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The Switch Point Algorithm is a new approach for solving optimal control problems whose solutions are either singular or bang-bang or both singular and bang-bang, and which possess a finite number of jump discontinuities in an optimal…

Optimization and Control · Mathematics 2021-07-20 Mahya Aghaee , William W. Hager

We develop an optimization-based framework for joint real-time trajectory planning and feedback control of feedback-linearizable systems. To achieve this goal, we define a target trajectory as the optimal solution of a time-varying…

Systems and Control · Electrical Eng. & Systems 2020-03-17 Tianqi Zheng , John Simpson-Porco , Enrique Mallada

An innovative numerical technique is presented to adjust the inflow to a supply chain in order to achieve a desired outflow, reducing the costs of inventory, or the goods timing in warehouses. The supply chain is modelled by a conservation…

Numerical Analysis · Mathematics 2015-03-20 Ciro D'Apice , Rosanna Manzo , Benedetto Piccoli

Gradient Descent (GD) is a ubiquitous algorithm for finding the optimal solution to an optimization problem. For reduced computational complexity, the optimal solution $\mathrm{x^*}$ of the optimization problem must be attained in a minimum…

Optimization and Control · Mathematics 2023-06-01 Revati Gunjal , Sushama Wagh , Syed Shadab Nayyer , Alex Stankovic , Navdeep M. Singh

Differential Dynamic Programming (DDP) is an efficient computational tool for solving nonlinear optimal control problems. It was originally designed as a single shooting method and thus is sensitive to the initial guess supplied. This work…

Robotics · Computer Science 2023-09-29 He Li , Wenhao Yu , Tingnan Zhang , Patrick M. Wensing

The optimal control input for linear systems can be solved from algebraic Riccati equation (ARE), from which it remains questionable to get the form of the exact solution. In engineering, the acceptable numerical solutions of ARE can be…

Systems and Control · Electrical Eng. & Systems 2022-01-07 Shengbo Wang , Shiping Wen , Kaibo Shi , Song Zhu , Tingwen Huang

We study gradient-based optimization methods obtained by direct Runge-Kutta discretization of the ordinary differential equation (ODE) describing the movement of a heavy-ball under constant friction coefficient. When the function is high…

Optimization and Control · Mathematics 2019-05-30 Jingzhao Zhang , Suvrit Sra , Ali Jadbabaie

We propose an {\em implementable} numerical scheme for the discretization of linear-quadratic optimal control problems involving SDEs in higher dimensions with {\em control constraint}. For time discretization, we employ the implicit Euler…

Analysis of PDEs · Mathematics 2024-12-12 Abhishek Chaudhary

Optimal control and sequential decision making are widely used in many complex tasks. Optimal control over a sequence of natural images is a first step towards understanding the role of vision in control. Here, we formalize this problem as…

Machine Learning · Computer Science 2026-05-07 Peter N. Loxley

Trajectory optimization considers the problem of deciding how to control a dynamical system to move along a trajectory which minimizes some cost function. Differential Dynamic Programming (DDP) is an optimal control method which utilizes a…

Systems and Control · Computer Science 2017-01-10 David D. Fan , Evangelos A. Theodorou

In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta…

Numerical Analysis · Mathematics 2017-07-17 Willem Hundsdorfer

This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…

Optimization and Control · Mathematics 2014-05-19 Shakoor Pooseh , Ricardo Almeida , Delfim F. M. Torres

In this paper, near optimal tracking of a class of nonlinear systems is addressed. Adaptive (approximate) dynamic programming approach is used to calculate the optimal control in closed form. ADP (Adaptive (approximate) dynamic programming)…

Optimization and Control · Mathematics 2021-09-22 Farshid Asadi , Ali Heydari

Numerical ``direct'' approaches to time-optimal control often fail to find solutions that are singular in the sense of the Pontryagin Maximum Principle, performing better when searching for saturated (bang-bang) solutions. In previous work…

Systems and Control · Electrical Eng. & Systems 2024-06-13 Arthur Castello Branco de Oliveira , Milad Siami , Eduardo D. Sontag

Selecting the best hyperparameters for a particular optimization instance, such as the learning rate and momentum, is an important but nonconvex problem. As a result, iterative optimization methods such as hypergradient descent lack global…

Machine Learning · Computer Science 2023-12-05 Xinyi Chen , Elad Hazan

Optimal tracking in switched systems with controlled subsystem and Discrete-time (DT) dynamics is investigated. A feedback control policy is generated such that a) the system tracks the desired reference signal, and b) the optimal switching…

Systems and Control · Electrical Eng. & Systems 2019-07-30 Tohid Sardarmehni , Xingyong Song

We propose a novel reformulation of the stochastic optimal control problem as an approximate inference problem, demonstrating, that such a interpretation leads to new practical methods for the original problem. In particular we characterise…

Machine Learning · Computer Science 2010-09-22 Konrad Rawlik , Marc Toussaint , Sethu Vijayakumar

Optimal control is a popular approach to synthesize highly dynamic motion. Commonly, $L_2$ regularization is used on the control inputs in order to minimize energy used and to ensure smoothness of the control inputs. However, for some…

Robotics · Computer Science 2022-07-18 Traiko Dinev , Wolfgang Merkt , Vladimir Ivan , Ioannis Havoutis , Sethu Vijayakumar

A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online…

Optimization and Control · Mathematics 2025-01-30 Anran Li , John P. Swensen , Mehdi Hosseinzadeh

We introduce a family of stochastic optimization methods based on the Runge-Kutta-Chebyshev (RKC) schemes. The RKC methods are explicit methods originally designed for solving stiff ordinary differential equations by ensuring that their…

Optimization and Control · Mathematics 2022-02-01 Tony Stillfjord , Måns Williamson