# 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)
Receding horizon revisited: An easy way to robustly stabilize and LTV system. (English) Zbl 0751.93059
Summary: Stabilization schemes are often based on infinite horizon optimization of a non-singular cost functional. For such schemes to make sense in a time varying context, a fairly good knowledge of the system parameters at all times is a prerequisite. That is a major disadvantage in adaptive implementations. When applicable, the receding horizon approach overcomes this difficulty as, though it relies on general qualitative long-term properties (such as controllability), it requires quantitative knowledge only of (temporally) local parameter values. Work done on receding horizon stabilization during the 1970’s focused on LQ (=‘${H}_{2}$’) optimization criteria. Looking for a stabilization method which carriers also the robustness properties of infinite horizon ${H}_{\infty }$ design, we consider here local minimization of the ${L}_{2}$-induced I/O norm (=‘${H}_{\infty }$ optimization’) as the design objective. Both state and observation based feedback scheme are derived, and relations to finite and infinite horizon optimization are discussed.
##### MSC:
 93C99 Control systems, guided systems 93C35 Multivariable systems, multidimensional control systems
time-dependent