Related papers: Modified Legendre-Gauss Collocation Method for Sol…
A new method is developed for solving optimal control problems whose solutions are nonsmooth. The method developed in this paper employs a modified form of the Legendre-Gauss-Radau orthogonal direct collocation method. This modified…
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…
Pseudospectral methods represent an efficient approach for solving optimal control problems. While Legendre-Gauss-Lobatto (LGL) collocation points have traditionally been considered inferior to Legendre-Gauss (LG) and Legendre-Gauss-Radau…
A mesh refinement method is described for solving optimal control problems using Legendre-Gauss-Radau collocation. The method detects discontinuities in the control solution by employing an edge detection scheme based on jump function…
A method is developed for solving bang-bang and singular optimal control problems using adaptive Legendre-Gauss-Radau (LGR) collocation. The method is divided into several parts. First, a structure detection method is developed that…
An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…
A new method is developed for accurately approximating the solution to state-variable inequality path constrained optimal control problems using a multiple-domain adaptive Legendre-Gauss-Radau collocation method. The method consists of the…
An adaptive mesh refinement and error estimation method for numerically solving optimal control problems is developed using Legendre-Gauss-Radau direct collocation. In regions of the solution where the desired accuracy tolerance has not…
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…
A method is presented for the numerical solution of optimal boundary control problems governed by parabolic partial differential equations. The continuous space-time optimal control problem is transcribed into a sparse nonlinear programming…
A mesh refinement method is developed for solving bang-bang optimal control problems using direct collocation. The method starts by finding a solution on a coarse mesh. Using this initial solution, the method then determines automatically…
An optimal guidance method is developed that reduces sensitivity to parameters in the dynamic model. The method combines a previously developed method for guidance and control using adaptive Legendre-Gauss-Radau (LGR) collocation and a…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
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…
A computational method is developed for desensitized optimal guidance using adaptive Gaussian quadrature collocation. The method computes a reference trajectory that reduces the sensitivity to uncertainties in the dynamic model by…
A general-purpose C++ software program called $\mathbb{CGPOPS}$ is described for solving multiple-phase optimal control problems using adaptive Gaussian quadrature collocation. The software employs a Legendre-Gauss-Radau direct orthogonal…
Recent low-thrust space missions have highlighted the importance of designing trajectories that are robust against uncertainties. In its complete form, this process is formulated as a nonlinear constrained stochastic optimal control…
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…
In this paper, a nonlinear 2D Optimal Control Problem (2DOCP) is considered. The quadratic performance index of a nonlinear cost function is endowed with the state and control functions. In this problem, the dynamic constraint of the system…
A local convergence rate is established for an orthogonal collocation method based on Radau quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently smooth solution and the Hamiltonian…