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This paper presents a method for optimal motion planning of continuum robots by employing Bernstein surfaces to approximate the system's dynamics and impose complex constraints, including collision avoidance. The main contribution is the…

Robotics · Computer Science 2023-12-20 Maxwell Hammond , Venanzio Cichella , Amirreza F. Golestaneh , Caterina Lamuta

Real world experiments are expensive, and thus it is important to reach a target in minimum number of experiments. Experimental processes often involve control variables that changes over time. Such problems can be formulated as a…

Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional…

Optimization and Control · Mathematics 2018-05-24 Xuefeng Bao , Zhi-Hong Mao , Nitin Sharma

A learning based method for obtaining feedback laws for nonlinear optimal control problems is proposed. The learning problem is posed such that the open loop value function is its optimal solution. This infinite dimensional, function space,…

Optimization and Control · Mathematics 2022-10-26 Karl Kunisch , Donato Vásquez-Varas , Daniel Walter

This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…

Optimization and Control · Mathematics 2025-04-01 Chuanzhi Lv , Xunmin Yin , Hongdan Li , Huanshui Zhang

Discrete time stochastic optimal control problems and Markov decision processes (MDPs), respectively, serve as fundamental models for problems that involve sequential decision making under uncertainty and as such constitute the theoretical…

Optimization and Control · Mathematics 2023-03-08 Christian Beck , Arnulf Jentzen , Konrad Kleinberg , Thomas Kruse

Iterated Bernstein polynomial approximations of degree n for continuous function which also use the values of the function at i/n, i=0,1,...,n, are proposed. The rate of convergence of the classic Bernstein polynomial approximations is…

Classical Analysis and ODEs · Mathematics 2009-10-16 Zhong Guan

We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…

Numerical Analysis · Mathematics 2019-10-23 Philipp A. Guth , Vesa Kaarnioja , Frances Y. Kuo , Claudia Schillings , Ian H. Sloan

We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…

Optimization and Control · Mathematics 2020-05-29 Rohit Kannan , James Luedtke

We address the problem of the best uniform approximation by linear combinations of a finite system of functions. If the system is Chebyshev and the problem is unconstrained, then the classical Remez algorithm provides a fast and precise…

Numerical Analysis · Mathematics 2025-07-08 Vladimir Yu. Protasov , Rinat Kamalov

We describe an approximate dynamic programming method for stochastic control problems on infinite state and input spaces. The optimal value function is approximated by a linear combination of basis functions with coefficients as decision…

Optimization and Control · Mathematics 2012-12-07 Tyler H. Summers , Konstantin Kunz , Nikolaos Kariotoglou , Maryam Kamgarpour , Sean Summers , John Lygeros

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Optimization and Control · Mathematics 2016-10-31 Insoon Yang , Samuel A. Burden , Ram Rajagopal , S. Shankar Sastry , Claire J. Tomlin

The numerical approximation of posterior expected quantities of interest is considered. A novel control variate technique is proposed for post-processing of Markov chain Monte Carlo output, based both on Stein's method and an approach to…

Computation · Statistics 2021-05-07 Leah F. South , Toni Karvonen , Chris Nemeth , Mark Girolami , Chris. J. Oates

The problem of minimizing a polynomial over the standard simplex is one of the basic NP-hard nonlinear optimization problems --- it contains the maximum clique problem in graphs as a special case. It is known that the problem allows a…

Optimization and Control · Mathematics 2014-10-29 Etienne de Klerk , Monique Laurent , Zhao Sun

Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…

Optimization and Control · Mathematics 2021-07-08 Morteza Boroun , Afrooz Jalilzadeh

We consider the problem of stochastic optimal control in the presence of an unknown disturbance. We characterize the disturbance via empirical characteristic functions, and employ a chance constrained approach. By exploiting properties of…

Optimization and Control · Mathematics 2020-12-16 Vignesh Sivaramakrishnan , Meeko M. K. Oishi

In the optimization of convex domains under a PDE constraint numerical difficulties arise in the approximation of convex domains in $\mathbb{R}^3$. Previous research used a restriction to rotationally symmetric domains to reduce shape…

Numerical Analysis · Mathematics 2023-11-23 Sören Bartels , Hedwig Keller , Gerd Wachsmuth

Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein…

Methodology · Statistics 2015-07-21 Zhong Guan

We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…

Optimization and Control · Mathematics 2021-07-09 Laurent Pfeiffer , Xiaolu Tan , Yulong Zhou

While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…

Optimization and Control · Mathematics 2018-11-09 Anatoli Torokhti , Pablo Soto-Quiros