# Sufficient Optimality Conditions in Stability Analysis for State-Constrained Optimal Control

## Abstract

A family of parametric linear-quadratic optimal control problems is considered. The problems are subject to state constraints. It is shown that if weak second-order sufficient optimality conditions and standard constraint qualifications are satisfied at the reference point, then, for small perturbations of the parameter, there exists a locally unique stationary point, corresponding to a solution. This point is a Lipschitz continuous function of the parameter.

- Authors:

- Systems Research Institute, Polish Academy of Sciences, ul.Newelska 6 (Poland), E-mail: kmalan@ibspan.waw.pl

- Publication Date:

- OSTI Identifier:
- 21064193

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Applied Mathematics and Optimization; Journal Volume: 55; Journal Issue: 2; Other Information: DOI: 10.1007/s00245-006-0890-1; Copyright (c) 2007 Springer; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONTROL THEORY; FUNCTIONS; MATHEMATICAL SOLUTIONS; OPTIMAL CONTROL; PERTURBATION THEORY; STABILITY

### Citation Formats

```
Malanowski, K.
```*Sufficient Optimality Conditions in Stability Analysis for State-Constrained Optimal Control*. United States: N. p., 2007.
Web. doi:10.1007/S00245-006-0890-1.

```
Malanowski, K.
```*Sufficient Optimality Conditions in Stability Analysis for State-Constrained Optimal Control*. United States. doi:10.1007/S00245-006-0890-1.

```
Malanowski, K. Thu .
"Sufficient Optimality Conditions in Stability Analysis for State-Constrained Optimal Control". United States.
doi:10.1007/S00245-006-0890-1.
```

```
@article{osti_21064193,
```

title = {Sufficient Optimality Conditions in Stability Analysis for State-Constrained Optimal Control},

author = {Malanowski, K.},

abstractNote = {A family of parametric linear-quadratic optimal control problems is considered. The problems are subject to state constraints. It is shown that if weak second-order sufficient optimality conditions and standard constraint qualifications are satisfied at the reference point, then, for small perturbations of the parameter, there exists a locally unique stationary point, corresponding to a solution. This point is a Lipschitz continuous function of the parameter.},

doi = {10.1007/S00245-006-0890-1},

journal = {Applied Mathematics and Optimization},

number = 2,

volume = 55,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}

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