an:01419424
Zbl 0952.93042
Antoniades, Charalambos; Christofides, Panagiotis D.
Robust control of nonlinear time-delay systems
EN
Int. J. Appl. Math. Comput. Sci. 9, No. 4, 811-837 (1999).
00060931
1999
j
93B51 93C23 93C10 93C95 93D30 93B52
model uncertainty; time-delays; nonlinear robust control; fluidized catalytic cracker
The paper is devoted to the robust control problem of the single-input single-output nonlinear system
\[
\begin{aligned} &\dot x=f(x(t),x(t-\alpha),\theta(t-\alpha_{\theta}))+ g(x(t),x(t-\alpha))u(t),\\ &y(t)=h(x(t)), \end{aligned}
\]
where \(x(t)\in\mathbb{R}^{n}\) denotes the vector of the state variables, \(u(t)\in\mathbb{R}\) is the input, \(\theta(t-\alpha_{\theta})\in\mathbb{R}^{q}\) is the vector of the uncertain variables, \(y(t)\in\mathbb{R}\) is the controlled output, \(f\), \(g\), \(h\) are locally Lipschitz nonlinear functions, \(f(0,0,0)=0\).
The authors address the problem of synthesizing nonlinear static state feedback control laws of the form \(u(t)=R(x(t),\bar v(t),x(t-\alpha),\bar v(t-\alpha))\), where \(R\) is a nonlinear scalar function, \(\bar v(s)=[v(s),v^{(1)}(s),\ldots, v^{(r-1)}(s)]^{T}\), \(s\in[t-\alpha,t]\), \(v^{(k)}\) is the \(k\)-th derivative of the reference input \(v\in\mathbb{R}\). A general methodology is developed for the synthesis of robust controllers that guarantee boundedness of the states and ensure that the ultimate discrepancy between the output and the reference output in the closed-loop system can be made arbitrarily small by a choice of controlled parameters. The controllers enforce these properties independently of the size of the state delay.
A novel combination of geometric technique and the method of Lyapunov functionals is used. The proposed methodology is applied to a model of a fluidized catalytic cracking unit.
Oleg Anashkin (Simferopol)