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

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

It is a self-contained advent to algebraic regulate for nonlinear platforms appropriate for researchers and graduate scholars. it's the first publication facing the linear-algebraic method of nonlinear regulate platforms in this sort of distinctive and wide type. It presents a complementary method of the extra conventional differential geometry and bargains extra simply with numerous vital features of nonlinear platforms.

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It is already known that ∂ 2 y (k) /∂u(s) = 0 is a necessary condition for the existence of an affine realization of a given input-output system [28, 29, 158]. 21. 28) holds. 24 which is applied to each auxiliary output yij , considering all state variables in Xi−1 as parameters. 30). 25. 32) 38 2 Modeling for which k = 2 and s = 1, define x1 = y (k−s−1) = y Let y12 = y˙ − u sin y y11 = sin y, Then k21 = 0, k22 = 1. The relation y˙ 12 = −y12 u cos y implies that s22 = 0. 33) which is both observable and accessible and therefore it is minimal.

Dy (k−1) , du, . . , du(s) } H1 = spanK {dy, dy, Obviously, any one-form in H1 has to be differentiated at least once to depend explicitly on du(s+1) . Let H2 denote the subspace of E which consists of all one-forms that have to be differentiated at least twice to depend explicitly on du(s+1) . 15), one easily computes H2 = spanK {dy, dy, ˙ . . , dy (k−1) , du, . . 5 Input-output Equivalence and Realizations 29 More generally, define Hi as the subspace of E which consists of all oneforms that have to be differentiated at least i times to depend explicitly on du(s+1) .

N , j = 1, . . 23. 29) is mentioned in [28, 158]. 14) as well as the differential equations relating the auxiliary outputs are affine in the highest time derivative of the input. 22). 29) are satisfied. State variables are defined in the procedure of the algorithm. 30). 14). Necessity: To prove the necessity condition we need a lemma, which is partly contained in [28, 29, 158]. 24. , u0 ) 2 in some suitable open dense subset of IRk+s+1 , then ∂ 2 y (k) /∂u(s) = 0, dy11 ∈ spanK {dx}, and dy12 ∈ spanK {dx}.

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