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:

 

  1. Basic methods of optimization. Regression analysis, Bayesian estimation, method of an empirical functional, method of a maximum likelihood, method of stochastic approximation.
  2. Estimation of parameters of linear models.
  3. Filtration of random processes. Wiener-Kolmogorov and Kalman-Busy filters. Randomized modifications of filters.
  4. Randomized algorithms of stochastic approximation in non-linear problems.
  5. 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:

 

  1. Granichin O.N., Polyak B.T. “Randomized algorithms of optimization and estimation under almost arbitrary noise”.  M.:Nauka, 2003, 260p.
  2. Fomin V.N. “Optimal and adaptive filtration”.  St.Pb.: SPbSU, 2002, 360p..
  3. 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.
  4. Granichin O.N. “Randomized algorithms for stochastic approximation  under arbitrary disturbances”  Automation and Remote Control,  2002, v.63, No.2, pp.209-219.
  5. Granichin O.N. “Nonminimax filtering under arbitrary bounded measurement noise”  Automation and Remote Control,  2002, v.63, No.9.
  6. 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.