zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
The explicit linear quadratic regulator for constrained systems. (English) Zbl 0999.93018
A technique to compute the explicit state-feedback solution of a discrete-time linear quadratic control problem subject to state and input constraints is presented. First the quadratic program (QP), which must be solved to determine the optimal control action, is derived. The original QP is viewed as a multi-parametric QP (mp-QP). The properties of an mp-QP are analysed, and an efficient algorithm to solve it is developed. It is shown that the closed form solution is piecewise affine and continuous for both the finite horizon problem (model predictive control, MPC) and the usual infinite time measure (constrained linear quadratic regulation). The controller can be implemented with substantially reduced on-line calculations preserving all performance and stability properties of MPC. The special on-line QP solvers are no longer required, only the evaluation of an explicitly defined piecewise linear function must be performed on-line. The proposed technique is attractive for a wide range of practical problems in which the computational complexity of on-line optimization is prohibitive.

93B40Computational methods in systems theory
93B51Design techniques in systems theory
93C55Discrete-time control systems
49N10Linear-quadratic optimal control problems
65Y20Complexity and performance of numerical algorithms