Author:
Vasile Sima
Affiliation:
National Institute for Research & Development in Informatics, Romania
Keyword(s):
Algebraic Riccati Equation, Numerical Methods, Optimal Control, Optimal Estimation.
Related
Ontology
Subjects/Areas/Topics:
Engineering Applications
;
Informatics in Control, Automation and Robotics
;
Intelligent Control Systems and Optimization
;
Optimization Algorithms
;
Robotics and Automation
;
Signal Processing, Sensors, Systems Modeling and Control
Abstract:
Improved algorithms for solving continuous-time algebraic Riccati equations using Newton’s method with or
without line search are discussed. The basic theory and Newton’s algorithms are briefly presented. Algorithmic
details the developed solvers are based on, the main computational steps (finding the Newton direction,
finding the Newton step size), and convergence tests are described. The main results of an extensive performance
investigation of the solvers based on Newton’s method are compared with those obtained using the
widely-used MATLAB solver. Randomly generated systems with orders till 2000, as well as the systems from
a large collection of examples, are considered. The numerical results often show significantly improved accuracy,
measured in terms of normalized and relative residuals, and greater efficiency than the MATLAB solver.
The results strongly recommend the use of such algorithms, especially for improving the solutions computed
by other solvers.