Optimal Control of a Class of Discrete Multivariable Nonlinear Systems. Application to a Fermentation Process

1982 ◽  
Vol 104 (3) ◽  
pp. 212-217 ◽  
Author(s):  
Joaqui´n Alvarez Gallegos ◽  
Jaime Alvarez Gallegos
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Fermentation Process ◽  
Closed Loop ◽  
Control Structure ◽  
Control Law ◽  
Loop Structure ◽  
Augmented System ◽  
Numerical Integrators ◽  
Multivariable Nonlinear Systems

The optimal control of a class of discrete multivariable nonlinear systems given by: xk+1 = a (xk) + B (xk) uk, yk = C xk, is analyzed. A closed-loop structure is obtained with the proposed performance index. The addition of numerical integrators to the output error and the design of an optimal control law for the resultant augmented system lead to a very robust control structure. The performance of this control law is evaluated by applying it to a simulated continuous culture fermentation process.

scholarly journals Robust Output Feedback of Minimum Phase Nonlinear Systems

2007 ◽  
Vol 30 (2) ◽  
pp. 83-91
Author(s):  
Emrod Elisante
Keyword(s):  
Nonlinear Systems ◽  
Output Feedback ◽  
Closed Loop ◽  
Control Structure ◽  
Chemical Reactor ◽  
Internal Model Control ◽  
Minimum Phase ◽  
Robust Tracking ◽  
Model Control ◽  
Multivariable Nonlinear Systems

A robust output feedback controller is synthesized for minimum phase multivariable nonlinear systems based on thedifferential geometry approach. Using the internal model control structure within the input-output (I/O) linearizationframework, the controller is combined with a closed-loop observer to estimate transformed states in the outer-loop. It isshown that the controller-observer combination achieves robust tracking and estimation using simple tuningparameters. The effectiveness of the proposed system is illustrated by a simulation example for control of concentrationin a chemical reactor.

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.

Fuzzy optimal control using generalized Takagi–Sugeno model for multivariable nonlinear systems

2015 ◽  
Vol 30 ◽  
pp. 205-213 ◽  
Author(s):  
Basil Mohammed Al-Hadithi ◽  
Agustín Jiménez ◽  
Ramón Galán López
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Sugeno Model ◽  
Takagi Sugeno ◽  
Multivariable Nonlinear Systems

scholarly journals Nonlinear suboptimal attitude control law for near-space hypersonic vehicle: Eigenvalue analysis and weight matrices design

2022 ◽  
Author(s):  
Peichao Mi ◽  
Qingxian Wu ◽  
Yuhui Wang
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Attitude Control ◽  
Stable Manifold ◽  
Closed Loop ◽  
Suboptimal Control ◽  
Control Law ◽  
Attitude Dynamics ◽  
Attitude Control System ◽  
Near Space

Abstract This paper considers a nonlinear suboptimal control problem for a near-space hypersonic vehicle's (NSHV's) attitude dynamics. The least-square and stable manifold methods first solve an unconstrained approximately optimal control law corresponding to the nonlinear attitude model. Then, to further meet the dynamic performance requirement of the attitude control system, a novel strategy based on the Koopman operator, symplectic geometric theory, and the stable manifold theorem is proposed to approximate the eigenvalues of the closed-loop nonlinear unconstrained approximated optimal control system. The weight matrices in the optimal performance index, which directly determine the output responses of the nonlinear attitude dynamics, can be appropriately designed according to the eigenvalues. The final control law considers the actuator constraints. The NSHV's closed-loop attitude control system is proved to be locally exponentially stable, and the suboptimality of the control law is analyzed. Numerical simulation demonstrates the effectiveness of the proposed scheme.

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.

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