Studies On The Decentralized Control And Output Tracking Control Of Fractional Order Interconnected Systems With Uncertainties

In recent years,the fractional order control system has become one of the hottest issues in the automation field.On the one hand,many real systems and natural phenom-ena can be characterized more comprehensively and accurately by fractional differential equations involving the so-called fractional derivatives and integrals.On the other hand,with the successful implementation of the physical fractional derivative,fractional order controllers have been widely introduced into various systems to improve the performance.Due to the uncertain factors existing objectively in system,the system quality deviate from its nominal quality,and the degree of deviation depends on the robustness to such factors.Similarly,for any system the disturbance is objective and unavoidable.H_?is a characteristic parameter which reflects the ability of disturbance rejection and robustness,so the H_?analysis and H_?control for uncertain system are important research content.In addition,the gain perturbation of real controller which is stable in theory results in the degradation of system performance,or even instability.For fractional order intercon-nected systems with uncertainties,those problems including the decentralized H_?con-trol,decentralized robust output tracking control,gain perturbations of these two kinds of decentralized controllers,are discussed.At first,The development about fractional calculus and the research progress of frac-tional order system are briefly introduced,and four typical representation form about un-certainties in systems are summarized.Moreover,to study the decentralized H_?control and output tracking,the preliminary knowledge is given.The problem of H_?analysis and synthesis for the fractional order interconnected sys-tems with element-bounded uncertainties is studied.Based on the H_?bounded lemma of the commensurate fractional order system,the sufficient condition for determining the H_?performance of the systems is proposed,and the feasible condition for the decentralized H_?controllers was derived.The problem about gain perturbations of the decentralized H_?controllers employed by fractional order interconnected systems with element-bounded uncertainties was dis-cussed.The gain perturbations are parameterized in the form of uncertainty.Based on the H_?bounded lemma of the commensurate fractional order system,the sufficient condi-tion for the feasibility of the non-fragile decentralized controllers is obtained in the form of the linear matrix inequalities.Furthermore,the gains of the controllers are optimized as low as possible by solving the convex optimization problem with linear matrix inequality constraints.The problem about decentralized robust output tracking for fractional order inter-connected systems with norm-bounded uncertainties is studied.By constructing the aug-mented system,the tracking problem is transformed into the stabilization problem.Based on the stability theorem of the commensurate fractional order system,the sufficient con-dition for the feasibility of the decentralized robust output tracking controllers is obtained.The problem about gain perturbations of decentralized output tracking controllers for fractional order interconnected systems with norm-bounded uncertainties is investi-gated.By constructing the augmented system,the tracking problem is transformed into the stabilization problem.The gain perturbations are parameterized to the uncertainties of the augmented system.the stability condition for the uncertain augmented system is deduced,and the sufficient condition for the feasibility of the non-fragile decentralized robust output tracking controllers is derived.