36] and kernel methods [23,29,51] have also been explored.…”

Section: Introductionmentioning

confidence: 99%

SOCKS: A Stochastic Optimal Control and Reachability Toolbox Using Kernel Methods

Thorpe,

Oishi

2022

Preprint

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We present SOCKS, a data-driven stochastic optimal control toolbox based in kernel methods. SOCKS is a collection of data-driven algorithms that compute approximate solutions to stochastic optimal control problems with arbitrary cost and constraint functions, including stochastic reachability, which seeks to determine the likelihood that a system will reach a desired target set while respecting a set of pre-defined safety constraints. Our approach relies upon a class of machine learning algorithms based in kernel methods, a nonparametric technique which can be used to represent probability distributions in a high-dimensional space of functions known as a reproducing kernel Hilbert space. As a nonparametric technique, kernel methods are inherently data-driven, meaning that they do not place prior assumptions on the system dynamics or the structure of the uncertainty. This makes the toolbox amenable to a wide variety of systems, including those with nonlinear dynamics, blackbox elements, and poorly characterized stochastic disturbances. We present the main features of SOCKS and demonstrate its capabilities on several benchmarks. CCS CONCEPTS• Computing methodologies → Computational control theory; Kernel methods; • Theory of computation → Stochastic control and optimization.

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Sablas: Learning Safe Control for Black-Box Dynamical Systems

Qin

Sun

Fan

2022

IEEE Robot. Autom. Lett.

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Control certificates based on barrier functions have been a powerful tool to generate probably safe control policies for dynamical systems. However, existing methods based on barrier certificates are normally for white-box systems with differentiable dynamics, which makes them inapplicable to many practical applications where the system is a black-box and cannot be accurately modeled. On the other side, model-free reinforcement learning (RL) methods for black-box systems suffer from lack of safety guarantees and low sampling efficiency. In this paper, we propose a novel method that can learn safe control policies and barrier certificates for black-box dynamical systems, without requiring for an accurate system model. Our method re-designs the loss function to back-propagate gradient to the control policy even when the black-box dynamical system is non-differentiable, and we show that the safety certificates hold on the black-box system. Empirical results in simulation show that our method can significantly improve the performance of the learned policies by achieving nearly 100% safety and goal reaching rates using much fewer training samples, compared to state-of-the-art black-box safe control methods. Our learned agents can also generalize to unseen scenarios while keeping the original performance. The source code can be found at https://github.com/Zengyi-Qin/bcbf.

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On-the-fly, data-driven reachability analysis and control of unknown systems

Cited by 4 publications

References 3 publications

Identifying the body force from partial observations of a 2D incompressible velocity field

Identifying the body force from partial observations of a 2D incompressible velocity field

SOCKS: A Stochastic Optimal Control and Reachability Toolbox Using Kernel Methods

Sablas: Learning Safe Control for Black-Box Dynamical Systems

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