Related papers: Direct Collocation for Numerical Optimal Control o…
Pseudospectral collocation methods have proven to be powerful tools to solve optimal control problems. While these methods generally assume the dynamics is given in the first order form $\dot{x} = f (x, u, t)$, where x is the state and u is…
This study introduces the reader to the theory of approximating the solution(s) of a non-linear, second order, ordinary differential equation (ODE) with piecewise polynomial functions by using the collocation method. It then focuses on 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…
In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…
The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the…
Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal…
The well-posedness of a class of optimal control problems is analysed, where the state equation couples a nonlinear degenerate Fokker-Planck equation with a system of Ordinary Differential Equations (ODEs). Such problems naturally arise as…
The Distributed Constraint Optimization Problem (DCOP) formulation is a powerful tool to model multi-agent coordination problems that are distributed by nature. The formulation is suitable for problems where variables are discrete and…
A new method is described for solving optimal control problems using direct collocation at Legendre-Gauss-Lobatto points. The approach of this paper employs a polynomial approximation of the right-hand side vector field of the differential…
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…
A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…
This paper introduces and analyses a continuous optimization approach to solve optimal control problems involving ordinary differential equations (ODEs) and tracking type objectives. Our aim is to determine control or input functions, and…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
Classical neural ordinary differential equations (ODEs) are powerful tools for approximating the log-density functions in high-dimensional spaces along trajectories, where neural networks parameterize the velocity fields. This paper…
We present an adaptation of direct collocation -- a trajectory optimization method commonly used in robotics and aerospace applications -- to quantum optimal control (QOC); we refer to this method as Pade Integrator COllocation (PICO). This…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. A sliding mode is coped with differential-algebraic equations (DAEs) and that guarantees accurate tracking of the sliding motion…
Explicit stabilized methods are an efficient alternative to implicit schemes for the time integration of stiff systems of differential equations in large dimension. In this paper, we derive explicit stabilized integrators of orders one and…
Direct multiple shooting (DMS) and direct collocation (DC) are two common transcription methods for solving optimal control problems (OCP) in biomechanics and robotics. They have rarely been compared in terms of solution and speed. Through…
A new problem is studied, the concept of exactness of a second order nonlinear ordinary differential equations is established. A method is constructed to reduce this class into a first order equations. If the second order equation is not…
This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that allows to characterize the structure of optimal controls on…