zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Backstepping design with local optimality matching. (English) Zbl 1007.93025

The authors study the nonlinear H -optimal control design for strict-feedback nonlinear systems with disturbance inputs:

x ˙ 1 =x 2 +f 1 (x 1 )+h 1 ' (x 1 )w,x ˙ 2 =x 3 +f 2 (x 1 ,x 2 )+h 2 ' (x 1 ,x 2 )w,x ˙ n =u+f n (x 1 ,,x n )+h n ' (x 1 ,,x n )u,

where x=(x 1 ,,x n ) is the state variable with x(0)=0; u is the scalar control input; w is the q-dimensional disturbance input generated by some adversary player according to w(t)=ν(t,x), where ν:[0,)× n p is piecewise continuous in t and locally Lipschitz in x. The authors construct globally stabilizing control laws to match the optimal control law up to any desired order and to be inverse optimal with respect to some computable cost functional. The recursive construction of a cost functional and the corresponding solution to the Hamilton-Jacobi-Isaacs equation employs a new concept of nonlinear Cholesky factorization. When the value function for the system has a nonlinear Cholesky factorization, the backstepping design procedure can be tuned to yield the optimal control law.

MSC:
93B36H -control
93D21Adaptive or robust stabilization
93C73Perturbations in control systems
93C10Nonlinear control systems