An improved algorithm for the solution of discrete regulation problems
- 1 October 1967
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 12 (5) , 522-528
- https://doi.org/10.1109/tac.1967.1098716
Abstract
This paper describes an improved algorithm for obtaining the steady-state feedback-gain matrix from the discrete matrix Riccati equation. This is of importance in the steady-state optimization of discrete linear systems with quadratic performance criteria. The solution of the Riccati equation by the natural iteration technique suggested by its dynamic programming derivation requires, in general,n(3n^{2}+3r^{2}+3nr+n+2r)/2+r^{2}(r+1)/2multiplications per step, wherenis the order of the system and r is the number of inputs. The improved algorithm requires onlyr(n^{2}+2nr+n)/2+r^{2}(r+1)/2multiplications per step, may converge in fewer iterations, and requires less storage. For the special caseR = 0(no weight on control effort), the number of multiplications can be reduced further tor(n-r)(n+r+1)/2+r^{2}(r+1)/2per iteration. The simplifications described above are accomplished in two ways. First, the characteristics of recently published canonical forms for controllable systems are exploited to reduce the number of free parameters appearing in the system matrices. Second, the concept of feedback-gain equivalence of performance criteria is used to derive a simply computed canonical form for the weighting matrix.Keywords
This publication has 1 reference indexed in Scilit:
- Observers for multivariable systemsIEEE Transactions on Automatic Control, 1966