By Nikolai Michailovich Filatov, Heinz Unbehauen

This monograph demonstrates how the functionality of assorted recognized adaptive controllers could be greater considerably utilizing the twin impression. The differences to include twin regulate are discovered individually and independently of the most adaptive controller with out complicating the algorithms. a brand new bicriterial technique for twin regulate is constructed and utilized to numerous kinds of renowned linear and nonlinear adaptive controllers. sensible functions of the designed controllers to a number of real-time difficulties are awarded. This monograph is the 1st publication delivering a whole exposition at the twin keep watch over challenge from the inception within the early Nineteen Sixties to the current state-of-the-art aiming at scholars and researchers in adaptive regulate in addition to layout engineers in undefined.

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8). This simplified model is an integrator with an unknown additive parameter. 2. Dual Effect and Neutral Systems for control optimization, eq. 15), with the setpoint w(k). This optimal control problem has a simple solution. 5. 6. System with direct adaptation (with indirect identification) y 3. 7. 2. Dual Effect and Neutral Systems where the covariance of the estimation error is determined as { } P(k ) = E (c − cˆ(k )) 2 ℑk . 8) Utilizing the CE approach, one assumes that all stochastic variables in the system are equal to their expectations, that is, ξ(k)=0 and P(k ) =0 in the considered case.

It can easily be verified that eq. 15) is identical to the RLS algorithm when Qε ( k ) ≡ 0 . The RLS algorithm with forgetting factor 0 < α ≤ 1 will be obtained when eq. 15) takes the form P (k + 1) = 1 [ P (k ) − q (k + 1)m T (k ) P (k )] . 16) Thus eq. 15) has the same form as eq. 15) if Qξ (k ) = 1−α [ P (k ) − q (k + 1) m T (k ) P (k )] . 17) The constant trace modification, where tr [ P (k + 1)] = tr [ P (k )] , can be obtained by appropriately choosing the matrix Qξ (k ) in eq. 15). 1. Parameter Estimation Qξ (k ) = tr [q(k + 1)m T (k ) P (k )] T tr [ P (k ) − q(k + 1)m (k ) P (k )] [ P (k ) − k (k + 1)m T (k ) P (k )] .

This assumption results in a suboptimal dual control scheme that is difficult to derive. The ρ-approximation, as in eq. 18), also coincides with the one for the OLF policy, eq. 12), if m = 0. The wide-sense dual (WSD) and the utility-costs (UC) control policies (BarShalom and Tse, 1976; Bayard and Eslami, 1985) are based on other approximations. The WSD control policy uses a linearization of the system equations around the nominal trajectory of the system where the OLF control policy is used. The utility costs approach (Bayard and Eslami, 1985), where various control policies may be used as a nominal trajectory of the systems for further linearization or other approximations, can be considered as a generalization of the WSD policy.

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