Sampled-Data Stochastic Stabilization of Markovian Jump Systems via an Optimizing Mode-Separation Method.

Area of Science:

• Control Theory
• Systems Engineering
• Stochastic Systems

Background:

• Markovian jump systems (MJSs) present unique control challenges due to their state-dependent switching behavior.
• Sampled-data controllers introduce further complexity in MJSs due to signal discretization and controller switching.

Purpose of the Study:

• To develop a novel stochastic stabilizing method for MJSs with sampled-data controllers.
• To address challenges associated with stochastic controller switching and sampled state signals.
• To achieve less conservative results compared to existing methods.

Main Methods:

• Optimization of mode separations, with the quantity determined by Stirling numbers of the second kind.
• Formulation of an optimization problem using an augmented Lagrangian cost function for guaranteed local optimality.
• Development of an improved hill-climbing algorithm enhanced with Q-learning for optimal attenuation coefficient selection.

Main Results:

• A novel method for stochastic stabilization of MJSs with sampled-data controllers is presented.
• The proposed method offers less conservative results than existing approaches.
• An efficient optimization algorithm is developed, reducing computational complexity.

Conclusions:

• The developed method effectively stabilizes Markovian jump systems under sampled-data control.
• The optimization strategy and enhanced algorithm provide a superior and computationally efficient approach.
• The findings are validated through two illustrative examples demonstrating effectiveness and superiority.