Solving practical optimal control problems (OCPs) that consist of multiple state, path, and control equality and inequality constraints can become challenging, but is necessary for improving the performance of modern ...
详细信息
ISBN:
(数字)9781624107115
ISBN:
(纸本)9781624107115
Solving practical optimal control problems (OCPs) that consist of multiple state, path, and control equality and inequality constraints can become challenging, but is necessary for improving the performance of modern engineering systems. A general and popular approach to solve practical OCPs is to transcribe the original continuous-time OCP into a nonlinear programming (NLP) problem that can be solved with a variety of mature NLP solvers. These direct optimization methods are differentiated by the adopted transcription scheme. A variety of different software programs that utilize direct methods exist, such as SOCS, OTIS, PSOPT, DIDO, and GPOPS-II. In this paper, we introduce an open-source, MATLAB-based optimization software, the Tiger Optimization Software (TOPS). TOPS employs several Legendre-Gauss pseudospectral transcriptions and is compatible with advanced NLP solvers such as IPOPT and SNOPT. In addition, TOPS is compatible with the open-source automatic differentiation software ADiGator to improve convergence performance of the NLP solvers. TOPS also features automatic mesh refinement and is compatible with a wide variety of OCP formulations. The goal of this paper is to outline the direct method employed by TOPS and showcase its capabilities using a small suite of OCPs and spacecraft trajectory optimization problems.
The purpose of this Note is to provide an alternative framework for arbitrary higher-order methods suitable for implementation on digital computers and in a reusable form. The optimal control problem is approximated b...
详细信息
The purpose of this Note is to provide an alternative framework for arbitrary higher-order methods suitable for implementation on digital computers and in a reusable form. The optimal control problem is approximated by a discrete nonlinear programming problem (NLP) by expanding the state trajectories using local Hermite interpolating polynomials. For high accuracy, the collocation points are selected from the family of Gauss-Lobatto points. This also allows the integral performance index to be approximated via Gauss-Lobatto quadrature rules. For optimal control problems of the Bolza form, the natural choice of quadrature points are the Legendre-Gauss-Lobatto (LGL) points, because they are derived on the basis of a unity weight function, giving the highest accuracy for polynomial integrands. The generalization of the approach is referred to as the Hermite-Legendre-Gauss-Lobatto (HLGL) approach throughout the remainder of this Note.
Numerical methods for optimal control of hybrid dynamical systems are considered where the discrete dynamics and the nonlinear continuous dynamics are tightly coupled. A decomposition approach for numerically solving ...
详细信息
Numerical methods for optimal control of hybrid dynamical systems are considered where the discrete dynamics and the nonlinear continuous dynamics are tightly coupled. A decomposition approach for numerically solving general mixed-integer continuous optimal control problems (MIOCPs) is discussed. In the outer optimization loop a branch-and-bound binary tree search is used for the discrete variables. The multiple-phase optimal control problems for the continuous state and control variables in the inner optimization loop are solved by a sparse direct collocation transcription method. A genetic algorithm is applied to improve the performance of the branch-and-bound approach by providing a good initial upper bound on the MIOCP performance index. Results are presented for motorized traveling salesmen problems, new benchmark problems in hybrid optimal control.
One of the most effective numerical techniques for the solution of trajectory optimization and optimal control problems is the direct transcription method. This approach combines a nonlinear programming algorithm with...
详细信息
One of the most effective numerical techniques for the solution of trajectory optimization and optimal control problems is the direct transcription method. This approach combines a nonlinear programming algorithm with discretization of the trajectory dynamics. The resulting mathematical programming problem is characterized by matrices that are large and sparse. Constraints on the path of the trajectory are then treated as algebraic inequalities to be satisfied by the nonlinear program. This paper describes a nonlinear programming algorithm that exploits the matrix sparsity produced by the transcription formulation. Numerical experience is reported for trajectories with both state and control variable equality and inequality path constraints.
One of the most effective numerical techniques for the solution of trajectory optimization and optimal control problems is the direct transcription method, This approach combines a nonlinear programming algorithm with...
详细信息
One of the most effective numerical techniques for the solution of trajectory optimization and optimal control problems is the direct transcription method, This approach combines a nonlinear programming algorithm with a discretization of the trajectory dynamics, When the resulting mathematical programming problem is solved using a sparse sequential quadratic programming algorithm, the technique produces solutions very rapidly and has demonstrated considerable robustness when applied to atmospheric acid orbital trajectories, This paper describes the application of the direct transcription technique to the optimal design of a commercial aircraft trajectory, subject to realistic constraints on the aircraft flight path, A primary result of the paper is to demonstrate that the transcription formulation leads to a very natural treatment of realistic Federal Aviation Administration (FAA) imposed path constraints within a high fidelity simulation, A second important result is to demonstrate that modeling tabular data using smooth approximations significantly improves the speed of convergence.
The most effective numerical techniques for the solution of trajectory optimization and optimal control problems combine a nonlinear iteration procedure with some type of parametric approximation to the trajectory dyn...
详细信息
The most effective numerical techniques for the solution of trajectory optimization and optimal control problems combine a nonlinear iteration procedure with some type of parametric approximation to the trajectory dynamics. Early methods attempted to parameterize the dynamics using a small number of variables because the iterative search procedures could not successfully solve larger problems. With the development of more robust nonlinear programming algorithms, it is now feasible and desirable to consider formulations of the trajectory optimization problem incorporating a large number of variables and constraints. The purpose of this paper is to address the manner in which a trajectory is parameterized and the design of the nonlinear programming algorithm to effectively deal with this formulation.
暂无评论