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Research on Input-To-State Stability of Discrete-Time Nonlinear Systems

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Tutor: LiuZhiYuan
School: Harbin Institute of Technology
Course: Control Theory and Engineering
Keywords: input-to-state stability,input-to-state practical stability,min-max MPC,backstep
Type: Master's thesis
Year:  2008
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Input-to-state stability ( ISS ) originally proposed by Professor Sontag in 1989 isa new concept which describes stability of forced dynamical system using state-spacemethod. With the development of 20 years, input-to-state stability together with otherconcepts derived from it formed the theoretical framework of input-to-state stability.At present, the input-to-state stability has become a very popular analysis and designmethod for nonlinear systems.In this thesis , delicate research is made with respect to some applications ofinput-to-state stability framework in the area of discrete-time nonlinear system.First of all, for a class of discrete time strict feedback nonlinear systems withadditive disturbance, a backstepping adaptive state regulation is designed to regulatethe state norm of system into a neighborhood of the origin, by using function approx-imation and on-line update of the approximators, and the ISpS is used to analyse thestability of the final closed-loop system.Then, we consider a class of discrete nonlinear system that is affected by externaldisturbance and parameter uncertainty, which is constrained on state and control .The min-max model predictive control ( MPC ) methodology is employed to obtaina dual-mode controller that robustly steers the state of the system towards a desiredequilibrium, and the stability is analysed by input-to-state stability. In this method, theterminal matrix and feedback matrix are computed with respect to the linear systemusing a enlarged weithted matrix of state in the cost function of the MPC strategy, thenit is proved that the matrices can also be used in the whole nonlinear system.The results obtained in this thesis solves some problems that exists in the applica-tions related with ISS framework, which proves its important theoretical and practicalsignificance.
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