Finite element solution of optimal control problems with state-control inequality constraints

Bless, Robert R.; Hodges, Dewey H.

doi:10.2514/3.20938

Cited by 20 publications

(5 citation statements)

References 3 publications

(4 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hodges and Bless (1991) solved the optimal control problem based on the weak Hamiltonian finite element method and then adopted this method to design the optimal ascent trajectory for a launch vehicle. This approach can accurately and efficiently solve the trajectory optimization problems with control constraints (Bless and Hodges, 1992;Warner and Hodges, 1999), and Bottasso and Ragazzi (2000) verified that the approach is equivalent to the Runge-Kutta schemes for the solution of boundary value problems.…”

Section: Introductionmentioning

confidence: 83%

Closed-loop atmospheric ascent guidance based on finite element method

Cui

et al. 2015

Aircraft Eng & Aerospace Tech

View full text Add to dashboard Cite

Purpose -The purpose of this paper is to study the closed-loop guidance algorithm for launch vehicles in an atmospheric ascent phase and present a numerical trajectory reconstruction algorithm to satisfy the real-time requirement of generating the guidance commands. Design/methodology/approach -An optimal control model for an atmospheric ascent guidance system is established directly; following that, the detailed process for necessary conditions of the optimal control problem is re-derived based on the calculus of variations. As a result, the trajectory optimization problem can be reduced to a root-finding problem of algebraic equations based on the finite element method (FEM). To obtain an accurate solution, the Newton method is introduced to solve the roots in a guidance update cycle. Findings -The presented approach can accurately and efficiently solve the trajectory optimization problems. A moderate number of unknowns can yield a good optimal solution, which is well suited for the open-loop guidance. To meet the requirements of the rapidity and accuracy for the close-loop guidance, the fewer number of unknowns is artificially chosen to reduce the calculation time, and the on-board trajectory planning strategy can increase the precision of the optimal solution along with the decrease of time-to-go. Practical implications -The closed-loop guidance algorithm based on an FEM can be found in this paper, which can solve the optimal ascent guidance problems for launch vehicles in the atmospheric flight phase rapidly, accurately and efficiently. Originality/value -This paper re-derives the necessary conditions of the optimal solution in a different way compared to the previous work, and the closed-loop guidance algorithm combined with the FEM is also a new thought for the optimal atmospheric ascent guidance problems.

show abstract

Section: Introductionmentioning

confidence: 83%

Closed-loop atmospheric ascent guidance based on finite element method

Cui

et al. 2015

Aircraft Eng & Aerospace Tech

View full text Add to dashboard Cite

show abstract

“…Ignoring the boundary conditions as before, the expression for the variation can be found in Ref. 3 as…”

Section: Calculus Of Variationsmentioning

confidence: 99%

Solving Optimal Control Problems Using hp-Version Finite Elements in Time

Warner

Hodges

2000

Journal of Guidance, Control, and Dynamics

Self Cite

View full text Add to dashboard Cite

A previously published temporal nite element method for optimal control problems is updated to include higherorder hierarchical shape functions. The accuracy and power of the analysis and corresponding code are illustrated on optimal control problems with nonlinear system dynamics, using interfaces based on symbolic mathematics to automatically generate the necessary derivative expressions and nonlinear algebraic equations to be solved. The class of problems includes those that can have free or xed nal time, multiple phases, nonlinear/periodic boundary conditions, and control constraints. This code has been tested on a variety of problems, culminating in a three-phase, seven-state, two-control missile problem with nonlinear system dynamics, where accuracy was found to be signi cantly improved over h-version results, with potential order-of-magnitude reductions in CPU time and numbers of parameters for a given level of error.

show abstract

“…He used the cross-sectional properties derived through VAM to investigate the free vibration behavior of composite beams [22] and he drew many significant conclusions. During this period, Dewey Hodges initiated a programme of research associated with Kanes's equation and multibody dynamics [47,52,54], optimal control problems in engineering [21,26,30,38] and the trapeze effect in finite element cross-sectional analysis in composite beams [37,63]. Since 2000, Dewey Hodges turned his attention to aeroelasticity of aircraft with high aspect ratio wings, both metallic and composites [39,41].…”

Section: Introductionmentioning

confidence: 99%

Dewey Hodges’s Research in Structural Dynamics, Aeroelasticity, and Composites: A Personal Perspective

Banerjee

2019

AIAA Journal

View full text Add to dashboard Cite

The contributions of Dewey Hodges within the specialized areas of structural dynamics, aeroelasticity and composites are highlighted in this paper. Dewey Hodges has published 215 journal and 170 conference papers covering a wide range of topics in aerospace structures. His research and academic career spans nearly five decades and it is difficult, if not impossible to give a detailed commentary on his colossal achievement in the confines of a single paper. It is widely acknowledged that Dewey Hodges' research record is no less than incredible. He has not only given an exceptional account of himself, but has also demonstrated his extraordinary versatility in research. The author of this paper has known him both personally and professionally for nearly three decades and with great humility he acknowledges the enormous benefit he has received from his association with him. Given the huge volume of work Dewey Hodges has produced and the enormity of the task of commenting on it, the author has understandably been highly selective in choosing which contributions to discuss. A sample of selected papers with Dewey Hodges' original and groundbreaking contributions is thus highlighted and commented on.

show abstract

Finite element solution of optimal control problems with state-control inequality constraints

Cited by 20 publications

References 3 publications

Closed-loop atmospheric ascent guidance based on finite element method

Closed-loop atmospheric ascent guidance based on finite element method

Solving Optimal Control Problems Using hp-Version Finite Elements in Time

Dewey Hodges’s Research in Structural Dynamics, Aeroelasticity, and Composites: A Personal Perspective

Contact Info

Product

Resources

About