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On the Convexity of Discrete Time Covariance Steering in Stochastic Linear Systems with Wasserstein Terminal Cost [article]

Isin M. Balci, Abhishek Halder, Efstathios Bakolas
2021 arXiv   pre-print
In this work, we analyze the properties of the solution to the covariance steering problem for discrete time Gaussian linear systems with a squared Wasserstein distance terminal cost.  ...  Here, we revisit the same covariance control problem but this time we focus on the analysis of the problem.  ...  INTRODUCTION In this work, we study the existence and uniqueness of solutions to the covariance steering problem for discrete time Gaussian linear systems with a squared Wasserstein distance terminal cost  ... 
arXiv:2103.13579v1 fatcat:bvjjpuv3sfa2jfyrnuedhp5svi

Covariance Steering of Discrete-Time Stochastic Linear Systems Based on Distribution Distance Terminal Costs [article]

Isin M. Balci, Efstathios Bakolas
2020 arXiv   pre-print
We consider a class of stochastic optimal control problems for discrete-time stochastic linear systems which seek for control policies that will steer the probability distribution of the terminal state  ...  In our problem formulation, the closeness between the terminal state distribution and the desired (goal) distribution is measured in terms of the squared Wasserstein distance which is associated with a  ...  INTRODUCTION We consider covariance steering problems for discretetime stochastic linear systems in which, however, the constraints on the terminal state covariance are enforced indirectly by means of  ... 
arXiv:2009.14252v1 fatcat:2q6qmfwdk5gt3glornplxcfueq

Exact SDP Formulation for Discrete-Time Covariance Steering with Wasserstein Terminal Cost [article]

Isin M. Balci, Efstathios Bakolas
2022 arXiv   pre-print
In this paper, we present new results on the covariance steering problem with Wasserstein distance terminal cost.  ...  that the stochastic optimal control problem can be reduced to a difference of convex functions program.  ...  CONCLUSION In this paper, we addressed a class of covariance steering problems for discrete-time stochastic linear systems with Wasserstein terminal cost.  ... 
arXiv:2205.10740v1 fatcat:whk46hhtnfg47ezdkqg5oshxfe

Minimum Variance and Covariance Steering Based on Affine Disturbance Feedback Control Parameterization [article]

Efstathios Bakolas
2020 arXiv   pre-print
The goal of this paper is to address finite-horizon minimum variance and covariance steering problems for discrete-time stochastic (Gaussian) linear systems.  ...  On the other hand, the covariance steering problem seeks for a control policy that will steer the covariance of the terminal state to a prescribed positive definite matrix.  ...  ACKNOWLEDGMENTS This research has been supported in part by NSF award CMMI-1937957.  ... 
arXiv:2011.05394v1 fatcat:z6zshsz2hrddvhdgmbt5rcqasi

Finite-Horizon Covariance Control of Linear Time-Varying Systems [article]

Maxim Goldshtein, Panagiotis Tsiotras
2017 arXiv   pre-print
We consider the problem of finite-horizon optimal control of a discrete linear time-varying system subject to a stochastic disturbance and fully observable state.  ...  We show that the resulting solution coincides with a LQG problem with particular terminal cost weight matrix. This fact provides an additional justification for using a linear in state controller.  ...  INTRODUCTION The work in this paper is aimed at solving the problem of the optimal steering of a discrete stochastic linear system, with a fully observable state, a known Gaussian distribution of the initial  ... 
arXiv:1707.04729v2 fatcat:bv24zqezsnaazebkpgs7euswp4

Stochastic control and non-equilibrium thermodynamics: fundamental limits [article]

Yongxin Chen, Tryphon Georgiou, Allen Tannenbaum
2018 arXiv   pre-print
We consider damped stochastic systems in a controlled (time-varying) quadratic potential and study their transition between specified Gibbs-equilibria states in finite time.  ...  The minimal gap between the work needed in a finite-time transition and the work during a reversible one, turns out to equal the square of the optimal mass transport (Wasserstein-2) distance between the  ...  By adjusting the quadratic potential, it is possible to steer the system from one Gaussian distribution to another in finite time t f .  ... 
arXiv:1802.01271v2 fatcat:y36g5royp5echlw2karomp3jlm

Discrete-Time Linear-Quadratic Regulation via Optimal Transport [article]

Mathias Hudoba de Badyn, Erik Miehling, Dylan Janak, Behçet Açıkmeşe, Mehran Mesbahi, Tamer Başar, John Lygeros, Roy S. Smith
2021 arXiv   pre-print
A closed-form solution for the optimal transport map in the case of linear-time varying systems is derived, along with an algorithm for computing the optimal map.  ...  In this paper, we consider a discrete-time stochastic control problem with uncertain initial and target states.  ...  related problem regarding the steering of an LTV systems to a terminal state with specified expected value and covariance [25] - [27] .  ... 
arXiv:2109.02347v1 fatcat:5y4heftxdjgjjmuv6p5xdz5bwu

Robust Motion Planning in the Presence of Estimation Uncertainty [article]

Lars Lindemann, Matthew Cleaveland, Yiannis Kantaros, George J. Pappas
2021 arXiv   pre-print
However, in many situations, the state of the system may not be known but only estimated using, for instance, a Kalman filter.  ...  Optimistic solutions require frequent replanning to not endanger the safety of the system.  ...  We complement the robust offline planning with an online replanning scheme and show an inherent trade-off in the size of the robustness margin and the frequency of replanning.  ... 
arXiv:2108.11983v1 fatcat:up4m6woz2vb3xj2agg3gdrgg4e

Optimal Steering of a Linear Stochastic System to a Final Probability Distribution, Part I

Yongxin Chen, Tryphon T. Georgiou, Michele Pavon
2016 IEEE Transactions on Automatic Control  
In earlier works, presented as Part I and Part II, we explored a generalization of the original SBP that amounts to optimal steering of linear stochastic dynamical systems between statedistributions, at  ...  In the zero-noise limit, we obtain the solution of a (deterministic) mass transport problem with general quadratic cost.  ...  We note that the control problems to steer a stochastic linear system between terminal distributions, for the case where stochastic excitation and control input enter in the same manner, admit a Bayesian-like  ... 
doi:10.1109/tac.2015.2457784 fatcat:2sdnkp43rnd6zdtedhqhgal54y

Optimal steering of a linear stochastic system to a final probability distribution, Part III [article]

Yongxin Chen, Tryphon T. Georgiou, Michele Pavon
2016 arXiv   pre-print
In earlier works, presented as Part I and Part II, we explored a generalization of the original SBP that amounts to optimal steering of linear stochastic dynamical systems between state-distributions,  ...  In the zero-noise limit, we obtain the solution of a (deterministic) mass transport problem with general quadratic cost.  ...  We note that the control problems to steer a stochastic linear system between terminal distributions, for the case where stochastic excitation and control input enter in the same manner, admit a Bayesian-like  ... 
arXiv:1608.03622v1 fatcat:j3f76h6abbfpnecjlvb3yjcpiu

Wasserstein Proximal Algorithms for the Schrödinger Bridge Problem: Density Control with Nonlinear Drift [article]

Kenneth F. Caluya, Abhishek Halder
2021 arXiv   pre-print
In control-theoretic language, this is a problem of minimum effort steering of a given joint state probability density function (PDF) to another over a finite time horizon, subject to a controlled stochastic  ...  The flows generated by such forward Kolmogorov PDEs, for the two aforementioned types of drift, in turn, enjoy gradient descent structures on the manifold of joint PDFs with respect to suitable distance  ...  These Wasserstein distances are computed by solving linear programs, i.e., discrete versions of (41).  ... 
arXiv:1912.01244v2 fatcat:4vy2ewutzzei5hxozqa6hmzwl4

Agile Autonomous Driving using End-to-End Deep Imitation Learning

Yunpeng Pan, Ching-An Cheng, Kamil Saigol, Keuntaek Lee, Xinyan Yan, Evangelos Theodorou, Byron Boots
2018 Robotics: Science and Systems XIV  
Built on these insights, our autonomous driving system demonstrates successful high-speed off-road driving, matching the state-of-the-art performance.  ...  We present an end-to-end imitation learning system for agile, off-road autonomous driving using only low-cost on-board sensors.  ...  The goal of IL is to perform as well as the expert with an error that has at most linear dependency on T .  ... 
doi:10.15607/rss.2018.xiv.056 dblp:conf/rss/PanCSLYTB18 fatcat:p3wthkfno5gdrammgarr32ujbq

Strict dissipativity analysis for classes of optimal control problems involving probability density functions

Arthur Fleig, ,Chair of Serious Games, University of Bayreuth, 95440 Bayreuth, Germany, Lars Grüne, ,Chair of Applied Mathematics, University of Bayreuth, 95440 Bayreuth, Germany
2019 Mathematical Control and Related Fields  
This enables us to perform an in-depth analysis of strict dissipativity for different cost functions. 2020 Mathematics Subject Classification. Primary: 35Q84, 35Q93, 60G15; Secondary: 49N35, 93C15.  ...  However, for the particular classes under investigation involving linear dynamics, linear feedback laws, and Gaussian probability density functions, we are able to significantly simplify these dynamics  ...  However, for OCPs with linear discrete-time dynamics z(k + 1) = Az(k) + Bu(k) + c =: f l (z(k), u(k)), (28) a convex constraint set and strictly convex stage cost , it is known [10] that the linear function  ... 
doi:10.3934/mcrf.2020053 fatcat:dmpc4sjvireh3n564szvyrkhxe

Optimal Feedback Control for Modeling Human-Computer Interaction [article]

Florian Fischer, Arthur Fleig, Markus Klar, Jörg Müller
2021 arXiv   pre-print
We propose that in this case, the dynamics of the human body and computer can be interpreted as a single dynamical system.  ...  The state of this system is controlled by the user via muscle control signals, and estimated from observations.  ...  ACKNOWLEDGMENTS We would like to thank Lars Grüne for his very helpful advice and comments on a preliminary version of this paper.  ... 
arXiv:2110.00443v1 fatcat:q3pmx3qhjrctxfbkvj26e5tp6m

Agile Autonomous Driving using End-to-End Deep Imitation Learning [article]

Yunpeng Pan, Ching-An Cheng, Kamil Saigol, Keuntaek Lee, Xinyan Yan, Evangelos Theodorou, Byron Boots
2019 arXiv   pre-print
Built on these insights, our autonomous driving system demonstrates successful high-speed off-road driving, matching the state-of-the-art performance.  ...  Compared with recent approaches to similar tasks, our method requires neither state estimation nor on-the-fly planning to navigate the vehicle.  ...  We wish to design an IL algorithm that can train a policy π to perform as well as the expert π with an error that has at most linear dependency on the time horizon of the problem T .  ... 
arXiv:1709.07174v6 fatcat:3rv55bnssvcx7ny7izyktbqjlu
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