Professor Phil Howlett

Philip George Howlett; Professor of Industrial and Applied Mathematics, UniSA; BSc (Hons); Adelaide, 1965; PhD, Adelaide, 1971.

1965 – 1989, Tutor, Senior Tutor, Lecturer, Senior Lecturer, SA Institute of Technology; 1990 – 1995, Senior lecturer, UniSA; 1996 – 2000, Associate Professor, UniSA; 2001 – 2004, Professor of Industrial and Applied Mathematics, UniSA.

School of Mathematics & Statistics

Centre for Industrial & Applied Mathematics

10 most significant publications

[1] P.G.Howlett, Input retrieval in finite dimensional linear systems, J. Austral. Math. Soc., Series B, 23, pp. 357-382, 1982. [I discuss a systematic method to invert a matrix power series when the leading coefficient is singular. The work is relevant to the theory of singular perturbations.]

[2] Phil Howlett, Peter Pudney & Ian Milroy, Energy-efficient train control, Control Engineering Practice, 2, No. 2, pp. 193-200, 1994. [We describe IFAC award-winning train control work.]

[3] P.G. Howlett and J. Cheng, Optimal driving strategies for a train on a track with continuously varying gradient, J.Aust.Math.Soc., Series B, 38, (3), pp. 388-411, 1997. [We extend the solution from track with piecewise constant gradient to track with continuously varying gradient. We derive the results directly and by taking the limit on a track with piecewise constant gradient.]

[4] P.G. Howlett and A. Torokhti, Weak interpolation and approximation of non-linear operators on the space C([0,1]), [Numerical Functional Analysis and Optimization, 19, 9 and 10, pp. 1025-1043, 1998. We establish conditions for a weak non-Lagrangian interpolation of a mapping defined by empirical data. The solution uses a novel application of sigmoidal functions.]

[5] P.G. Howlett and P.J. Pudney, An optimal driving strategy for a solar powered car on an undulating road, Dynamics of Continuous, Discrete and Impulsive Systems, 4, 4, pp. 553-568, 1998.

[6] P.G. Howlett and A. Leizarowitz, Optimal strategies for vehicle control problems with finite control sets, Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications & Algorithms, 8, pp. 41-69, 2001.

[7] P. G. Howlett, A Markov Model for the Stochastic Optimal Control of a Solar Powered Car, Optimization Methods and Applications, X. Yang, K. L. Teo and L. Caccetta, Eds., Kluwer, pp. 331-341, 2001.

[8] P.G. Howlett and K. Avrachenkov, Laurent series for the inversion of perturbed linear operators on Hilbert space, Progress in Optimisation III, Contributions from Australasia, A. Rubinov Ed., Kluwer, pp. 325-342, 2001. [We extend work by Schweitzer and Stewart on matrix operators to general bounded linear operators on Hilbert space. This natural generalisation of [2] is realised by studying the relevant null and range spaces and their orthogonal complements.]

[9] P.G. Howlett, A.P. Torokhti and C.E.M. Pearce, A Philosophy for the Modelling of Realistic Non-linear Systems, Proc. of Amer. Math. Soc., 132, 2, pp. 353-363, 2003. [The key idea is my interpretation of the auxilliary operator suggested by Daugavet as an operator mapping the complete history of the input onto the complete history of the output.]

[10] P.G. Howlett, V. Ejov and K.E. Avrachenkov, Inversion of perturbed linear operators that are singular at the origin, Proceedings of 42nd IEEE Conference on Decision and Control, Maui, Hawai, pp. 5628-5631 (on Compact Disc), December 2003. [We use a theorem of von Neumann that guarantees the existence of the inverse of a particular type of positive self-adjoint operator to extend the work in [8] to unbounded linear operators. The innovativel idea is to use the energy space following Sobolev to reformulate the unbounded operator as a bounded operator.]