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1. A Numerical Method for a Class of Mixed Switching and Impulsive Optimal Control Problems

Author

Liu, Yanqun, Eberhard, A., and Teo, Kok Lay

Subjects
*MATHEMATICAL optimization, *MATHEMATICAL models, *SIMULATION methods & models, *MATHEMATICAL analysis, *MATHEMATICAL statistics
Abstract

In this paper, we consider a class of optimal control problems in which the dynamical system involves both switching and impulsive controls. The number of switching times are supposed to be finite and, without loss of generality, to occur together with the impulses. We show that this class of optimal control problems is equivalent to a special class of optimal parameter selection problems. The gradient formulae for the cost functional and the constraint functional are derived. On this basis, the control parameterization is shown to be applicable for numerical solution. A numerical example is solved for illustration. [Copyright &y& Elsevier]

Published
2006
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2. Optimal mixed-level supersaturated design with general number of runs

Author

Chen, Jie and Liu, Min-Qian

Subjects
*FACTORIAL experiment designs, *EXPERIMENTAL design, *MATHEMATICAL optimization, *MATHEMATICAL analysis, *MATHEMATICAL statistics, *MATHEMATICAL models
Abstract

Abstract: Supersaturated design (SSD) has received much interest because of its potential in factor screening experiments. Most studies focused mainly on balanced designs. This paper considers SSDs with general run sizes. The lower bounds of the proposed by [Yamada, S., Lin, D.K.J., 1999. Three-level supersaturated designs. Statist. Probab. Lett. 45, 31–39] and proposed by [Fang, K.T., Lin, D.K.J., Liu, M.Q., 2003b. Optimal mixed-level supersaturated design. Metrika 58, 279–291] are obtained along with the sufficient and necessary conditions for achieving them, respectively. Some construction methods for optimal mixed-level SSDs with general run sizes are proposed. Many new designs are also tabulated for practical uses. [Copyright &y& Elsevier]

Published
2008
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3. On the E-optimality of complete designs under an interference model

Author

Filipiak, Katarzyna, Różański, Rafał, Sawikowska, Aneta, and Wojtera-Tyrakowska, Dominika

Subjects
*MATHEMATICAL optimization, *MATHEMATICAL models, *BLOCK designs, *MATHEMATICAL statistics, *MATHEMATICAL analysis, *COMBINATORICS
Abstract

Abstract: In the experiments in which the response to a treatment can be affected by other treatments, the interference model with neighbor effects is usually applied. It is known, that circular neighbor balanced designs (CNBDs) are universally optimal under this model. However, such designs cannot exist for each combination of design parameters. If in the class of block designs with a given number of blocks there exists CNBD, then such a design cannot exist in the class with one block less or more. The aim of this paper is to identify the E-optimal complete block designs under the interference model with neighbor effects over such classes of designs. The results are based on algebraic properties of the information matrix. [Copyright &y& Elsevier]

Published
2008
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