Posted on

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

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

This can be a self-contained advent to algebraic keep watch over for nonlinear platforms appropriate for researchers and graduate scholars. it's the first publication facing the linear-algebraic method of nonlinear regulate platforms in the sort of special and broad type. It offers a complementary method of the extra conventional differential geometry and offers extra simply with numerous very important features of nonlinear structures.

Similar system theory books

Control Theory and Systems Biology

A survey of the way engineering innovations from keep an eye on and structures thought can be utilized to assist biologists comprehend the habit of mobile platforms.

Nonlinear Dynamics in Complex Systems: Theory and Applications for the Life-, Neuro- and Natural Sciences

With many parts of technological know-how achieving throughout their obstacles and turning into an increasing number of interdisciplinary, scholars and researchers in those fields are faced with suggestions and instruments no longer coated via their specific schooling. in particular within the lifestyles- and neurosciences quantitative versions in accordance with nonlinear dynamics and intricate structures have gotten as often applied as conventional statistical research.

Chaotic Logic: Language, Thought, and Reality from the Perspective of Complex Systems Science

This publication summarizes a community of interrelated rules which i've got constructed, on and off, over the last 8 or ten years. The underlying topic is the mental interaction of order and chaos. Or, to place it differently, the interaction of deduction and induction. i'm going to attempt to clarify the connection among logical, orderly, awake, rule-following cause and fluid, self­ organizing, habit-governed, subconscious, chaos-infused instinct.

Extra resources for Algebraic Methods for Nonlinear Control Systems (Communications and Control Engineering)

Sample text

Of the lowest order. We introduce deﬁnitions of reduced diﬀerential form, reduced input-output system and irreducible diﬀerential form, etc. to reach that goal. 9 (Reduced diﬀerential form). 14) if (a) dφ ≡ 0 (b) dφ ∈ H∞ . 10 (Reduced input-output system). 17) 2 such that ∂φ /∂y (k ) = 0, ∂φ /∂u(s ) = 0, and ∂ 2 φ /∂y (k ) ≡ 0 with k > 0, s ≥ 0. 14). 11 (Irreducible diﬀerential form). 14). 8 cont’d). d(y−u) ˙ ∈ H∞ and y˙ = u is an irreducible system. Thus, φ = y˙ − u = 0 is an irreducible input-output system of y¨ = u˙ + (y˙ − u)2 .

Y1 .. (sj ) = hj j (φ(y1 , . . , y1 1 , yj , . . , yj j ), u, . . , u(γ) ) .. (s ) (s −1) (s −1) = hp p (φ(y1 , . . , y1 1 , . . , yp , . . , yp p ), u, . . , u(γ) ) y1 yj (sp ) yp (s ) (s1 −1) (s ) 25 ), u, . . 6) are not uniquely deﬁned since, for instance, if K is less than n, diﬀerent choices of the functions gi (x, u, . . 3). Instead of {s1 , . . , sp }, it is possible to use the observability indices as deﬁned in Chapter 4 to derive an analogous input-output equation. 2. For the system ⎧ x˙ 1 ⎪ ⎪ ⎪ ⎪ ⎨ x˙ 2 x˙ 3 ⎪ ⎪ y1 ⎪ ⎪ ⎩ y2 = = = = = x3 u1 u1 u2 x1 x2 we have y˙ 1 = x3 u1 , y¨1 = u2 u1 + x3 u˙ 1 , and ﬁnally y¨1 = u2 u1 + (y˙ 1 /u1 )u˙ 1 The last equation holds at every point in which u1 = 0.

U(s) ) .. ˙ . . , u(s) ) xk = ξk (y, y, xk+1 = u .. 23) xk+s+1 = u(s) k From Hs+2 ⊂ Hs+1 , it follows dξ˙i = j=1 αdξ + βdu, for each j = 1, . . , k. Let x = (x1 , . . , xk ). 24) The assumption k > s indicates that the output y depends only on x. 14). Since the state-space system is proper, necessarily k > s. H1 = spanK {dx, du, . . , du(s) } .. 23), the spaces Hi are integrable as expected. 17. Let y¨ = u˙ 2 , and compute ˙ du, du} ˙ H1 = spanK {dy, dy, H2 = spanK {dy, dy, ˙ du} H3 = spanK {dy, dy˙ − 2udu)} ˙ Since H3 is not integrable, there does not exist any state-space system generating y¨ = u˙ 2 .