The problem of minimax mean square filtration in parabolic systems: PMM vol. 42, no. 6, 1978, pp, 1016–1025

Abstract

The problem of estimating parameters of state of a distributed parabolic system by observation results is considered. The system is assumed to function under conditions of undefined perturbations in the measurement channel and specified initial distribution. The problem is considered in minimax formulation [1] in conformity with the scheme accepted for ordinary differential equations [2].( ∗ ∗ See A. B. Kurzhanskii and Iu. S. Osipov, Control and estimation problems in systems with distributed parameters. Preprints International Federation of Automatic Contron, 6-th Triennial World Congress, Boston, 1975. Pittsburg, Pa., Instrument Society of America, 1975. ), Analytic definition of sets X (/ gJ, y (·)) (/ gJ > 0) of states of a parabolic system compatible at instant /gJ with the realizable signal y ( t) ( t ϵ [0, / gJ]) is obtained. An element of region X (/ gJ, y (·)) which satisfies the specified minimax criterion is chosen as the optimal estimate of the true state at instant /gJ. Integradifferential equations in partial derivatives are derived for parameters that define the evolution of regions X (/ gJ, y (·)) in time. One of the methods of approximating the input problem of observation by similar problems for systems of ordinary differential equations is discussed on a specific example. Problems of observation for distributed systems in different formulations appear in [3 – 6].