H_∞ control for uncertain linear system over networks with Bernoulli data dropout and actuator saturation

Area of Science:

• Control Theory
• Networked Systems
• Systems Engineering

Background:

• Networked control systems are susceptible to data dropout and actuator saturation, impacting stability.
• Uncertain linear systems require robust control strategies to maintain performance.
• Existing methods often struggle to simultaneously address both data dropout and actuator saturation.

Purpose of the Study:

• To develop effective H_∞ controllers for uncertain linear systems over networks.
• To account for random communication data dropout and actuator saturation concurrently.
• To provide a systematic design methodology for robust control under network constraints.

Main Methods:

• Modeling random data dropout using a Bernoulli distributed white sequence.
• Confining actuator saturation within a convex hull using auxiliary matrices.
• Developing non-convex matrix inequality conditions via a quadratic Lyapunov function.
• Solving non-convex feasibility problems using the Cone Complementarity Linearization (CCL) procedure.

Main Results:

• Effective conditions for state feedback-based H_∞ controllers are derived.
• Effective conditions for observer-based H_∞ controllers are derived.
• The proposed methods successfully integrate considerations for data dropout and actuator saturation.
• Simulation examples validate the efficacy of the developed control techniques.

Conclusions:

• The proposed H_∞ control design techniques effectively address uncertain linear systems with network-induced constraints.
• The integration of random data dropout and actuator saturation is achieved through novel mathematical formulations.
• The CCL procedure provides a viable solution for the non-convex feasibility problems encountered in controller design.