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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  ...  Finite-horizon covariance control problems for continuous-time linear systems were recently studied in [5, 6, 7, 8] .  ... 
arXiv:2009.14252v1 fatcat:2q6qmfwdk5gt3glornplxcfueq

Optimal Switching Synthesis for Jump Linear Systems with Gaussian initial state uncertainty [article]

Kooktae Lee, Raktim Bhattacharya
2014 arXiv   pre-print
Combining with the receding horizon framework, an optimal switching sequence for jump linear systems can be obtained by minimizing the objective function that is expressed in terms of Wasserstein distance  ...  In order to cope with Gaussian initial state uncertainty and to measure the system performance, Wasserstein metric that defines the distance between probability density functions is used.  ...  ACKNOWLEDGMENT This research was supported through National Science Foundation award #1349100, with Dr. Almadena Y. Chtchelkanova as a program manager.  ... 
arXiv:1408.4859v1 fatcat:s7nc2bqokbhhpdh4j3ih2uwbcy

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.  ...  distance terminal cost.  ...  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

Safe Zero-Shot Model-Based Learning and Control: A Wasserstein Distributionally Robust Approach [article]

Aaron Kandel, Scott J. Moura
2021 arXiv   pre-print
We address the identified problem of single-episode zero-shot control by presenting a Wasserstein distributionally robust approach which, coupled with a receding horizon control scheme, can safely learn  ...  We identify and focus on scenarios of learning and controlling a system from scratch, starting with a randomly initialized model based on the strongest possible limitations on our prior knowledge of the  ...  ∈ R p is the vector of inputs at time k; θ(t) ∈ R h is the estimate of the model parameters at time t; J k (x(k), u(k)) : R n × R p → R is the instantaneous cost at time k as a function of the states  ... 
arXiv:2004.00759v3 fatcat:znxsbd35azdlld44japrbp5xuq

Comparison of Sampling Methods for Dynamic Stochastic Programming

M. A. H. Dempster, Elena Medova
2014 Social Science Research Network  
or Wasserstein distance.  ...  Here, we present a Wasserstein-based heuristic for discretization of a continuous state path probability distribution.  ...  We also wish to acknowledge the use of Cambridge System Associates Limited STOCHASTIC SUITE TM DSP generation and optimization software and of their computing facilities for the extensive computations  ... 
doi:10.2139/ssrn.2543500 fatcat:p6zyxoyduvdjzdpnv3faj4oski

Comparison of Sampling Methods for Dynamic Stochastic Programming [chapter]

Michael A.H. Dempster, Elena A. Medova, Yee Sook Yong
2011 International Series in Operations Research and Management Science  
or Wasserstein distance.  ...  Here, we present a Wasserstein-based heuristic for discretization of a continuous state path probability distribution.  ...  We also wish to acknowledge the use of Cambridge System Associates Limited STOCHASTIC SUITE TM DSP generation and optimization software and of their computing facilities for the extensive computations  ... 
doi:10.1007/978-1-4419-9586-5_16 fatcat:aklslnzlgvaj7chnrn5vpkxcia

Wasserstein Distributionally Robust Motion Control for Collision Avoidance Using Conditional Value-at-Risk [article]

Astghik Hakobyan, Insoon Yang
2020 arXiv   pre-print
By choosing the ambiguity set as a statistical ball with its radius measured by the Wasserstein metric, we achieve a probabilistic guarantee of the out-of-sample risk, evaluated using new sample data generated  ...  To resolve the infinite-dimensionality issue inherent in the distributionally robust MPC problem, we reformulate it as a finite-dimensional nonlinear program using modern distributionally robust optimization  ...  The MPC problem is solved for T = 50 iterations by discretizing the quadrotor model with sample time T s = 0.1 sec.  ... 
arXiv:2001.04727v1 fatcat:ouzrikpcwzebnelngvzc3ymkoi

Data-driven Distributionally Robust MPC: An indirect feedback approach [article]

Christoph Mark, Steven Liu
2021 arXiv   pre-print
This paper presents a distributionally robust stochastic model predictive control (SMPC) approach for linear discrete-time systems subject to unbounded and correlated additive disturbances.  ...  The approach is demonstrated on a four-room temperature control example.  ...  : R n → R is the terminal cost function that approximates the finite horizon tail for t = {N, . . . , N T }, l 1 : R nN → R ≥0 denotes the state and l 2 : R mN → R ≥0 the input cost function.  ... 
arXiv:2109.09558v1 fatcat:kbshmr3w7fcbtgsubfqek664l4

Distributionally Robust Surrogate Optimal Control for High-Dimensional Systems [article]

Aaron Kandel, Saehong Park, Scott Moura
2021 arXiv   pre-print
This paper presents a novel methodology for tractably solving optimal control problems for high-dimensional systems.  ...  First, we identify a surrogate modeling methodology which takes as input the initial state and a time series of control inputs, and outputs an approximation of the objective function and constraint functions  ...  For optimal control problems with a short time horizon, we obtain approximate solutions by optimizing the models a single time.  ... 
arXiv:2105.10070v1 fatcat:qrujeb2vdzgfbjjrayqsrczmqe

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  ...  For generic nonlinear drift, we reduce the SBP to solving a system of forward and backward Kolmogorov partial differential equations (PDEs) that are coupled through the boundary conditions, with unknowns  ...  INTRODUCTION The Schrödinger bridge problem (SBP) is a non-standard finite horizon stochastic optimal control problem in continuous time.  ... 
arXiv:1912.01244v2 fatcat:4vy2ewutzzei5hxozqa6hmzwl4

Shared Prior Learning of Energy-Based Models for Image Reconstruction [article]

Thomas Pinetz and Erich Kobler and Thomas Pock and Alexander Effland
2020 arXiv   pre-print
We derive several time discretization schemes of the gradient flow and verify their consistency in terms of Mosco convergence.  ...  Finally, in shared prior learning, both aforementioned optimal control problems are optimized simultaneously with shared learned parameters of the regularizer to further enhance unsupervised image reconstruction  ...  Acknowledgements All authors acknowledge support from the European Research Council under the Horizon 2020 program, ERC starting grant HOMOVIS (No. 640156).  ... 
arXiv:2011.06539v2 fatcat:abgzu2a2ujg6lk3jjjhxk2qanm

Efficient Multi-Robot Exploration with Energy Constraint based on Optimal Transport Theory [article]

Rabiul Hasan Kabir, Kooktae Lee
2020 arXiv   pre-print
This paper addresses an Optimal Transport (OT)-based efficient multi-robot exploration problem, considering the energy constraints of a multi-robot system.  ...  The proposed multi-robot exploration scheme is also applicable to a time-varying distribution, where the spatio-temporal evolution of the given reference distribution is desired.  ...  Using the Euclidean distance c(x, y) = x − y p with p th order (p ≥ 1), we introduce the Wasserstein distance [53] of order p, which has been widely employed to broad dynamical systems including system  ... 
arXiv:2009.00862v1 fatcat:jlepwnomurar3lgl6v2ctuygum

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  
Motivated by the stability and performance analysis of model predictive control schemes, we investigate strict dissipativity for a class of optimal control problems involving probability density functions  ...  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.  ...  Then we can consider nonlinear discrete time control systems z(k + 1) = f (z(k), u(k)), z(0) = z 0 , (17) with state z(k) ∈ X ⊂ Z and control u(k) ∈ U ⊂ U , where Z and U are metric spaces and state and  ... 
doi:10.3934/mcrf.2020053 fatcat:dmpc4sjvireh3n564szvyrkhxe

Interpretable Stochastic Model Predictive Control using Distributional Reinforced Estimation for Quadrotor Tracking Systems [article]

Yanran Wang, James O'Keeffe, Qiuchen Qian, David Boyle
2022 arXiv   pre-print
We demonstrate our system to improve the cumulative tracking errors by at least 66% with unknown and diverse aerodynamic forces compared with recent state-of-the-art.  ...  Most current quadrotor tracking systems therefore treat them as simple 'disturbances' in conventional control approaches.  ...  We consider a nonlinear discrete system of quadrotor dynamics with state x ∈ X ⊆ R n , an additive disturbance w ∈ W ⊆ R nw , and control input u ∈ R nu , defined for all time steps k ∈ N by: x k+1 = f  ... 
arXiv:2205.07150v1 fatcat:6vdhnisjs5fz3klggt2mcnxtv4

Recent developments in controlled crowd dynamics [article]

M.K. Banda, M. Herty, T. Trimborn
2019 arXiv   pre-print
We survey recent results on controlled particle systems. The control aspect introduces new challenges in the discussion of properties and suitable mean field limits.  ...  Some of the aspects are highlighted in a detailed discussion of a particular controlled particle dynamics. The applied techniques are shown on this simple problem to illustrate the basic methods.  ...  For nonlinear P, most of the research has focused on suboptimal control based on instantaneous or short time horizon control.  ... 
arXiv:1911.03625v1 fatcat:ebdu6p4cyneqnitayf27z7l7dy
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