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We introduce the concept of an obstacle skeleton which is a set of line segments inside a polygonal obstacle $\omega$ that can be used in place of $\omega$ when performing intersection tests for obstacle-avoiding network problems in the…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
This work is devoted to studying dynamic interpolation for obstacle avoidance. This is a problem that consists of minimizing a suitable energy functional among a set of admissible curves subject to some interpolation conditions. The given…
Deep sequence models have achieved notable success in time-series analysis, such as interpolation and forecasting. Recent advances move beyond discrete-time architectures like Recurrent Neural Networks (RNNs) toward continuous-time…
The optimal transport (OT) problem can be reduced to a linear programming (LP) problem through discretization. In this paper, we introduced the random block coordinate descent (RBCD) methods to directly solve this LP problem. Our approach…
Neural Ordinary Differential Equations (Neural ODEs) represent continuous-time dynamics with neural networks, offering advancements for modeling and control tasks. However, training Neural ODEs requires solving differential equations at…
Optimal control problems naturally arise in many scientific applications where one wishes to steer a dynamical system from a certain initial state $\mathbf{x}_0$ to a desired target state $\mathbf{x}^*$ in finite time $T$. Recent advances…
Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…
In the present work, we study the optimal control paths in the Zermelo navigation problem from the geometric and differential equations point of view rather than the optimal control point of view, where the latter has been carried out in…
We present and analyze a new method for solving optimal control problems for Volterra integral equations, based on approximating the controlled Volterra integral equations by a sequence of systems of controlled ordinary differential…
The Variation Evolving Method (VEM), which seeks the optimal solutions with the variation evolution principle, is further developed to be more flexible in solving the Optimal Control Problems (OCPs) with terminal constraint. With the…
Optimization-based (OB) alternatives to traditional flux limiters couch preservation of properties such as local bounds and maximum principles into optimization problems, which impose these properties through inequality constraints. In this…
We discuss the opportunities for parallelization in the recently proposed QPALM-OCP algorithm, a solver tailored to quadratic programs arising in optimal control. A significant part of the computational work can be carried out independently…
Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…
We study the Optimal Control Problem (OCP) for regular linear differential-algebraic systems (DAEs). To this end, we introduce the input index, which allows, on the one hand, to characterize the space of consistent initial values in terms…
This paper proposes a new indirect solution method for solving state-constrained optimal control problems by revisiting the well-established optimal control theory and addressing the long-standing issue of discontinuous control and costate…
This article provides quasi-optimal a priori error estimates for an optimal control problem constrained by an elliptic obstacle problem where the finite element discretization is carried out using the symmetric interior penalty…
Many robotics tasks, such as path planning or trajectory optimization, are formulated as optimal control problems (OCPs). The key to obtaining high performance lies in the design of the OCP's objective function. In practice, the objective…
A key appeal of the recently proposed Neural Ordinary Differential Equation (ODE) framework is that it seems to provide a continuous-time extension of discrete residual neural networks. As we show herein, though, trained Neural ODE models…
The compact Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. It is further developed to be more flexible in solving the…