A review of pseudospectral optimal control: From theory to flight

Ross, I. Michael; Karpenko, Mark

doi:10.1016/j.arcontrol.2012.09.002

Cited by 306 publications

(216 citation statements)

References 46 publications

Supporting

Mentioning

216

Contrasting

Order By: Relevance

“…Applying this discretization results in a standard optimal control problem which is solved using a pseudospectral discretization scheme in the time domain (Gong, Ross, Kang, & Fahroo, 2008;Ross & Karpenko, 2012). The NLP package SNOPT (Gill, Murray, & Saunders, 2005) is used to calculate the solution to NLP problem produced by this sequence of approximations.…”

Section: Application On Optimal Searchmentioning

confidence: 99%

“…4), Runge-Kutta (Kameswaran & Biegler, 2008;Schwartz & Polak, 1996), and Pseudospectral (Gong, Kang, & Ross, 2006;Kang, 2010;Ross & Karpenko, 2012). These computational optimal control methods have achieved great success in many areas of control applications (Bedrossian, Bhatt, Kang, & Ross, 2009;Bedrossian, Karpenko, & Bhatt, 2012;Chung, Polak, Royset, & Sastry, 2011;Li, Ruths, Yu, & Arthanari, 2011).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Consistent approximation of a nonlinear optimal control problem with uncertain parameters

et al. 2014

View full text Add to dashboard Cite

a b s t r a c tThis paper focuses on a non-standard constrained nonlinear optimal control problem in which the objective functional involves an integration over a space of stochastic parameters as well as an integration over the time domain. The research is inspired by the problem of optimizing the trajectories of multiple searchers attempting to detect non-evading moving targets. In this paper, we propose a framework based on the approximation of the integral in the parameter space for the considered uncertain optimal control problem. The framework is proved to produce a zeroth-order consistent approximation in the sense that accumulation points of a sequence of optimal solutions to the approximate problem are optimal solutions of the original problem. In addition, we demonstrate the convergence of the corresponding adjoint variables. The accumulation points of a sequence of optimal state-adjoint pairs for the approximate problem satisfy a necessary condition of Pontryagin Minimum Principle type, which facilitates assessment of the optimality of numerical solutions.

show abstract

Section: Application On Optimal Searchmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Consistent approximation of a nonlinear optimal control problem with uncertain parameters

et al. 2014

View full text Add to dashboard Cite

show abstract

“…These optimal control methods take two main forms, indirect and direct. Recent surveys of these techniques are provided by Betts [29,30], Trélat [31] and Ross [32] and a historical perspective by Stryk et al [33]. Indirect methods (such as the shooting and multiple shooting methods) solve Pontryagin's necessary conditions for optimality.…”

Section: Numerical Methods For Optimal Controlmentioning

confidence: 99%

Galerkin Optimal Control

Boucher

Kang

Gong

2016

J Optim Theory Appl

View full text Add to dashboard Cite

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington ABSTRACT (maximum 200 words)A Galerkin-based family of numerical formulations is presented for solving nonlinear optimal control problems. This dissertation introduces a family of direct methods that calculate optimal trajectories by discretizing the system dynamics using Galerkin numerical techniques and approximate the cost function with Gaussian quadrature. In this numerical approach, the analysis is based on L 2 -norms. An important result in the theoretical foundation is that the feasibility and consistency theorems are proved for problems with continuous and/or piecewise continuous controls. Galerkin methods may be formulated in a number of ways that allow for efficiency and/or improved accuracy while solving a wide range of optimal control problems with a variety of state and control constraints. Numerical formulations using Lagrangian and Legendre test functions are derived. One formulation allows for a weak enforcement of boundary conditions, which imposes end conditions only up to the accuracy of the numerical approximation itself. Additionally, the multi-scale formulation can reduce the dimension of multi-scale optimal control problems, those in which the states and controls evolve on different timescales. Finally, numerical examples are shown to demonstrate the versatile nature of Galerkin optimal control. SUBJECT TERMS

show abstract

“…Since 1990s, the application of the pseudospectral methods for solving optimal control problems has been popular due to their computational efficiency (Li, 2017;Limebeer, Perantoni, & Rao, 2014;Ross & Karpenko, 2012;Shamsi, 2011). For recent advances in the pseudospectral methods, see, for example, Gong, Ross, and Fahroo (2016) ;Tang, Liu, and Hu (2016).…”

Section: Introductionmentioning

confidence: 99%

A mixed-binary non-linear programming approach for the numerical solution of a family of singular optimal control problems

Foroozandeh

Shamsi

Pinho

2017

International Journal of Control

View full text Add to dashboard Cite

This paper presents a new approach for the efficient and accurate solution of Singular Optimal Control Problems (SOCP). A novel feature of the proposed method is that it does not require a priori knowledge of the structure of the solution. As the first step of this method, the SOCP is converted into a binary optimal control problem. Then, by utilizing the pseudospectral method, the resulting problem is transcribed to a mixed-binary non-linear programming problem. This mixed-binary non-linear programming problem, which can be solved by well-known solvers, allows us to detect the structure of the original optimal control and to compute the approximating solution of it (getting both the optimal state and control). The main advantages of the present method are that: (i) without a priori information, the structure of optimal control is detected; (ii) it produces good results even using a small number of collocation points; and (iii) the switching times can be captured accurately. These advantages are illustrated through a numerical implementation of the method on four examples.

show abstract

A review of pseudospectral optimal control: From theory to flight

Cited by 306 publications

References 46 publications

Consistent approximation of a nonlinear optimal control problem with uncertain parameters

Consistent approximation of a nonlinear optimal control problem with uncertain parameters

Galerkin Optimal Control

A mixed-binary non-linear programming approach for the numerical solution of a family of singular optimal control problems

Contact Info

Product

Resources

About