| State-feedback stabilization problem for a class of high-order nonlinear systems with unknown control directions, and output-feedback stabilization problem for a class of nonlinear time-delay systems with unknown control directions are investigated in this thesis, which is divided into the following two parts.1. The problem of state-feedback stabilization for a class of high-order nonlinear systems with unknown control directions.Consider the following high-order nonlinear systemxi(t)=xi+1Pi(t)+(?)i(xi),i=1,…,n-1,xn(t)=guPn(t)+(?)n(xn),where x= [x1,…,xn]T∈Rn and u∈R are measurable state vector and control input,respectively, g is a nonzero constant with unknown control direction, pi≥1 are odd integers,i = 1,…, n, and (?)i(xi) are smooth functions which satisfy the following Assumptions 1-2 with (?)i(0) = 0.Assumption 1: For each a (?)i(xi),i=1,…,n,xi=[x1,…,xi]T∈Ri(i=1,…,n),there exists a known nonnegative smooth functionρi(·) such that|(?)i(xi)|≤(|x1|P1+…+|xi|Piρi(xi).Assumption 2:P0≥P1≥P2≥…≥Pn≥1．The control objective of this part is to design a state-feedback controller under Assumptions1-2 such that all the signals in the closed-loop system are bounded and states of the closed-loop system converge to zero.2. The problem of output-feedback stabilization for a class of nonlinear time-delay systems with unknown control directions.Consider the following nonlinear time-delay systemxi(t)=xi+1(t)+fi(y(t))+hi(y(t-d)), i=1,…,n-1,xn(t)=gu(t)+fn(y(t))+hn(y(t-d)),y(t)=x1(t),where x=[x1,…,xn]T∈Rn,u∈R and y∈R are unmeasurable state vector, controlinput and measurable output, respectively, fi(y(t)) and hi(y(t-d)) are uncertain functions with fi(0) = 0 and hi(0) = 0, i = 1,…,n, g is a nonzero constant with unknown control direction, and d > 0 is a constant.The control objective is to design a output-feedback adaptive controllerxc=fc(y,xc(ξ,(?),ζ)), u=hc(y,xc(ξ,(?),ζ)),such that all the signals in the closed-loop system are bounded and states of the closed-loop system converge to zero. |
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