By Gang Tao

ISBN-10: 0471274526

ISBN-13: 9780471274520

Perceiving a necessity for a scientific and unified figuring out of adaptive regulate conception, electric engineer Tao offers and analyzes universal layout techniques with the purpose of masking the basics and state-of-the-art of the sector. Chapters hide structures concept, adaptive parameter estimation, adaptive kingdom suggestions keep watch over, continuous-time version reference adaptive keep watch over, discrete-time version reference adaptive keep an eye on, oblique adaptive keep watch over, multivariable adaptive keep an eye on, and adaptive regulate of platforms with nonlinearities.

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29). 23). 23). 23). 19). (d) It is clear that + + + II8(t) - e^(t - k ) l p + = II&t) - &t - 1) &t - 1) - &t - 2) Then, using the Schwarz inequality, Sec. 3 . . &t Equation Error Methods for Deterministic Systems -k + 1) - &t - k)llz 53 - 8(t - k)ll2 + + + I k(llJ(t) - 8(t - I)[[' . - . 26) since k is finite. 27). 2 is a slightly modified version of a result that was first given in Goodwin, Ramadge, and Gaines (1978a) in the context of discrete-time adaptive control. We pause to discuss briefly the implications of the properties described in the lemma.

Strict sequential observability implies strong uniform observability. The converse is true for n = 1 and 2 but may not be true for n 2 3. Proof. It can be readily verified that det M = constant for a system in the second standard form. A counterexample to the converse for n = 3 has been given in Funahashi (1979). VTV We now turn to the relationship between observable bilinear state-space models and input-output models. 4 that in the linear 38 Models for Deterministic Dynamical Systems Chap. 2 case, there is a one-to-one relationship between observable state-space models and left difference operator representations, (or equivalently, DARMA input-output models).

5. 6. 2. 7. Determine the two-sided z-transform of the following sequence and specify the region of convergence. {Zk ak= for k 2 0 for k < 0. 8. 9. Show that if U(z) is unimodular, and is partitioned as [ U1 dz)] Ul l(Z) UZl(Z> UZZW then Uz,(z) and Uzz(z) are left coprime. 10. Consider a simple system with disturbances as in Fig. 14) to express the model in observer form. 2 to show that the corresponding DARMA model has the form y(t) = y(r - 1) + u(t - 1) - u(t - 2); t 20 with corresponding left difference operator representation (q2 - qlY(r) = (q - I)u(t); Chap.

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