Stabilizing Optimal Density Control of Nonlinear Agents with Multiplicative Noise

Bakshi, Kaivalya; Theodorou, Evangelos A.; Grover, Piyush

doi:10.1109/cdc42340.2020.9304371

Cited by 2 publications

(1 citation statement)

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“…A PDEbased optimal robotic swarm coverage control policy is obtained by deriving necessary conditions of optimality in [18]. For systems affected by multiplicative noise, infinite horizon optimal density steering laws have been derived in [19]. Finally, in [20], a hierarchical clustering-based density steering algorithm is presented for distributed large-scale applications.…”

Section: Introductionmentioning

confidence: 99%

Covariance Steering of Discrete-Time Stochastic Linear Systems Based on Wasserstein Distance Terminal Cost

Balci

Bakolas

2021

2021 American Control Conference (ACC)

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In this paper, we study the finite-horizon optimal density steering problem for discrete-time stochastic linear dynamical systems. Specifically, we focus on steering probability densities represented as Gaussian mixture models which are known to give good approximations for general smooth probability density functions. We then revisit the covariance steering problem for Gaussian distributions and derive its optimal control policy. Subsequently, we propose a randomized policy to enhance the numerical tractability of the problem and demonstrate that under this policy the state distribution remains a Gaussian mixture. By leveraging these results, we reduce the Gaussian mixture steering problem to a linear program. We also discuss the problem of steering general distributions using Gaussian mixture approximations. Finally, we present results of non-trivial numerical experiments and demonstrate that our approach can be applied to general distribution steering problems.

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Section: Introductionmentioning

confidence: 99%