Sliding Mode Fuzzy Control of Stochastic Nonlinear Systems Under Cyber-Attacks

Area of Science:

• Control Theory
• Nonlinear Systems
• Cyber-Physical Systems

Background:

• Investigates integral sliding mode control (ISMC) for nonlinear systems with stochastic dynamics.
• Addresses the challenge of cyber-attacks impacting control system performance and stability.
• Utilizes Takagi-Sugeno fuzzy models to represent complex nonlinear stochastic systems.

Purpose of the Study:

• To develop and analyze a dynamic integral sliding mode control (ISMC) scheme for nonlinear stochastic systems under cyber-attack.
• To ensure finite-time convergence to the integral sliding surface and guarantee closed-loop stability.
• To demonstrate the boundedness of all signals and asymptotic stochastic stability of the system states.

Main Methods:

• Modeling the control system and cyber-attack using Itô-type stochastic differential equations.
• Applying a universal dynamic integral sliding mode control (ISMC) scheme.
• Employing linear matrix inequalities (LMIs) to analyze system stability and performance.
• Utilizing a Takagi-Sugeno fuzzy model approach for nonlinear system representation.

Main Results:

• The proposed fuzzy ISMC scheme confines system trajectories to the integral sliding surface in finite time.
• Stability of the closed-loop system under cyber-attack is guaranteed using linear matrix inequalities.
• All signals in the closed-loop system are shown to be bounded, with asymptotic stochastic stability achieved under specified conditions.

Conclusions:

• The developed dynamic fuzzy ISMC is effective for controlling nonlinear stochastic systems susceptible to cyber-attacks.
• The control strategy ensures finite-time convergence and robust stability against external disturbances and adversarial actions.
• The inverted pendulum example validates the practical applicability and effectiveness of the proposed control scheme.