Probabilistic Control of Heterogeneous Swarms Subject to Graph Temporal Logic Specifications: A Decentralized and Scalable Approach

Djeumou, Franck; Xu, Zhe; Cubuktepe, Murat; Topcu, Ufuk

doi:10.1109/tac.2022.3176797

Cited by 2 publications

(3 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The constraints in (6b) and (6c) correspond to the mean and covariance steering constraints in the problem defined in (6). Since the state mean depends on Ū and the state covariance depends on L, and the objective function is separable in Ū and L, the mean and covariance steering problems can be decoupled.…”

Section: Optimal Covariance Steering For Gaussian Distributionsmentioning

confidence: 99%

“…Control policies are designed for this PDE using Lyapunov-based methods [3], [4]. The second approach considers a discrete state space and employs Markov chain-based methods, and utilizes convex optimization tools to design a transition matrix of the Markov chain for steering the probability distribution [5], [6]. Lastly, optimal mass transport-based approaches treat the dynamic problem as a static mass transport problem using transition costs between initial and terminal states.…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, Markov chain-based density steering methods also rely on discretizing the continuous state space to synthesize a Markov chain that characterizes the probabilistic motion of individual agents. In the infinite horizon case, formulating this Markov chain can be cast as a convex semidefinite program [5], while in the finite horizon case the problem is not convex and should be addressed as a general nonlinear program [6], [14].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Balci

Bakolas

2021

2021 American Control Conference (ACC)

View full text Add to dashboard Cite

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.

show abstract

Section: Optimal Covariance Steering For Gaussian Distributionsmentioning

confidence: 99%