PID Parameters Tuning for the Control of Nonlinear Systems Using Measure Theory

2011 ◽  
Vol 110-116 ◽  
pp. 4389-4397
Author(s):  
Assef Zare ◽  
A.V. Kamyad
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Pid Controller ◽  
Measure Theory ◽  
Infinite Horizon ◽  
Finite Horizon ◽  
Step Response ◽  
Control Law ◽  
Time Interval ◽  
Change Of Variable

This paper presents a new approach for tuning PID controller parameters in the control of nonlinear systems. The design is based on optimal tracking of step response for nonlinear systems. The problem is first restated as a non linear optimal control infinite horizon problem, then with a suitable change of variable, the time interval is transferred to the finite horizon [0 1). This change of variable, poses a time varying problem. This problem is then transferred to measure space, and it is shown that an optimal measure must be determined which is equivalent to a linear programming problem with infinite dimension. Then, using finite horizon approximations, the optimal control law as piece wise constant function is determined. Finally, PID controller parameters are Determined using the optimal control law. Simulations are provided to show the effectiveness of the proposed methodology.

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.

Extended Finite Time Inverse Optimal Control of Nonlinear Systems

2011 ◽  
Vol 403-408 ◽  
pp. 1499-1502
Author(s):  
Xin Jun Ren ◽  
Yan Jun Shen
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Finite Time ◽  
Lyapunov Functions ◽  
Control Law ◽  
Inverse Optimal Control ◽  
Closed Loop System ◽  
Affine Nonlinear Systems ◽  
Definition Of ◽  
The Cost

In this paper, we use the definition of control Lyapunov functions to study finite time inverse optimal control for affine nonlinear systems. Based on control Lyapunov functions, a finite time universal control formula is presented, which can ensure the closed-loop system is finite time stable. From this, less conservative conditions for the finite time inverse optimal control are derived. We design a finite time inverse optimal control law, which minimizes the cost functional. A numerical example verifies the validity of the proposed method.

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