Download PDF by Giuseppe Conte, Claude H. Moog, Anna Maria Perdon: Algebraic Methods for Nonlinear Control Systems

By Giuseppe Conte, Claude H. Moog, Anna Maria Perdon

ISBN-10: 1846285941

ISBN-13: 9781846285943

ISBN-10: 184628595X

ISBN-13: 9781846285950

This can be a self-contained advent to algebraic keep an eye on for nonlinear platforms compatible for researchers and graduate scholars. it's the first publication facing the linear-algebraic method of nonlinear keep an eye on platforms in one of these specified and broad model. It presents a complementary method of the extra conventional differential geometry and offers extra simply with numerous vital features of nonlinear structures.

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Additional info for Algebraic Methods for Nonlinear Control Systems (Communications and Control Engineering)

Sample text

41) ⎟+⎜ ˙ ⎟ ⎜0 0 ⎟ ⎟ ⎜ 1/J dt ⎜ ⎜θ⎟ ⎜ ⎟ u2 ⎜ ⎟ ⎝ φ ⎠ ⎝ φ˙ 0 ⎠ ⎠ ⎝ 0 1 ˙ r ˙ φ ˙ − mr2 0 φ −2 r ˙ + mr2 dφ˙ + Jdθ). ˙ The latter is not accessible and H∞ is spanned by (2mrφdr 2 ˙ ˙ this one-form is exact and equals d(mr φ+J θ). This is the kinetic momentum of the hopping robot and is constant. Its minimal realization has not dimension 6. 42) Apply the procedure again, compute the new extended system Σe , whose dimension is 5 now, and check H∞ = . A minimal realization of the hopping robot (without gravity) thus has dimension 5.

Xn dx1 − dxn−1 } and more generally, for 2 ≤ k ≤ n − 1, Hk = spanK {x3 dx1 − dx2 , . . , xn−k+2 dx1 − dxn−k+1 } Hn−1 = spanK {x3 dx1 − dx2 } Hn = H∞ = 0 Thus, h1 = 2, h2 = 1, h3 = 1, . 9. ✟✟❆ ✟ ✟ ✛ ❆ ✟ ✟✟ ✟ ❆✟ ✟ ❆ ❆ ✉✟ ✟ ❆ ❆ ✻ ✂✂ ✙ ❆ ψ ❆ ✟ ✟ ✂ ❆ ✟ ❆ ✂ ✟✟ ❆✟ ✂ r ✂ ✂ ✂✂ ❍ ✂ ✂ ✂ ✂ ✂ ✂ ✂❍ ✂ ❍✂ ✂ ③ ✂ m ✟ ✟ ✥ θ Fig. 3. 19) is not accessible, because, as remarked previously, H∞ is spanned by (2mx1 x6 dx1 + mx21 dx6 + Jdx4 ). The kinetic momentum mx21 x6 + Jx4 of the hopping robot is constant and it represents a noncontrollable component of the state.

If ∀ ≥ r1j , dy1j ∈ X2 , set s1j = −1, for j = 1, 2. ( ) If ∃ ≥ r1j , dy1j ∈ X2 , then define s1j ≥ 0 as the smallest integer such that, abusing the notation, one has locally (r y1j1j +s1j ) (r = y1j1j +s1j ) (σ ) (σ ) (y (λ) , y1111 , y1212 , u, . . , u(s1j ) ) where 0 ≤ λ < r, 0 ≤ σ11 < r11 + s11 , 0 ≤ σ12 < r12 + s12 . 2 (r +s ) • If s11 ≥ 0 and ∂ 2 y1111 11 /∂(u(s11 ) ) = 0 2 (r +s ) or if s12 ≥ 0 and ∂ 2 y1212 12 /∂(u(s12 ) ) = 0 stop! 2 (r +s ) • If X2 + U = Y + U, and ∂ 2 y1j1j 1j /∂(u(s1j ) ) = 0 whenever s1j ≥ 0, then the algorithm stops and the realization is complete.

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Algebraic Methods for Nonlinear Control Systems (Communications and Control Engineering) by Giuseppe Conte, Claude H. Moog, Anna Maria Perdon


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