Unified Approach for Closed-Loop Optimal Control

2007 ◽  
Author(s):  
Yoshiko Imura ◽  
D. Subbaram Naidu
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Unified Approach

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Unified approach for open-loop optimal control

2007 ◽  
Vol 28 (2) ◽  
pp. 59-75 ◽  
Author(s):  
Y. Imura ◽  
D. S. Naidu
Keyword(s):  
Optimal Control ◽  
Open Loop ◽  
Unified Approach

Discrete Time-Delay Optimal Control Method for Experimental Active Chatter Suppression and Its Closed-Loop Stability Analysis

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Xingwu Zhang ◽  
Ziyu Yin ◽  
Jiawei Gao ◽  
Jinxin Liu ◽  
Robert X. Gao ◽  
...  
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Control Method ◽  
Trial And Error ◽  
Stability Lobe Diagram ◽  
Weighting Matrix ◽  
Chatter Suppression ◽  
Stability Lobe ◽  
Optimal Control Method ◽  
Discrete Time Delay

Chatter is a self-excited and unstable vibration phenomenon during machining operations, which affects the workpiece surface quality and the production efficiency. Active chatter control has been intensively studied to mitigate chatter and expand the boundary of machining stability. This paper presents a discrete time-delay optimal control method for chatter suppression. A dynamical model incorporating the time-periodic and time-delayed characteristic of active chatter suppression during the milling process is first formulated. Next, the milling system is represented as a discrete linear time-invariant (LTI) system with state-space description through averaging and discretization. An optimal control strategy is then formulated to stabilize unstable cutting states, where the balanced realization method is applied to determine the weighting matrix without trial and error. Finally, a closed-loop stability lobe diagram (CLSLD) is proposed to evaluate the performance of the designed controller based on the proposed method. The CLSLD can provide the stability lobe diagram with control and evaluate the performance and robustness of the controller cross the tested spindle speeds. Through many numerical simulations and experimental studies, it demonstrates that the proposed control method can make the unstable cutting parameters stable with control on, reduce the control force to 21% of traditional weighting matrix selection method by trial and error in simulation, and reduce the amplitude of chatter frequency up to 78.6% in experiment. Hence, the designed controller reduces the performance requirements of actuators during active chatter suppression.

Adaptive Tuning Functions Tracking Control with Nonlinear Adaptive Observers

2014 ◽  
Vol 11 (2) ◽  
pp. 14-21
Author(s):  
R. Mishkov ◽  
V. Petrov
Keyword(s):  
Tracking Control ◽  
Closed Loop ◽  
Adaptive System ◽  
Permanent Magnet Synchronous Motor ◽  
Unified Approach ◽  
Closed Loop System ◽  
Estimation Errors ◽  
Nonlinear Adaptive Control ◽  
Performance Specifications ◽  
System Time

Abstract The paper is dedicated to the derivation of a unified approach for nonlinear adaptive closed loop system design with nonlinear adaptive state and parameter observers combined with tuning functions-based nonlinear adaptive control for trajectory tracking. The proposed approach guarantees asymptotic stability of the closed loop nonlinear adaptive system with respect to the tracking and state estimation errors and Lyapunov stability of the parameter estimator. The advantages of the approach are the lack of over-parametrization, resulting in a minimal number of estimator equations and the preservation of the overdamped performance specifications of the closed loop nonlinear adaptive system in its whole range of operation. The application of the approach to a permanent magnet synchronous motor driven inverted pendulum concludes with simulation of the closed loop nonlinear adaptive system time responses.

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