Abstract
In this paper, a robust fuzzy controller for stochastic nonlinear systems subject to multiple performance constraints is discussed. To solve the problem of stochastic behaviors in nonlinear systems, the covariance control theory and passive control theory are applied based on the concept of energy. Additionally, the pole placement method is considered for the better transient behaviors of the system responses. However, it is known that the control inputs and maximum overshoot of the system responses may become bigger at the same time when the settling time or converge rate of the system is required to be faster. Due to this reason, the input constraint is also considered in the fuzzy controller design method to limit the value of the control gain. Moreover, an effective robust control method is applied to deal with the perturbation of the nonlinear systems. Based on the above performance constraints, the sufficient conditions can be obtained to achieve the stability in the sense of mean square and the multi-performance requirements. Finally, simulation results of the nonlinear synchronous generator system are presented to verify the feasibility and efficiency of the proposed control method.
Highlights
Based on the SPT-SFM, a stability analysis and robust fuzzy controller design method subject to multiple performance constraints are proposed for the stochastic nonlinear systems with perturbations in this paper
The state variance constraint and minimized output variance constraint are applied to suppress the energy of the system state and output under the stochastic behaviors effect
The passive constraint is combined into the design method to dissipate the energy of stochastic behaviors
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Via the applications of the upper bound state covariance matrix and variance constraint, the performance of nonlinear systems under the effect of stochastic behaviors can be guaranteed based on the T-S fuzzy model. In [26,27], it is seen that the input constraint is combined into the fuzzy controller design based on the T-S fuzzy model and applied in practical systems successfully. Perturbated T-S Fuzzy Model (SPT-SFM) based nonlinear systems subject to multiple performances, including the individual state variance constraint, output variance constraint, input constraint, passive constraint, and D-stable pole constraint. Considering the passivity theory and selecting the dissipate rate, the passive constraint is combined into the design method such that the SPT-SFM can dissipate the energy of stochastic behaviors.
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