Spec. course "Optimization of Real-Time
Systems"
Lecturer: Prof. O.N.Granichin
Students: 4 year, computer science department
Summary:
One of the basic problems at designing
and development of electron devices working as a real-time system is an
optimization of their activity. Until recently the optimization have been
achieved based on the preliminary simulation of activity and the selection of
the best parameters of a system. The using of feedback approach for the
parameters correcting in operating time was limited by backwardness of the
theory of recurrent optimization. In particular, the strong limitation in
application of standard procedures of optimization was the assumption about
random character of uncertainties in a system and their independence and
zero-mean. But just these limitations may be very strong in the real time
systems. Therefore some heuristic
algorithms theoretically unreasonable are used in practice. The development of
the fundamentals of the theory of recurrent stochastic optimization at almost
arbitrary noises largely removes these limitations.
Themes of the course:
- Basic methods of optimization.
Regression analysis, Bayesian estimation, method of an empirical
functional, method of a maximum likelihood, method of stochastic
approximation.
- Estimation of
parameters of linear models.
- Filtration of
random processes. Wiener-Kolmogorov and Kalman-Busy filters. Randomized
modifications of filters.
- Randomized
algorithms of stochastic approximation in non-linear problems.
- Examples of
possible applications of randomized algorithms: the optimization of
process of loading of channels in the computer network, adaptive selection
of the characteristics of the server maintaining queue of tasks, the
calculation of options price in real-time mode in exchange trade.
References:
- Granichin O.N., Polyak B.T. “Randomized
algorithms of optimization and estimation under almost arbitrary noise”. M.:Nauka, 2003, 260p.
- Fomin V.N. “Optimal and adaptive filtration”. St.Pb.: SPbSU, 2002, 360p..
- Granichin O.N. “Estimating the
parameters of linear regression in
an arbitrary noise” Automation and
Remote Control, 2002, v.63, No.1,
p. 25-35.
- Granichin O.N. “Randomized
algorithms for stochastic approximation
under arbitrary disturbances”
Automation and Remote Control,
2002, v.63, No.2, pp.209-219.
- Granichin O.N. “Nonminimax
filtering under arbitrary bounded measurement noise” Automation and Remote Control, 2002, v.63, No.9.
- Spall J.C. “An overview of the simultaneous perturbation method for
efficient optimization”. Johns Hopkins APL Technical Digest, 1998, vol.19,
p.482--492, http://techdigest.jhuapl.edu/td/td1904/spall.pdf.