By A.I. Matasov
When fixing the keep an eye on and layout difficulties in aerospace and naval engi neering, energetics, economics, biology, etc., we have to recognize the kingdom of investigated dynamic techniques. The presence of inherent uncertainties within the description of those procedures and of noises in size units results in the need to build the estimators for corresponding dynamic structures. The estimators get better the mandatory information regarding process country from mea surement facts. An try and clear up the estimation difficulties in an optimum means leads to the formula of alternative variational difficulties. the sort and complexity of those variational difficulties depend upon the method version, the version of uncertainties, and the estimation functionality criterion. an answer of variational challenge determines an optimum estimator. Howerever, there exist a minimum of explanation why we use nonoptimal esti mators. the 1st cause is that the numerical algorithms for fixing the corresponding variational difficulties might be very tricky for numerical imple mentation. for instance, the measurement of those algorithms should be very high.
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Example text
47 Guaranteed Parameter Estimation cos(t - x:) cos Z f------F" e t o 27r - cosz Fig. 2. 31) t- H(t)II>+(t)dt+j H(t)II>-(t)dt. 32) Generally, the sets t+={tE[0,27rl! 27), are quite complicated (see Figure 2). 32). 32) in the form (= Jof21r max (11)+ (t), 0) dt f21r a= Jo 121r 0 H(t) max (11)+ (t), 0) dt+ min (11)- (t), 0) dt, f21r Jo H(t)min(II>-(t),O)dt. 34) are 27r-periodic. Consequently, 48 Chapter 1 12"Tr-" H(t + 11:) max (~+(t + 11:), 0) dt a= + 12"Tr-" H(t + 11:) min (~-(t + 11:),0) dt = 1 3Tr/2 -Tr/2 H(t + 11:) max (w+(t), 0) dt + 13Tr/2 -Tr/2 H(t + 11:) min (w- (t), 0) dt, where w+(t) = - 0"( [cost r cosz + 1], w- (t) = - 0"( [cost r cosz 1].
32) in the form (= Jof21r max (11)+ (t), 0) dt f21r a= Jo 121r 0 H(t) max (11)+ (t), 0) dt+ min (11)- (t), 0) dt, f21r Jo H(t)min(II>-(t),O)dt. 34) are 27r-periodic. Consequently, 48 Chapter 1 12"Tr-" H(t + 11:) max (~+(t + 11:), 0) dt a= + 12"Tr-" H(t + 11:) min (~-(t + 11:),0) dt = 1 3Tr/2 -Tr/2 H(t + 11:) max (w+(t), 0) dt + 13Tr/2 -Tr/2 H(t + 11:) min (w- (t), 0) dt, where w+(t) = - 0"( [cost r cosz + 1], w- (t) = - 0"( [cost r cosz 1]. 36) respectively. Define more exactly the form of the parameter being estimated.
Ldt s iT Icp(t)ldt. Maximizing the left-hand side of this inequality in >. 16), we get 1° = sup a'>. S inf iT Icp(t)ldt = 1o. 2). 2) is a general result of the optimization theory. There is a rule for constructing the dual problem [75], [51] (see also Chapter 2). ' (a - iT H(t)CP(t) dt) . )). 2). In fact, :,':l'. :r iT D H (t) 4> (t) dt)} (I