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Time-Varying And Discontinuous Control For Uncertain Nonlinear Systems

Posted on:2016-07-04Degree:DoctorType:Dissertation
Country:ChinaCandidate:Y C ManFull Text:PDF
GTID:1108330482963584Subject:Control theory and control engineering
Abstract/Summary:PDF Full Text Request
Feedback control of uncertain nonlinear systems is a hotspot research area in control theory, which is widely used in robot systems, aerospace systems, power systems, economic systems and so on. Compared with the linear systems, the nonlinear systems is more accurate in describing the practical systems, but is more complicated, since it often requires the abstract modern mathematical tools and complex control design method. On the other hand, in practical systems, mainly due to the measurement error and the external disturbance, the uncertainties inevitably exists in the systems. The existence of these uncertainties increases the difficulties of the control design, and presents the challenges to the existing control theory. Therefore, the study on the feedback control of the uncertain nonlinear systems has both theoretical and practical significance.In general, compared with continuous feedback control, the time-varying continuous one and discontinuous one have stronger control ability. Motivated by this, this paper develops the time-varying and discontinuous feedback control methods for the global stabilization of nonlinear systems with serious uncertain-ties/unknowns, serious time-variations or strong nonlinearities, which cannot be solved by the existing control scheme.First, this paper investigates the global output-feedback stabilization for a class of uncertain time-varying nonlinear systems. The remarkable structure of the systems is the presence of uncertain control coefficients and unmeasured states dependent growth whose rate is inherently time-varying and of unknown polynomial-of-output, and consequently the systems have heavy nonlinearities, serious uncertainties/unknowns and serious time-variations. This forces us to explore a time-varying plus adaptive methodology to realize the task of output-feedback stabilization, rather than a purely adaptive one. The designed controller is still valid when the system has an additive input disturbance which, essentially different from those studied previously, may not be periodic or bounded by any known constant.Then, this paper considers the global stabilization via time-varying output-feedback for a class of high-order uncertain nonlinear systems with rather weak as- sumptions. Essentially different from the existing literature, the systems under in-vestigation simultaneously have more serious nonlinearities, unknowns, immeasur-ableness and time-variations, which are indicated from the unknown time-varying control coefficients and the higher-order and lower-order unmeasured states depen-dent growth with the rate of unknown function of time and output. Recognizing that adaptive technique is quite hard to apply, a time-varying design scheme is proposed by combining time-varying approach, certainty equivalence principle and homogeneous domination approach. With the appropriate choice of the involved design functions, the designed controller makes all the signals of the closed-loop system globally bounded and ultimately converge to zero.Third, this paper addresses the global adaptive stabilization via switching and learning strategies for a class of uncertain nonlinear systems. Remarkably, the systems in question simultaneously have unknown control directions, unknown input disturbance and serious parameter unknowns, which makes the problem in question challenging to solve and essentially different from those in the existing literature. To solve the problem, an adaptive scheme via switching and learning is proposed by skillfully integrating the techniques of backstepping design, adaptive learning and adaptive switching. The designed controller guarantees that all the signals of the resulting closed-loop systems are bounded, and furthermore, the closed-loop system states globally converge to zero.Finally, this paper considers the adaptive control design for a class of high-order uncertain nonlinear systems with unknown control coefficients. Although this problem has been solved, the involved controller is in a nonlinear form and hence is complex. Different from the existing literature, in this part, by skillfully applying adding a power integrator and switching adaptive control techniques, a linear feedback controller is successfully proposed, which is simpler and easy to implement, and can guarantee that, the system states are bounded and ulti-mately converge to zero. It is worth mentioning that, compared with the works on switching adaptive control, the nonlinear systems in this part possess more serious uncertainties/unknowns and stronger nonlinearities, mainly reflected by the unknown control coefficients and the higher system orders.It is necessary to point out that the compensation methods developed in present paper have strong ability to deal with serious uncertainties/unknowns and serious time-variations, and are relatively easy to combine with the existing control design schemes, which provides new way for dealing with the unsolved problems by the existing schemes. Moreover, the corresponding simulation examples are all presented, and hence illustrate the effectiveness of the control design method proposed in the paper.
Keywords/Search Tags:Uncertain nonlinear systems, unmeasure states dependent growth, unknown control direction, additive input disturbance, time-varying method, switch- ing method, learning method, global output-feedback stabilization
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