Variance and passivity constrained sliding mode fuzzy control for continuous stochastic non-linear systems

A multiple performance constrained sliding mode fuzzy control problem is investigated in this paper for continuous-time stochastic non-linear systems. The stability constraint, passivity constraint and individual state variance constraint are simultaneously considered in this paper. By combining sliding mode control, variance constrained control and model-based fuzzy control, a novel performance constrained fuzzy control approach is developed. Applying Lyapunov function, some sufficient conditions are derived in term of linear matrix inequalities that can be solved by convex optimal programming algorithm. The main contribution of this paper is to develop a parallel distributed compensation based sliding mode fuzzy controller such that closed-loop system can achieve multiple performance constraints. At last, a numerical example for the control of translational oscillations with a rotational actuator system is given to demonstrate the validity and effectiveness of proposed sliding mode fuzzy control method.