# On large-scale nonlinear programming techniques for solving optimal control problems

## Abstract

The formulation of decision problems by Optimal Control Theory allows the consideration of their dynamic structure and parameters estimation. This paper deals with techniques for choosing directions in the iterative solution of discrete-time optimal control problems. A unified formulation incorporates nonlinear performance criteria and dynamic equations, time delays, bounded state and control variables, free planning horizon and variable initial state vector. In general they are characterized by a large number of variables, mostly when arising from discretization of continuous-time optimal control or calculus of variations problems. In a GRG context the staircase structure of the jacobian matrix of the dynamic equations is exploited in the choice of basic and super basic variables and when changes of basis occur along the process. The search directions of the bound constrained nonlinear programming problem in the reduced space of the super basic variables are computed by large-scale NLP techniques. A modified Polak-Ribiere conjugate gradient method and a limited storage quasi-Newton BFGS method are analyzed and modifications to deal with the bounds on the variables are suggested based on projected gradient devices with specific linesearches. Some practical models are presented for electric generation planning and fishery management, and the application of the code GRECOmore »

- Authors:

- Publication Date:

- OSTI Identifier:
- 35991

- Report Number(s):
- CONF-9408161-

TRN: 94:009753-0259

- Resource Type:
- Conference

- Resource Relation:
- Conference: 15. international symposium on mathematical programming, Ann Arbor, MI (United States), 15-19 Aug 1994; Other Information: PBD: 1994; Related Information: Is Part Of Mathematical programming: State of the art 1994; Birge, J.R.; Murty, K.G. [eds.]; PB: 312 p.

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 22 NUCLEAR REACTOR TECHNOLOGY; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; COMPUTERIZED CONTROL SYSTEMS; OPTIMIZATION; MATRICES; NUMERICAL SOLUTION; NEWTON METHOD; ALGORITHMS; CONVERGENCE; ACCURACY

### Citation Formats

```
Faco, J.L.D.
```*On large-scale nonlinear programming techniques for solving optimal control problems*. United States: N. p., 1994.
Web.

```
Faco, J.L.D.
```*On large-scale nonlinear programming techniques for solving optimal control problems*. United States.

```
Faco, J.L.D. Sat .
"On large-scale nonlinear programming techniques for solving optimal control problems". United States.
doi:.
```

```
@article{osti_35991,
```

title = {On large-scale nonlinear programming techniques for solving optimal control problems},

author = {Faco, J.L.D.},

abstractNote = {The formulation of decision problems by Optimal Control Theory allows the consideration of their dynamic structure and parameters estimation. This paper deals with techniques for choosing directions in the iterative solution of discrete-time optimal control problems. A unified formulation incorporates nonlinear performance criteria and dynamic equations, time delays, bounded state and control variables, free planning horizon and variable initial state vector. In general they are characterized by a large number of variables, mostly when arising from discretization of continuous-time optimal control or calculus of variations problems. In a GRG context the staircase structure of the jacobian matrix of the dynamic equations is exploited in the choice of basic and super basic variables and when changes of basis occur along the process. The search directions of the bound constrained nonlinear programming problem in the reduced space of the super basic variables are computed by large-scale NLP techniques. A modified Polak-Ribiere conjugate gradient method and a limited storage quasi-Newton BFGS method are analyzed and modifications to deal with the bounds on the variables are suggested based on projected gradient devices with specific linesearches. Some practical models are presented for electric generation planning and fishery management, and the application of the code GRECO - Gradient REduit pour la Commande Optimale - is discussed.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sat Dec 31 00:00:00 EST 1994},

month = {Sat Dec 31 00:00:00 EST 1994}

}