arXiv subjects

Kazuhide Okamoto

Publications and source records attributed to Kazuhide Okamoto.

8 recordsLinked to original sources

arXiv2020

Chance Constrained Covariance Control for Linear Stochastic Systems With Output Feedback

We consider the problem of steering, via output feedback, the state distribution of a discrete-time, linear stochastic system from an initial Gaussian distribution to a terminal Gaussian distribution with prescribed mean and maximum covariance, subject to probabilistic path constraints on the state. The filtered state is obtained via a Kalman filter, and the problem is formulated as a deterministic convex program in terms of the distribution of the filtered state. We observe that, in the presence of constraints on the state covariance, and in contrast to classical Linear Quadratic Gaussian (LQG) control, the optimal feedback control depends on both the process noise and the observation model. The effectiveness of the proposed approach is verified using a numerical example.

math.OC↗

arXiv2020

Covariance Steering for Discrete-Time Linear-Quadratic Stochastic Dynamic Games

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 other player maximizes the same payoff, but it is assumed to be indifferent to the terminal constraint. At first, the unconstrained version of the game is examined, and the necessary conditions for the existence of a saddle point are obtained. We then show that obtaining a solution for the one-sided constrained dynamic game is not guaranteed, and subsequently the players' best responses are analyzed. Finally, we propose to numerically solve the problem of steering the distribution under adversarial scenarios using the Jacobi iteration method. The problem of guiding a missile during the endgame is chosen to analyze the proposed approach. A numerical simulation corresponding to the case where the terminal distribution is not achieved is also included, and discuss the necessary conditions to meet the terminal constraint.

math.OC↗

arXiv2019

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

This work develops a stochastic model predictive controller~(SMPC) for uncertain linear systems with additive Gaussian noise subject to state and control constraints. 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. We call our approach covariance steering-based SMPC, or CS-SMPC. We show that the proposed approach has several advantages over traditional SMPC approaches in the literature. Specifically, it is shown that the newly developed algorithm can deal with unbounded Gaussian additive noise while ensuring stability and recursive feasibility, and incurs lower computational cost than previous similar approaches. The effectiveness of the proposed CS-SMPC approach is confirmed using numerical simulations.

math.OC↗

arXiv2019

Input Hard Constrained Optimal Covariance Steering

We address the optimal covariance steering (OCS) problem for stochastic discrete linear systems with additive Gaussian noise under state chance constraints and input hard constraints. Because the system state can be unbounded due to the unbounded noise, the state constraints are formulated as probabilistic (chance) constraints, i.e., the maximum probability of constraint violation is constrained. In contrast, because it is hard to interpret the appropriate control action when the control command violates the constraints, probabilistically formulating the control constraints are difficult, and deterministic hard constraints are preferable. In this work we introduce an OCS approach subject to simultaneous state chance constraints and input hard constraints and validate the approach using numerical simulations.

math.OC↗

arXiv2019

Vision-Based Autonomous Vehicle Control using the Two-Point Visual Driver Control Model

This work proposes a new self-driving framework that uses a human driver control model, whose feature-input values are extracted from images using deep convolutional neural networks (CNNs). The development of image processing techniques using CNNs along with accelerated computing hardware has recently enabled real-time detection of these feature-input values. The use of human driver models can lead to more "natural" driving behavior of self-driving vehicles. Specifically, we use the well-known two-point visual driver control model as the controller, and we use a top-down lane cost map CNN and the YOLOv2 CNN to extract feature-input values. This framework relies exclusively on inputs from low-cost sensors like a monocular camera and wheel speed sensors. We experimentally validate the proposed framework on an outdoor track using a 1/5th-scale autonomous vehicle platform.

cs.CV↗

arXiv2019

Nonlinear Uncertainty Control with Iterative Covariance Steering

This paper considers the problem of steering the state distribution of a nonlinear stochastic system from an initial Gaussian to a terminal distribution with a specified mean and covariance, subject to probabilistic path constraints. An algorithm is developed to solve this problem by iteratively solving an approximate linearized problem as a convex program. This method, which we call iterative covariance steering (iCS), is numerically demonstrated by controlling a double integrator with quadratic drag force subject to additive Brownian noise while satisfying probabilistic path constraints.

math.OC↗

arXiv2018

Optimal Stochastic Vehicle Path Planning Using Covariance Steering

This work addresses the problem of vehicle path planning in the presence of obstacles and uncertainties, which is a fundamental problem in robotics. While many path planning algorithms have been proposed for decades, many of them have dealt with only deterministic environments or only open-loop uncertainty, i.e., the uncertainty of the system state is not controlled and, typically, increases with time due to exogenous disturbances, which leads to the design of potentially conservative nominal paths. In order to deal with disturbances and reduce uncertainty, generally, a lower-level feedback controller is used. We conjecture that, if a path planner can consider the closed-loop evolution of the system uncertainty, it can compute less conservative but still feasible paths. To this end, in this work we develop a new approach that is based on optimal covariance steering, which explicitly steers the state covariance for stochastic linear systems with additive noise under non-convex state chance constraints. The proposed framework is verified using simple numerical simulations.

math.OC↗

arXiv2018

Optimal Covariance Control for Stochastic Systems Under Chance Constraints

This work addresses the optimal covariance control problem for stochastic discrete-time linear time-varying systems subject to chance constraints. Covariance steering is a stochastic control problem to steer the system state Gaussian distribution to another Gaussian distribution while minimizing a cost function. To the best of our knowledge, covariance steering problems have never been discussed with probabilistic chance constraints although it is a natural extension. In this work, first we show that, unlike the case with no chance constraints, the covariance steering with chance constraints problem cannot decouple the mean and covariance steering sub-problems. Then we propose an approach to solve the covariance steering with chance constraints problem by converting it to a semidefinite programming problem. The proposed algorithm is verified using two simple numerical simulations.

math.OC↗