Related papers: Direct Collocation for Numerical Optimal Control o…
It is often unnoticed that the predominant way to use collocation methods is fundamentally flawed when applied to optimal control in robotics. Such methods assume that the system dynamics is given by a first order ODE, whereas robots are…
Direct collocation methods are widely used numerical techniques for solving optimal control problems. The discretization of continuous-time optimal control problems transforms them into large-scale nonlinear programming problems, which…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
We introduce basic aspects of new operator method, which is very suitable for practical solving differential equations of various types. The main advantage of the method is revealed in opportunity to find compact exact operator solutions of…
We present a method to solve fractional optimal control problems, where the dynamic depends on integer and Caputo fractional derivatives. Our approach consists to approximate the initial fractional order problem with a new one that involves…
Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…
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…
Time delays are ubiquitous in industry, and they must be accounted for when designing control strategies. However, numerical optimal control (NOC) of delay differential equations (DDEs) is challenging because it requires specialized…
Second-order optimization methods exhibit fast convergence to critical points, however, in nonconvex optimization, these methods often require restrictive step-sizes to ensure a monotonically decreasing objective function. In the presence…
In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a…
This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system…
We present a parameter estimation method in Ordinary Differential Equation (ODE) models. Due to complex relationships between parameters and states the use of standard techniques such as nonlinear least squares can lead to the presence of…
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…
Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to…
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,…
In this work, we present a second-order numerical scheme to address the solution of optimal control problems constrained by the evolution of nonlinear Fokker-Planck equations arising from socio-economic dynamics. In order to design an…
Direct collocation methods are powerful tools to solve trajectory optimization problems in robotics. While their resulting trajectories tend to be dynamically accurate, they may also present large kinematic errors in the case of constrained…
We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordinary differential equations (ODE) modelling interacting…
Second-order dynamical systems are important tools for solving optimization problems, and most of existing works in this field have focused on unconstrained optimization problems. In this paper, we propose an inertial primal-dual dynamical…