Description: KL_TeoTitle: Optimal Discrete-Valued Control Computation: An Exact Penalty

Function Approach

Kok Lay Teo

John Curtin Distinguished Professor, Curtin University, Australia.

 

Abstract: We consider an optimal control problem in which the control takes values from a discrete set. The state and control are subject to continuous inequality constraints. By introducing auxiliary controls and applying a time-scaling transformation, we transform this optimal discrete valued control problem into an equivalent problem subject to additional linear and quadratic constraints. The feasible region defined by these additional constraints is disconnected, and thus standard optimization methods struggle to handle these constraints. We introduce a novel exact penalty function to penalize constraint violations, and then append this penalty function to the objective function forming a new appended objective function. This leads to an approximate optimal control problem that can be handled by standard optimal control technique and, in particular, the general optimal control software packages, such as MISER, are applicable. Convergence results show that any local solution of the approximate problem is also a local solution of the original problem. For demonstrate the effectiveness of the method, two train control problems are solved by using the method proposed.

Biography: Kok Lay Teo (John Curtin Distinguished Professor) received his PhD degree in electrical engineering from the University of Ottawa, Canada. He was with the Department of Applied Mathematics, University of New South Wales, Australia, the Department of Industrial and Systems Engineering, National University of Singapore, Singapore, the Department of Mathematics, the University of Western Australia, Australia. In 1996, he joined the Department of Mathematics and Statistics, Curtin University of Technology, Australia, as Professor. He then took up the position of Chair Professor of Applied Mathematics and Head of Department of Applied Mathematics at the Hong Kong Polytechnic University, China, from 1999 to 2004. He returned to Curtin University of Technology as Professor and Head of Department of Mathematics and Statistics from 2005-2010. He is currently John Curtin Distinguished Professor at Curtin University. He has published 5 books and over 400 journal papers. He has a software package, MISER3.3, for solving general constrained optimal control problems. His editorial positions are:

 

·         Editor-in-Chief: (i) “Journal of Industrial and Management Optimization”; (ii) “Dynamics of Continuous, Discrete and Impulsive Systems, Series B”; and (iii) “Numerical Algebra, Control and Optimization”.

·         Regional Editor: “Nonlinear Dynamics and Systems Theory”

·         Member of Editorial Board: (i) Automatica; (ii) Journal of Global Optimization; (iii) Journal of Optimization Theory and Applications, (iv) Optimization and Engineering, (v) Discrete and Continuous Dynamic Systems, (vi) Optimization Letters, (vii) Differential Equations and Dynamical Systems, (viii) Journal of Inequality and Applications. (ix) Journal of ANZIAM; (x) Dynamics of Continuous, Discrete and Impulsive Systems, Series A; (xi) Pacific Journal of Optimization; and (xii) International Journal of Innovational Computing & Information Control.

The International Conference on Optimization and Control (ICOCO 2010) was held in Guiyang, China during July 18-23, 2010, dedicated to Professors Kok Lay Teo and Jie Sun. For further details, see the conference homepage at http://sci.gzu.edu.cn/a/icoco..html. Two special issues, one for Discrete and Continuous Dynamical Systems - Series B, and one for International Journal of Innovational Computing and Information Control are being dedicated to Professor Kok Lay Teo and Professor Jie Sun. They are published in 2011 and 2012, respectively.

Professor Teo’s research interests include both the theoretical and practical spects of optimal control and optimization, and their practical applications such as in signal processing in telecommunications, and financial portfolio optimization.