Stabilization for sampled-data neural-network-based control systems.

Area of Science:

• Control Systems Engineering
• Artificial Neural Networks
• Systems Theory

Background:

• Sampled-data systems present unique challenges in stability analysis due to discrete-time state updates.
• Neural network control introduces complexity, especially when combined with time-varying delays inherent in sampled-data implementations.
• Existing methods often oversimplify the dynamics of variable sampling, leading to conservative stability criteria.

Purpose of the Study:

• To develop a robust stabilization method for sampled-data neural-network-based control systems.
• To achieve optimal guaranteed cost performance under uncertain and variable sampling intervals.
• To overcome the limitations of treating sampled-data systems as simple continuous-time systems with delays.

Main Methods:

• Definition of a novel piecewise Lyapunov functional to accurately model sampled-data system characteristics.
• Application of a convex combination technique to integrate system states and sampling variations.
• Formulation of a delay-dependent stabilization criterion using linear matrix inequalities (LMIs).

Main Results:

• A new criterion for stabilization is derived, directly accounting for variable sampling intervals.
• The method yields less conservative and less complex results compared to existing approaches.
• Maximal sampling intervals and minimal guaranteed costs are explicitly determined.

Conclusions:

• The proposed method effectively captures the essential dynamics of sampled-data systems with neural network controllers.
• The LMI-based criterion provides a less conservative and more practical approach to guaranteed cost stabilization.
• Demonstrated effectiveness through application examples highlights the benefits for robust control design.