Reliable control for positive switched systems with random nonlinearities.

Area of Science:

• Control Theory
• Systems Engineering
• Stochastic Systems

Background:

• Positive switched systems are crucial in various applications but vulnerable to random nonlinearities and actuator faults.
• These vulnerabilities can compromise system security and reliability.
• Existing control methods may not adequately address these combined challenges.

Purpose of the Study:

• To propose a reliable control strategy for positive switched systems with random nonlinearities and actuator faults.
• To enhance the security and robustness of these systems against stochastic disturbances.
• To develop a control design methodology applicable to systems with exogenous disturbances.

Main Methods:

• Utilizing a switched linear copositive Lyapunov function for system analysis.
• Employing a matrix decomposition approach to formulate the controller gain matrix.
• Designing a reliable controller using linear programming to handle actuator faults.
• Incorporating stochastic variables obeying Bernoulli distribution to model random nonlinearities.

Main Results:

• A reliable controller is designed, effectively mitigating security risks from random nonlinearities and actuator faults.
• The proposed control strategy demonstrates robustness against exogenous disturbances.
• The controller design is validated through two illustrative examples, confirming its efficacy.

Conclusions:

• The developed reliable control approach ensures the security and stability of positive switched systems under random nonlinearities and actuator faults.
• The methodology provides a robust framework for designing controllers for systems subject to stochastic uncertainties and component failures.
• The findings offer a valuable contribution to the field of robust control for complex dynamical systems.