Adaptive dual control: theory and applications by Nikolai Michailovich Filatov, Heinz Unbehauen

By Nikolai Michailovich Filatov, Heinz Unbehauen

This monograph demonstrates how the functionality of varied recognized adaptive controllers will be more desirable considerably utilizing the twin influence. The variations to include twin keep an eye on are learned individually and independently of the most adaptive controller with out complicating the algorithms. a brand new bicriterial method for twin keep an eye on is constructed and utilized to numerous varieties of renowned linear and nonlinear adaptive controllers. useful functions of the designed controllers to numerous real-time difficulties are awarded. This monograph is the 1st publication offering an entire exposition at the twin keep watch over challenge from the inception within the early Nineteen Sixties to the current cutting-edge aiming at scholars and researchers in adaptive keep watch over in addition to layout engineers in undefined.

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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.

Differentiation of the eq. 28) gives the condition for the minimum as ∂J kc = 2[bˆ12 (k ) + pb1 (k )]u (k ) − 2bˆ1 (k ) w(k + 1) ∂ u (k ) + 2( pˆ 0T (k )bˆ1 (k ) + pbT p (k ))m 0 (k ) 1 0 +2ru (k ) + 2ru (k − 1) = 0 . Thus the minimization of eq. 28) gives the cautious control action as uc (k ) = bˆ1 (k ) w(k + 1) − [bˆ1 (k ) pˆ 0T (k ) + pbT p (k )] m0 (k ) + ru (k − 1) 1 0 bˆ12 (k ) + pb1 (k ) + r . 30) Minimization of eq. 22), with constraints according to eq. 31) see also eqs. 21). After substituting of eq.

31) see also eqs. 21). After substituting of eq. 2) into eq. 20) and taking the expectation (compare Appendix D) using eqs. 32) 40 4. BICRITERIAL SYNTHESIS METHOD FOR DUAL CONTROLLERS J ka (u c (k ) − θ (k )) − J ka (uc (k ) + θ (k )) = − pb1 (k )[u c (k ) − θ (k )]2 − 2 pbT p (k )m 0 (k )(uc (k ) − θ (k )) 1 0 + pb1 (k )[uc (k ) + θ (k )] 2 + 2 pbT p 1 0 (k )m 0 (k )(u c (k ) + θ (k )) = 4 pb1 (k )θ (k )uc (k ) + 4 pbT p (k )m 0 (k )θ (k ) . 33) Substituting eq. 31) provides the adaptive dual control law u (k ) = uc (k ) + θ (k )sgn [ pb1 (k )uc (k ) + pbT p (k )m 0 (k )] .

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