An invariant subspace method for large-scale algebraic Riccati equation

2010 ◽  
Vol 60 (11) ◽  
pp. 1067-1082 ◽  
Author(s):  
L. Amodei ◽  
J.-M. Buchot
Keyword(s):  
Invariant Subspace ◽  
Riccati Equation ◽  
Large Scale ◽  
Algebraic Riccati Equation ◽  
Subspace Method

Stability Analysis of Large-Scale Time-Delay Systems Via Evolutionary Programming Algorithm

1999 ◽  
Vol 123 (2) ◽  
pp. 293-296 ◽  
Author(s):  
Jun-Juh Yan ◽  
Jason Sheng-Hong Tsai and ◽  
Ing Eh Sheen
Keyword(s):  
Time Delay ◽  
Riccati Equation ◽  
Large Scale ◽  
Evolutionary Programming ◽  
System Stability ◽  
Algebraic Riccati Equation ◽  
Delay Systems ◽  
Programming Approach ◽  
Hamiltonian Matrix ◽  
Time Delay Systems

A sufficient condition for delay-independent asymptotic stability of large-scale time-delay systems is derived. An evolutionary programming approach is newly developed to decompose the system matrix such that our result can be further improved. For testing the system stability, we do not attempt to solve the Lyapunov or Riccati equation, but need only to check the eigenvalues of a Hamiltonian matrix to guarantee the solvability of an algebraic Riccati equation. The present method is simple and less conservative than those proposed in the literature.

scholarly journals Numerical Solution of SDRE Control Problem – Comparison of the Selected Methods

2020 ◽  
Vol 45 (2) ◽  
pp. 79-95
Author(s):  
Krzysztof Hałas ◽  
Eugeniusz Krysiak ◽  
Tomasz Hałas ◽  
Sławomir Stępień
Keyword(s):  
Control Systems ◽  
Riccati Equation ◽  
Computational Effort ◽  
Linear Control ◽  
Algebraic Riccati Equation ◽  
Linear Control Systems ◽  
Nonlinear Constraints ◽  
State Dependent ◽  
Suboptimal Solution ◽  
Problem Comparison

AbstractMethods for solving non-linear control systems are still being developed. For many industrial devices and systems, quick and accurate regulators are investigated and required. The most effective and promising for nonlinear systems control is a State-Dependent Riccati Equation method (SDRE). In SDRE, the problem consists of finding the suboptimal solution for a given objective function considering nonlinear constraints. For this purpose, SDRE methods need improvement.In this paper, various numerical methods for solving the SDRE problem, i.e. algebraic Riccati equation, are discussed and tested. The time of computation and computational effort is presented and compared considering selected nonlinear control plants.

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