Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0999.93018
Bemporad, Alberto; Morari, Manfred; Dua, Vivek; Pistikopoulos, Efstratios N.
The explicit linear quadratic regulator for constrained systems. (English)
[J] Automatica 38, No.1, 3-20 (2002). ISSN 0005-1098

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.
[Ingmar Randvee (Tallinn)]

MSC 2000:: *93B40 Computational methods in systems theory
93B51 Design techniques in systems theory
93C55 Discrete-time control systems
49N10 Linear-quadratic optimal control problems
65Y20 Complexity and performance of numerical algorithms

Keywords: on-line computation; model predictive control; discrete-time linear quadratic control; state and input constraints; quadratic program

Cited in: Zbl 1145.93345

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]