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 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 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 Refined Upper Solution Bound of the Continuous Coupled Algebraic Riccati Equation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Li Wang
Keyword(s):  
Riccati Equation ◽  
Positive Semidefinite ◽  
Algebraic Riccati Equation ◽  
Positive Semidefinite Matrix ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Upper Solution ◽  
Solution Bound ◽  
Semidefinite Matrix ◽  
Two Parameter

The continuous coupled algebraic Riccati equation (CCARE) has wide applications in control theory and linear systems. In this paper, by a constructed positive semidefinite matrix, matrix inequalities, and matrix eigenvalue inequalities, we propose a new two-parameter-type upper solution bound of the CCARE. Next, we present an iterative algorithm for finding the tighter upper solution bound of CCARE, prove its boundedness, and analyse its monotonicity and convergence. Finally, corresponding numerical examples are given to illustrate the superiority and effectiveness of the derived results.

scholarly journals Time-optimality by distance-optimality for parabolic control systems

2020 ◽  
Vol 54 (1) ◽  
pp. 79-103
Author(s):  
Lucas Bonifacius ◽  
Karl Kunisch
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Optimal Control Problems ◽  
Time Optimal Control ◽  
Control Problems ◽  
Numerical Examples ◽  
Algorithmic Solution ◽  
Time Optimal ◽  
Time Optimality

The equivalence of time-optimal and distance-optimal control problems is shown for a class of parabolic control systems. Based on this equivalence, an approach for the efficient algorithmic solution of time-optimal control problems is investigated. Numerical examples are provided to illustrate that the approach works well in practice.

Nonlinear robust control of high-speed supercavitating vehicle in the vertical plane

2019 ◽  
Vol 234 (2) ◽  
pp. 510-519
Author(s):  
Bui Duc Hong Phuc ◽  
Sang-Do Lee ◽  
Sam-Sang You ◽  
Natwar Singh Rathore
Keyword(s):  
Robust Control ◽  
Riccati Equation ◽  
High Speed ◽  
Vertical Plane ◽  
Algebraic Riccati Equation ◽  
Control Synthesis ◽  
External Disturbances ◽  
Nonlinear Robust Control ◽  
Supercavitating Vehicle ◽  
Nonlinear Robust

The supercavitating vehicle can quickly become unstable under the influence of the planing force and external disturbances due to waves and currents. The planing force demonstrates nonlinear characteristics which can be described by the vehicle state variables. Strict standards for maneuvering strategy are required for high-speed vehicles to operate, particularly guidance, navigation, and control of underwater maneuver. In reality, the high-speed supercavitating vehicle dynamics present various control issues and challenges. This article proposes the nonlinear robust control synthesis to manipulate the vertical plane of the high-speed supercavitating vehicle against the planing force or parameter variations as well as external disturbances. The control synthesis is implemented by solving an algebraic Riccati equation at each iteration of the control algorithm with the updated system states, which is a so-called state-dependent Riccati equation. The control loops in the dive-plane satisfy an [Formula: see text] performance criterion that can reject external disturbances with perturbations. Simulation results show that the controlled vehicle system guarantees fast transient responses with steady-state performance. Besides, the proposed controller can eliminate up to 62% of disturbances and provides the robust performance against large planing force and parametric uncertainties. This new vehicle technology with active controller offers the potential strategy of higher speed and higher maneuverability solutions for various purposes of underwater maneuvering.

Sign in / Sign up

Export Citation Format

Share Document