scholarly journals An Improved Iterative Method for Solving the Discrete Algebraic Riccati Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Li Wang
Keyword(s):  
Optimal Control ◽  
Iterative Method ◽  
Control Systems ◽  
Riccati Equation ◽  
Newton Method ◽  
Iterative Algorithms ◽  
Networked Systems ◽  
Algebraic Riccati Equation ◽  
Numerical Example ◽  
Discrete Algebraic Riccati Equation

The discrete algebraic Riccati equation has wide applications, especially in networked systems and optimal control systems. In this paper, according to the damped Newton method, two iterative algorithms with a stepsize parameter is proposed to solve the discrete algebraic Riccati equation, one of which is an extension of Algorithm (4.1) in Dai and Bai (2011). A numerical example demonstrates the convergence effect of the presented algorithm.

scholarly journals Numerical Algorithms of the Discrete Coupled Algebraic Riccati Equation Arising in Optimal Control Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Li Wang
Keyword(s):  
Optimal Control ◽  
Robust Control ◽  
Control Systems ◽  
Riccati Equation ◽  
Numerical Algorithms ◽  
Iterative Algorithms ◽  
Iterative Solution ◽  
Algebraic Riccati Equation ◽  
Initial Value ◽  
Numerical Examples

The discrete coupled algebraic Riccati equation (DCARE) has wide applications in robust control, optimal control, and so on. In this paper, we present two iterative algorithms for solving the DCARE. The two iterative algorithms contain both the iterative solution in the last iterative step and the iterative solution in the current iterative step. And, for different initial value, the iterative sequences are increasing and bounded in one algorithm and decreasing and bounded in another. They are all monotonous and convergent. Numerical examples demonstrate the convergence effect of the presented algorithms.

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.

scholarly journals Inversion Free Algorithms for Computing the Principal Square Root of a Matrix

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Nicholas Assimakis ◽  
Maria Adam
Keyword(s):  
Riccati Equation ◽  
Newton Method ◽  
Continuous Time ◽  
Iterative Algorithms ◽  
Algebraic Method ◽  
Matrix Inversion ◽  
Square Root ◽  
Special Case ◽  
New Algorithms

New algorithms are presented about the principal square root of ann×nmatrixA. In particular, all the classical iterative algorithms require matrix inversion at every iteration. The proposed inversion free iterative algorithms are based on the Schulz iteration or the Bernoulli substitution as a special case of the continuous time Riccati equation. It is certified that the proposed algorithms are equivalent to the classical Newton method. An inversion free algebraic method, which is based on applying the Bernoulli substitution to a special case of the continuous time Riccati equation, is also proposed.

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