scholarly journals A periodic linear–quadratic controller for suppressing rotor-blade vibration

2019 ◽  
Vol 25 (17) ◽  
pp. 2351-2364 ◽  
Author(s):  
J. F. Camino ◽  
I. F. Santos
Keyword(s):  
Rotor Blade ◽  
Linear Time ◽  
Linear Quadratic Regulator ◽  
Time Varying ◽  
Linear Quadratic ◽  
Blade Vibration ◽  
Linear Quadratic Optimal Control ◽  
Riccati Differential Equation ◽  
Periodic Linear ◽  
Lqr Problem

This paper presents an active control strategy, based on a time-varying linear–quadratic optimal control problem, to attenuate the tip vibration of a two-dimensional coupled rotor-blade system whose dynamics is periodic. First, a periodic full-state feedback controller based on the linear–quadratic regulator (LQR) problem is designed. If all the states are not available for feedback, then an optimal periodic time-varying estimator, using the Kalman–Bucy filter, is computed. Both the Kalman filter gain and the LQR gain are obtained as the solution of a periodic Riccati differential equation (PRDE). Together, these gains provide the observer-based linear–quadratic–Gaussian (LQG) controller. An algorithm to solve the PRDE is also presented. Both controller designs ensure closed-loop stability and performance for the linear time-varying rotor-blade equation of motion. Numerical simulations show that the LQR and the LQG controllers are able to significantly attenuate the rotor-blade tip vibration.

Control of a Linear Time-Varying System With a Forward Riccati Formulation in Wavelet Domain

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Biswajit Basu ◽  
Andrea Staino
Keyword(s):  
Linear Time ◽  
Control Strategies ◽  
Linear Quadratic Regulator ◽  
Time Varying ◽  
Wavelet Domain ◽  
Nonlinear Controller ◽  
Linear Quadratic ◽  
Time Frequency ◽  
Future System ◽  
Control Feedback

A wavelet domain forward differential Ricatti formulation is proposed in this paper for control of linear time-varying (LTV) systems. The control feedback gains derived are time-frequency dependent, and they can be appropriately tuned for each wavelet scale or frequency band. The gains in the proposed forward formulation are functions of the present and past states and hence lead to a nonlinear controller. This nonlinear controller does not require information or approximation about future system matrices. The proposed controller is suitable for systems with time-varying (TV) system matrices and also for controlling transient dynamics. The performance of the proposed controller is compared with two other control strategies, namely, a TV linear quadratic regulator (LQR) based on a backward formulation of the differential Ricatti equation (DRE) and a multiscale wavelet-LQR controller based on asymptotic assumptions. Two numerical examples demonstrate promising results on the performance of the controller.

scholarly journals Convergence results for an averaged LQR problem with applications to reinforcement learning

2021 ◽  
Author(s):  
Andrea Pesare ◽  
Michele Palladino ◽  
Maurizio Falcone
Keyword(s):  
Optimal Control ◽  
Reinforcement Learning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Current System ◽  
Numerical Test ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Lqr Problem ◽  
Quadratic Optimal Control

AbstractIn this paper, we will deal with a linear quadratic optimal control problem with unknown dynamics. As a modeling assumption, we will suppose that the knowledge that an agent has on the current system is represented by a probability distribution $$\pi $$ π on the space of matrices. Furthermore, we will assume that such a probability measure is opportunely updated to take into account the increased experience that the agent obtains while exploring the environment, approximating with increasing accuracy the underlying dynamics. Under these assumptions, we will show that the optimal control obtained by solving the “average” linear quadratic optimal control problem with respect to a certain $$\pi $$ π converges to the optimal control driven related to the linear quadratic optimal control problem governed by the actual, underlying dynamics. This approach is closely related to model-based reinforcement learning algorithms where prior and posterior probability distributions describing the knowledge on the uncertain system are recursively updated. In the last section, we will show a numerical test that confirms the theoretical results.

Existence of Solutions of Riccati Differential Equations

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Sinan Kilicaslan ◽  
Stephen P. Banks
Keyword(s):  
Differential Equation ◽  
Nonlinear Systems ◽  
Existence Of Solutions ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Time Varying ◽  
Riccati Differential Equation ◽  
Riccati Differential Equations ◽  
Time Varying Systems

A necessary condition for the existence of the solution of the Riccati differential equation for both linear, time varying systems and nonlinear systems is introduced. First, a necessary condition for the existence of the solution of the Riccati differential equation for linear, time varying systems is proposed. Then, the sufficient conditions to satisfy the necessary condition are given. After that, the existence of the solution of the Riccati differential equation is generalized for nonlinear systems.

Design of a stabilizing controller for a ten-degree-of-freedom bipedal robot using linear quadratic regulator theory

2001 ◽  
Vol 215 (1) ◽  
pp. 27-43
Author(s):  
D Akdas ◽  
G A Medrano-Cerda
Keyword(s):  
Control System ◽  
Linear Quadratic Regulator ◽  
Biped Robot ◽  
Degree Of Freedom ◽  
Linear Quadratic ◽  
External Disturbances ◽  
Linear Quadratic Optimal Control ◽  
Stabilizing Controller ◽  
Double Support ◽  
Stabilizing Controllers

This paper considers the design and evaluation of stabilizing controllers for a ten-degree-of-freedom (10 DOF) biped robot using linear quadratic optimal control techniques and reduced-order observers. The controllers are designed using approximate planar dynamical models for the sagittal and lateral planes. Experiments were carried out to test the control system when the biped robot was in the double-support phase and the robot was subject to external disturbances. Although the control system is based on single-support models, the experimental results have shown that the robot successfully kept its given posture under disturbances.

scholarly journals Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systems

2010 ◽  
Vol 20 (4) ◽  
pp. 655-664 ◽  
Author(s):  
Keyword(s):  
Semidefinite Programming ◽  
Linear Quadratic Regulator ◽  
Descriptor Systems ◽  
Programming Approach ◽  
State Control ◽  
Linear Quadratic ◽  
Control Pair ◽  
Elegant Method ◽  
Lqr Problem ◽  
Primal Dual

Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systemsThis paper deals with the Linear Quadratic Regulator (LQR) problem subject to descriptor systems for which the semidefinite programming approach is used as a solution. We propose a new sufficient condition in terms of primal dual semidefinite programming for the existence of the optimal state-control pair of the problem considered. The results show that semidefinite programming is an elegant method to solve the problem under consideration. Numerical examples are given to illustrate the results.

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