ISSN:
1573-2878
Keywords:
Optimal control
;
descriptor systems
;
singular systems
;
discrete systems
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The present paper deals with the investigation of the linear quadratic optimal control problem for the discrete-time descriptor systemsEx k+1=Ax k +Bu k , whereE is in general a singular matrix and the system structure is in general noncausal. The problem is considered in its general form, having singular cost matrices and cross-weighting term in the cost functional. The key idea for the solution approach is the use of the Weierstrass theorem for regular pencils, combined with a suitable permutation transformation, to form a base for the image ofE. The optimization problem is solved by forcing causality to the Hamiltonian equations, which are produced by considering the entireN-stage process as a large system of linear equations. The feedback gain matrix is obtained as a manifold which is generated by the intersection of two other manifolds.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00962798
Permalink