Nonlinear and Adaptive Control of Complex Systems by Alexander L. Fradkov, Iliya V. Miroshnik, Vladimir O.

By Alexander L. Fradkov, Iliya V. Miroshnik, Vladimir O. Nikiforov (auth.)

This quantity offers a theoretical framework and keep an eye on method for a category of advanced dynamical structures characterized by means of excessive country area size, a number of inputs and outputs, major nonlinearity, parametric uncertainty, and unmodeled dynamics. a distinct function of the authors' technique is the combo of rigorous innovations and strategies of nonlinear keep watch over (invariant and attracting submanifolds, Lyapunov services, targeted linearisation, passification) with approximate decomposition effects in line with singular perturbations and decentralisation. a few effects released formerly within the Russian literature and never popular within the West are dropped at gentle. simple thoughts of recent nonlinear keep watch over and motivating examples are given.
Audience: This ebook could be helpful for researchers, engineers, college academics and postgraduate scholars specialising within the fields of utilized arithmetic and engineering, comparable to computerized keep watch over, robotics, and regulate of vibrations.

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Example text

15) An important particular type of the penalty function has the view Q = (y - Yr)2 , where Yr is the rejerence output prescribing the desired behavior of the regulated variable y . 15) [or atu) () E ne. Unlike the introduced control problem, classical control theory is based on the assumption that () is exactly known a priori. In this case one can use the controllaw explicitly depending on () u = U(y,() ,t). , when we deal with an unecrtain plant), the posed design problem could be solved in two steps.

Usually, such cases are causeel by nonuniformity of the syst em performance in the vicinity of x", Wh en the system behavior does not qualitatively el epend on the Initial condition Xo (anel to for time-var ying syst ems) the corresponding st a bility property is uniform. 3) . 6. 13) t -+CX) is achi eved un iformly untli respeci to Xo E [O( x*) To verify the latter property and , mo reov er , estimate th e syst em performance in the neighborhooel of z ", on e can use a majorizing inequality introdu ced in the following definition .

In the case n = u the function

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