Finite-Time Fuzzy Sliding Mode Control for Nonlinear Descriptor Systems

This article addresses the finite-time boundedness(FTB)problem for nonlinear descriptor systems.Firstly,the nonlinear descriptor system is represented by the Takagi-Sugeno(T-S)model,where fuzzy representation is assumed to be appearing not only in both the state and input matrices but also in the derivative matrix.By using a descriptor redundancy approach,the fuzzy representation in the derivative matrix is reformulated into a linear one.Then,we introduce a fuzzy sliding mode control(FSMC)law,which ensures the finite-time boundedness(FTB)of closed-loop fuzzy control systems over the reaching phase and sliding motion phase.Moreover,by further employing the descriptor redundancy representation,the sufficient condition for designing FSMC law,which ensures the FTB of the closed-loop control systems over the entire finite-time interval,is derived in terms of linear matrix inequalities(LMIs).Finally,a simulation study with control of a photovoltaic(PV)nonlinear system is given to show the effectiveness of the proposed method.

Adaptive PID controller based on Q-learning algorithm

An adaptive proportional–integral–derivative(PID)controller based on Q-learning algorithm is proposed to balance the cart–pole system in simulation environment.This controller was trained using Q-learning algorithm and implemented the learned Q-tables to change the gains of linear PID controllers according to the state of the system during the control process.The adaptive PID controller based on Q-learning algorithm was trained from a set of fixed initial positions and was able to balance the system starting from a series of initial positions that are different from the ones used in the training session,which achieved equivalent or even better performances in comparison with the conventional PID controller and the controller only uses Q-learning algorithm.This indicates the advantage of the adaptive PID controller based on Q-learning algorithm both in the generality of balancing the cart–pole system from a relatively wide range of initial positions and in the stabilisability of achieving smaller steady-state error.