Nonlinear and adaptive control : tools and algorithms for by Alessandro Astolfi

By Alessandro Astolfi

This ebook summarizes the most effects accomplished in a four-year eu undertaking on nonlinear and adaptive keep watch over. The venture includes prime researchers from top-notch associations: Imperial university London (Prof A Astolfi), Lund college (Prof A Rantzer), Supelec Paris (Prof R Ortega), collage of expertise of Compiegne (Prof R Lozano), Grenoble Polytechnic (Prof C Canudas de Wit), collage of Twente (Prof A van der Schaft), Politecnico of Milan (Prof S Bittanti), and Polytechnic collage of Valencia (Prof P Albertos). The e-book additionally offers an advent to theoretical advances in nonlinear and adaptive keep watch over and an outline of novel functions of complex regulate conception, fairly issues at the keep an eye on of in part identified structures, under-actuated platforms, and bioreactors.

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Anderson. A system theory criterion for positive real matrices. SZAM J . Control, 5(2):171-182, 1967. 4. I. Bar-Kana. Parallel feedforward and simplified adaptive control. Int. J . Adaptive Control and Signal Processing, 1:95-109, 1987. 5. I. Byrnes, A. C. Willems. Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems. IEEE Trans. Automatic Control, 36( 11):1228-1240, 1991. 6. J. Collado, R. Lozano, and R. Johansson. On Kalman-Yakubovich-Popov Lemma for stabilizable systems.

2. Asymptotic stabilirability by control of constant sign In this section we present a general result on the asymptotic stabilizability of linear stable systems with bounded control of constant sign, that is a consequence of Proposition 2 or Corollary 2. 63) with A such that det(A) # 0, i s asymptotically stabilizable by positive (or negative) control. Proof: Note first that because det(A) # 0, the matrix A has no zero eigenvalue. 64) 5 0, d e t ( J ) # 0. e. F is Hurwitz. 65) for all E > 0 and for some appropriately chosen' K E I R l X P .

Kulaoru and A . Astolfi 46 Using [28] and [4] it is easy to show that a linear system is asymptotically controllable with positive (or negative) bounded control if and only if spec(A) c C - U { C o \ (0)). 6 . 3 . Asymptotic stabilization of the T O R A In this section we apply the results of Section 4 to solve the asymptotic stabilization problem for the TORA [3]. 66) where xd is the translational position, 'ud = i d the translational velocity, 4 the angular position, w = the angular velocity and 0 < y < 1 a constant depending on the physical parameters of the device.

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