scholarly journals An Interaction Coordination Algorithm with Modified Performance Index for Optimal Control of Coupled Nonlinear Systems

1977 ◽  
Vol 13 (5) ◽  
pp. 463-469
Author(s):  
Takeo OJIKA ◽  
Yoshikazu NISHIKAWA ◽  
Hiroaki SHIMAZUTSU ◽  
Masashi OKUDAIRA
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Performance Index

scholarly journals A nonlinear plate control without linearization

2017 ◽  
Vol 15 (1) ◽  
pp. 179-186
Author(s):  
Kenan Yildirim ◽  
Ismail Kucuk
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Control Problem ◽  
Performance Index ◽  
Control Function ◽  
Initial Boundary ◽  
Quadratic Functional ◽  
Penalty Term ◽  
Nonlinear Plate ◽  
Optimal Control Function

Abstract In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

scholarly journals Adaptive Optimal Robust Control for Uncertain Nonlinear Systems Using Neural Network Approximation in Policy Iteration

2021 ◽  
Vol 11 (5) ◽  
pp. 2312
Author(s):  
Dengguo Xu ◽  
Qinglin Wang ◽  
Yuan Li
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Robust Control ◽  
Nonlinear Systems ◽  
Policy Iteration ◽  
Control Law ◽  
Globally Asymptotically Stable ◽  
Control Approach ◽  
Input Uncertainties ◽  
Theoretical Results

In this study, based on the policy iteration (PI) in reinforcement learning (RL), an optimal adaptive control approach is established to solve robust control problems of nonlinear systems with internal and input uncertainties. First, the robust control is converted into solving an optimal control containing a nominal or auxiliary system with a predefined performance index. It is demonstrated that the optimal control law enables the considered system globally asymptotically stable for all admissible uncertainties. Second, based on the Bellman optimality principle, the online PI algorithms are proposed to calculate robust controllers for the matched and the mismatched uncertain systems. The approximate structure of the robust control law is obtained by approximating the optimal cost function with neural network in PI algorithms. Finally, in order to illustrate the availability of the proposed algorithm and theoretical results, some numerical examples are provided.

A novel actor–critic–identifier architecture for approximate optimal control of uncertain nonlinear systems

Automatica ◽  
2013 ◽  
Vol 49 (1) ◽  
pp. 82-92 ◽  
Author(s):  
S. Bhasin ◽  
R. Kamalapurkar ◽  
M. Johnson ◽  
K.G. Vamvoudakis ◽  
F.L. Lewis ◽  
...  
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Uncertain Nonlinear Systems
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