Design Of Guaranteed Cost Control For Takagi-Sugeno Fuzzy Systems

As the development and continuous breakthroughs of science and technology,how to find reliable and effective control algorithm for complex nonlinear systems becomes an urgent demand.Fuzzy control technique plays important role in mitigating this emergency.T-S fuzzy systems nonlinearly synthesize many linear time invariant(LTI)systems to approximate the original nonlinear dynamics.This establishes a powerful bridge between nonlinear system and linear system so that the nonlinear system control problems are possible to be solved by the mature and abundant linear system control theories.When a control algorithm is being designed,in addition to guaranteeing the stability of closed-loop system,additional certain control performance is also desired.The guaranteed cost control aims at stabilizing the systems and minimizing the upper bound of a quadratic performance index at the same time.However,existing guaranteed cost control methods can not adjust the response speed effectively,and due to their conservativeness,in many cases no satisfactory control laws can be found.To this end,in this paper,for nonlinear systems represented by T-S fuzzy systems,guaranteed cost control is further investigated,and following results are achieved:1.Exponentiallly stable guaranteed cost control methods for continuous-and discrete-time T-S fuzzy systems are presented.By minimizing the upper bound of a quadratic performance function with exponential term,the proposed guaranteed cost control could consider the effects of system response speed,output regulation error and control input simultaneously,so that a proper trade-off could be found among these three elements.As a result,the system response speed would be enhanced effectively while an acceptable level of optimality would also be guaranteed.2.Based on a relaxed basic stability condition,a new guaranteed cost tracking control strategy is proposed for T-S fuzzy systems.Then this new strategy is applied to the tracking task of a well-known boiler-turbine model.Thanks to the less conservative stability condition,more candidates are available when the controller is being designed, which increases the possibility of achieving better performance.3.A relaxed condition for quadratic stability of guaranteed cost control for T-S fuzzy systems is derived.Different from existing sufficient only conditions,the proposed condition for quadratically stable guaranteed cost control is sufficient and asymptotically necessary.As a related parameter increases,this condition would be less and less conservative.The resulting guaranteed cost is non-increasing with respect to this parameter.At the limiting case,The resulting guaranteed cost would be optimal under quadratic stability.For input-affine nonlinear systems,the proposed conditions are adapted to consider the modelling errors in order to reduce the computational efforts.