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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  ...  of the system close to a desired Gaussian distribution.  ...  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

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.  ...  In our previous work, we have addressed covariance steering and minimum variance steering problems for discrete-time stochastic linear systems under both full state and partial state information based  ... 
arXiv:2011.05394v1 fatcat:z6zshsz2hrddvhdgmbt5rcqasi

Greedy Finite-Horizon Covariance Steering for Discrete-Time Stochastic Nonlinear Systems Based on the Unscented Transform [article]

Efstathios Bakolas, Alexandros Tsolovikos
2020 arXiv   pre-print
In this work, we consider the problem of steering the first two moments of the uncertain state of a discrete time nonlinear stochastic system to prescribed goal quantities at a given final time.  ...  The latter control policy is comprised of the first elements of the control policies that solve a sequence of corresponding linearized covariance steering problems.  ...  Collection of Finite-Horizon Linearized Covariance Steering Problems Next, we associate the DTSN system (1) at stage t = k ∈ [0, N − 1] d with a discrete-time stochastic linear system.  ... 
arXiv:2003.03679v2 fatcat:cgi72j35lney7e2kbvozqnjmfi

Covariance Steering for Discrete-Time Linear-Quadratic Stochastic Dynamic Games [article]

Venkata Ramana Makkapati and Tanmay Rajpurohit and Kazuhide Okamoto and Panagiotis Tsiotras
2020 arXiv   pre-print
This paper addresses the problem of steering a discrete-time linear dynamical system from an initial Gaussian distribution to a final distribution in a game-theoretic setting.  ...  One of the two players strives to minimize a quadratic payoff, while at the same time tries to meet a given mean and covariance constraint at the final time-step.  ...  The current work addresses a class of linear-quadratic (LQ) stochastic dynamic games in discrete-time with finite-time horizon.  ... 
arXiv:2003.03045v1 fatcat:lyrysnqz4badxj3apkkyds2q4m

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.  ...  Since the Gaussian distribution can be fully defined by its first two moments, this problem can be described as a finitetime optimal mean and covariance steering of a stochastic time-varying discrete linear  ... 
arXiv:1707.04729v2 fatcat:bv24zqezsnaazebkpgs7euswp4

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.  ...  show that under the latter policy, the problem can be equivalently formulated as a semi-definite program (SDP) which is in sharp contrast with our previous results that could only guarantee that the stochastic  ...  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

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

Nonlinear Covariance Control via Differential Dynamic Programming [article]

Zeji Yi, Zhefeng Cao, Evangelos Theodorou, Yongxin Chen
2019 arXiv   pre-print
Our objective is to find an optimal control strategy to steer the state from an initial distribution to a terminal one with specified mean and covariance.  ...  This problem is considerably more complicated than previous studies on covariance control for linear systems.  ...  Covariance Control Covariance steering/control [5] is about controlling the state of the stochastic system from the initial random vector x(0) at t = 0 to a terminal one x(T ) at t = T via a control  ... 
arXiv:1911.09283v1 fatcat:zigisj4hhnbjzfg25ocg4f4x5e

Stochastic Model Predictive Control for Constrained Linear Systems Using Optimal Covariance Steering [article]

Kazuhide Okamoto, Panagiotis Tsiotras
2019 arXiv   pre-print
The proposed approach is based on the recently developed finite-horizon optimal covariance steering control theory, which steers the mean and the covariance of the system state to prescribed target values  ...  at a given terminal time.  ...  The authors would also like the thank the anonymous reviewers for their excellent suggestions to improve this paper and for also pointing out the connections of CS-SMPC with the work of [33] .  ... 
arXiv:1905.13296v2 fatcat:34dcxkck2jehloc3tz57knr5dm

Sampling Complexity of Path Integral Methods for Trajectory Optimization [article]

Hyung-Jin Yoon, Chuyuan Tao, Hunmin Kim, Naira Hovakimyan, Petros Voulgaris
2022 arXiv   pre-print
Then we apply the result to a linear time-varying dynamical system with quadratic cost and an indicator function cost to avoid constraint sets.  ...  The sampling complexity result shows that the variance of the estimated control value is upper-bounded in terms of the expectation of the cost.  ...  Calculation of the expectation with linear system and a class of cost functions Consider the following linear time-varying (LTV) discretetime stochastic system that belongs to the discrete time diffusion  ... 
arXiv:2203.10067v1 fatcat:7gtg3nhblrcy7fcjsopylevdki

Speeding up Gaussian Belief Space Planning for Underwater Robots Through a Covariance Upper Bound

Huan Yu, Wenjie Lu, Dikai Liu, Yongqiang Han, Qinghe Wu
2019 IEEE Access  
Based on a closed-loop stochastic control framework, we propose a fast Gaussian belief space planning approach for coupled optimization of trajectory, localization and control, resulting in a non-linear  ...  In particular, as opposed to advancing the covariance by a Kalman filter in the existing literature, we utilize an upper bound of the trace propagation of the covariance, thereby avoiding to solve Riccati  ...  PLANNING BASED ON MULTIPLE RESOLUTION PROCESSES The continuous-time system in Eq. (1) can be discretized into a discrete system with discrete time interval dT .  ... 
doi:10.1109/access.2019.2933067 fatcat:343q67ksbzg7llqsckdygr7isq

Stochastic Entry Guidance [article]

Jack Ridderhof and Panagiotis Tsiotras and Breanna J. Johnson
2022 arXiv   pre-print
The entry guidance, which is parameterized as a sequence of linear feedback gains, is designed to steer the probability distribution of the entry trajectories while satisfying bounds on the allowable control  ...  inputs and on the maximum allowable state errors.  ...  Thus, one may solve for the nominal control to steer the mean of the state distribution, while also solving for the feedback gain to steer the covariance [13] .  ... 
arXiv:2103.05168v2 fatcat:7ao3y7ugkrb2xnftt5g2raojca

Feedback Dual Controller Design and Its Application to Monocular Vision-Based Docking

Jinwhan Kim, Stephen Rock
2009 Journal of Guidance Control and Dynamics  
That is, the system is linear, the cost criterion is quadratic, and the noise is Gaussian.  ...  At the start of this terminal phase, the vehicle is located at a certain distance away from the target dock.  ... 
doi:10.2514/1.41957 fatcat:kt5bponipbcjhae3iewez7lzim

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

Lars Lindemann, Matthew Cleaveland, Yiannis Kantaros, George J. Pappas
2021 arXiv   pre-print
We propose a novel sampling-based approach that builds trees exploring the reachable space of Gaussian distributions that capture uncertainty both in state estimation and in future measurements.  ...  Optimistic solutions require frequent replanning to not endanger the safety of the system.  ...  In particular, we proposed a novel sampling-based approach that introduces robustness margins into the offline planning to account for uncertainty in the state estimates based on a Kalman filter.  ... 
arXiv:2108.11983v1 fatcat:up4m6woz2vb3xj2agg3gdrgg4e

DISCO: Double Likelihood-free Inference Stochastic Control [article]

Lucas Barcelos, Rafael Oliveira, Rafael Possas, Lionel Ott, Fabio Ramos
2020 arXiv   pre-print
The posterior distribution over simulation parameters is propagated through a potentially non-analytical model of the system with the unscented transform, and a variant of the information theoretical model  ...  Accurate simulation of complex physical systems enables the development, testing, and certification of control strategies before they are deployed into the real systems.  ...  PRELIMINARIES We consider the problem of controlling a discrete-time stochastic system described by a non-linear set of difference equations of the form: x t+1 = f (x t , v t ) (1) where f is the transition  ... 
arXiv:2002.07379v3 fatcat:l7tb6xktojfs3f7ach5io4xxje
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