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Extra resources for Control Theory, Numerical Methods and Computer Systems Modelling: International Symposium, Rocquencourt, June 17–21, 1974
Sample text
33) In any case, the application of these recursive filtering formulas requires determining the gain function K t , which is usually done by solving a matrix Riccati equation. In this paper, however, we shall take a different course and, for the case when x is stationary, develop a different set of equations for K t from basic principles. This will be done in the following sections. Finally, we should point out that of course the results of this section do not require that the matrices Hand F be constant as our notations suggest.
3). 20). 3) we could use 1 R*t+1 = R* t - U'H'Rt'. 30). 3) provide us with 2mn + V,m(m+1) scalar equations to determine Qt' for Qt and Ut are m x n - matrices and Rt' is a symmetric m x m - matrix. 5). 3) becomes superfluous and only 2n scalar equations are needed. This should be compared with the V,n(n+1) scalar equations of the Riccati equation; a much larger number whenever, as often is the case, m «n. Other versions of the above algorithm can now be constructed by instead using a different auxiliary function.
Control Theory Centre Report No 24. University of Warwick, England. (Submitted to Siam J. Control). 6. 7. F. J. The Infinite Dimensional Riccati Equation. C. K. J. Math. Anal. Appl. i£ Hereditary Differential Systems with Constant Del~s I - General Case (J. Diff Eqns 12 (1972), 213-235) II-A Class of Affine Systems and the Adjoint Problem. J. Diff Eqns. 8. C. K. Controllability, Observability and Optimal Feedback Control of Hereditary Differential Systems, SIAM J Control, Kailath'l. 12 (1972), 298-328.