Discrete state space modeling and control of nonlinear unknown systems.

Area of Science:

• Control Systems Engineering
• Artificial Intelligence
• Nonlinear System Modeling

Background:

• Industrial modeling and control of nonlinear systems present significant challenges.
• Conventional techniques often struggle with unknown nonlinear dynamics.
• Accurate system modeling is crucial for effective control design.

Purpose of the Study:

• To propose a novel procedure for designing industrial modeling and control systems for nonlinear unknown systems.
• To develop a new recurrent neural network architecture for discrete-time state-space representation.
• To integrate neural network-based models with conventional control design techniques.

Main Methods:

• A discrete state-space neural network (DSSNN) was constructed to represent nonlinear dynamical systems.
• Training was performed using the back-propagation through time (BPTT) algorithm and Levenberg-Marquardt (LM) optimization.
• A linearization procedure derived linear state-space models from the DSSNN for analysis and controller design.

Main Results:

• The DSSNN successfully obtained discrete-time state-space representations of nonlinear systems.
• Linear state-space models were derived, allowing examination of controllability, observability, and stability.
• State feedback controllers (LQR, pole placement) and observers were designed and validated for SISO and MIMO systems.

Conclusions:

• The proposed DSSNN procedure effectively models and facilitates control design for nonlinear unknown systems.
• Integration of neural networks with conventional methods offers a powerful approach for industrial control.
• The method demonstrated robust performance in both single- and multiple-input, multiple-output nonlinear control problems.