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Robust Control And Regulation For Multi-Input Multi-Output Nonlinear Systems

Posted on:2017-02-26Degree:DoctorType:Dissertation
Country:ChinaCandidate:L WangFull Text:PDF
GTID:1108330485992761Subject:Control Science and Engineering
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Multi-input multi-output (MIMO) nonlinear systems are widely applied to practical engineering. Since the early of 1970s, there has been some theoretical results reported on the control of MIMO nonlinear systems. However, since its extremely complicated struc-ture, the development of MIMO nonlinear control theory is still at a preliminary stage. Especially, in the recent twenty years, it becomes hard to see much work reported in the literature. With the fast development of modern industry and technology, the controlled systems have been increasingly multivariable and highly complex, the common design ap-proach based on the single-input single-output (SISO) nonlinear system theory becomes powerless. Thus, it is quite of practical significance and urgent to develop more effec-tive MIMO nonlinear systems theory. In general, MIMO nonlinear systems possessing a well-defined relative degree vector can be (globally) asymptotically stabilized by state and output feedback law by means of trivially extending existing SISO nonlinear systems the-ory. While as for those more general MIMO systems, such as MIMO nonlinear systems having uncertain high-frequency gain matrix, invertible MIMO nonlinear systems and so on, a new design approach is needed, instead of that trivial extension.This thesis mainly investigates the problem of robust control and regulation for several nontrivial kinds of MIMO nonlinear systems, which can be concluded as follows.1) Provides a method for (semi-global) asymptotic stabilization of a nonlinear minimum-phase MIMO system, under a mild hypothesis of the so-called "high-frequency gain" matrix. This result is based on a non-trivial extension, to the MIMO setting, of the approach based on the use of extended observers. As a byproduct, a dynamic output feedback control is obtained, that asymptotically stabilizes the equilibrium of the closed-loop system, in spite of uncertainties in the high-frequency gain matrix.2) Considers the class of input-affine MIMO nonlinear systems which are assumed to be invertible and input-output linearizable. It is shown that if a system in this class is strongly minimum phase, it is globally stabilizable via partial-state feedback or semiglobally stabilizable via (dynamic) output feedback. The result substantially broadens the class of nonlinear MIMO systems for which global/semiglobal stabi-lization via limited state information is known to be possible.3) Addresses the problem of output regulation for a broad class of MIMO nonlinear systems which are invertible and input-output linearizable. It is shown that if a sys-tem in this class is strongly minimum phase, the problem of output regulation can be solved via partial-state feedback or via (dynamic) output feedback by means of in-ternal model-based method proposed by Marconi and Praly. The result substantially broadens the class of nonlinear MIMO systems for which the problem in question is known to be possible.4) Investigates the problem of global stabilization of a rather general class of MIMO nonlinear systems. The systems considered in the thesis are invertible, have a triv-ial zero dynamics and possess a "normal form" in which certain multipliers are functions of the state vector of a special kind. While special structural dependence of such multipliers on the components state vector has been exploited before in the context of achieving stabilization (via full-state feedback, though), the novelty in the approach of this thesis is that a peculiar structure is identified which happens to be intimately related to the property of uniform complete observability (thus making the design of observers possible) and to the property of uniform invertibility, relations never established before in the literature. As a result, for this class of MIMO non-linear systems, a dynamic output feedback law can be designed, yielding semiglobal (and even global, under appropriate assumptions) asymptotic stability.5) Studies the problem of state observation for systems having a well-defined observ-ability canonical form by means of high-gain observers. The main goal is to show that, for this class of systems, observers can be designed with the high-gain param- eter powered just up to the order 2 regardless of the dimension of the state system. In this way we substantially overtake the main limitations of standard design pro-cedures in which the high-gain parameter is powered up to the order of the system. The observer structure then can be used in all those contexts where fast state obser-vation is required, such as in the design of output feedback stabilizers by means of the nonlinear separation principle.
Keywords/Search Tags:Multi-Input Multi-Output Nonlinear Systems, State Feedback, Output Feedback, Invertibility, Structure Algorithm, High-gain Observers, Nonlinear Sepa- ration Principle
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