Output Feedback Control and Stabilization for Multiplicative Noise Systems With Intermittent Observations

Area of Science:

• Control Theory
• Stochastic Systems
• Networked Control Systems

Background:

• Stochastic control problems with multiplicative noise and intermittent observations present significant challenges.
• Existing methods often rely on the separation principle, which is not directly applicable here.

Purpose of the Study:

• To develop optimal output feedback control and stabilization methods for discrete-time multiplicative noise systems with intermittent observations.
• To overcome limitations of the separation principle in stochastic control for these systems.
• To establish necessary and sufficient stabilization conditions.

Main Methods:

• Optimal estimation based on the measurement process.
• Dynamic programming principle for controller design.
• Design of a controller with feedback gain derived from coupled Riccati equations.

Main Results:

• Overcoming the separation principle barrier for stochastic control problems with multiplicative noise.
• Development of the first necessary and sufficient mean-square stabilization conditions for systems with intermittent observations.
• Explicit determination of packet loss rates for networked control system applications.

Conclusions:

• The developed methods provide a novel approach to optimal output feedback control and stabilization for discrete-time multiplicative noise systems.
• The findings are applicable to networked control systems, specifically addressing user datagram protocol (UDP) network scenarios.
• The study explicitly defines allowable packet loss rates, offering practical insights for system design.