EU Regional School - Uciński Seminar
Prof. Dariusz Uciński Ph.D. - Optimum Experimental Design for Distributed Parameter System Identification
Institute of Control and Computation Engineering, University of Zielona Góra, Poland
The impossibility of observing the states of distributed parameter systems over the entire spatial domain raises the question of where to locate measurement sensors so as to estimate the unknown system parameters as accurately as possible. Both researchers and practitioners do not doubt that making use of sensors placed in an ‘intelligent’ manner may lead to dramatic gains in the achievable accuracy of the parameter estimates, so efficient sensor location strategies are highly desirable. In turn, the complexity of the sensor location problem implies that there are few sensor placement methods which are readily applicable to practical situations. What is more, they are not well known among researchers. The aim of the minicourse is to give account of both classical and recent original work on optimal sensor placement strategies for parameter identification in dynamic distributed systems modeled by partial differential equations. The reported work constitutes an attempt to meet the needs created by practical applications, especially regarding environmental processes, through the development of new techniques and algorithms or adopting methods which have been successful in akin fields of optimal control and optimum experimental design. While planning, real-valued functions of the Fisher information matrix of parameters are primarily employed as the performance indices to be minimized with respect to the sensor positions. Particular emphasis is placed on determining the ‘best’ way to guide moving and scanning sensors, and making the solutions independent of the parameters to be identified. A couple of case studies regarding the design of air quality monitoring networks are adopted as an illustration aiming at showing the strength of the proposed approach in studying practical problems. The course will be complemented by a discussion of more advanced topics including the related problem of optimum input design and the Bayesian approach to deal with the ill-posedness of parameter estimation.