id: 01619884
dt: j
an: 01619884
au: Fang, Huajing
ti: Observer based $l^1$ robust fault detection.
so: Control Theory Appl. 18, No.1, 36-40 (2001).
py: 2001
pu: South China University of Technology, Guangzhou
la: ZH
cc:
ut: factorization; robust fault detection; $l^1$ optimization theory; discrete
systems; perturbation; residual function; integer linear programming
ci: Zbl 0624.93003; Zbl 0703.93068
li:
ab: In the present paper, based on the factorization of a control system output
observer, the author proposes a new robust fault detection strategy by
means of the $l^1$ optimization theory. Denote by $A$ the set of all
stable impulse transition functions of the discrete systems under
consideration. Consider the system $$y(z)= [G_p(z)+ δG_p]u(z)+ G_d(z)
d(z)+ G_f(z) f(z),$$ where $y$, $u$, $d$ are the observed, input and
exterior perturbation signal respectively, $f$ denotes the fault, $G_p$
and $G_d$ are the ideal model transition function and the perturbation
distribution transition function respectively, and $δG_p$ denotes the
perturbation of the system. It is assumed that $G_p$ and $G_d$ are
stable. According to {\it B. A. Francis} [A course in $H_\infty$
control theory, Berlin, Springer-Verlag (1987; Zbl 0624.93003)] and
{\it X. Ding} and {\it P. M. Frank} [Syst. Control Lett. 14, 431-436
(1990; Zbl 0703.93068)], the residual function of the system can be
formulated explicitly as $$r(z)= P(z) M_l(z) [δG_pu(z)+ G_d(z) d(z)+
G_f(z) f(z)], \tag 1$$ where $M_l\in A$ and $P\in A$ is an arbitrary
and stable transition function. Under the assumption that there is no
perturbation involved, the author constructs the $l^1$ optimization
problem of (1) as follows $$μ= \min_{p(z)\in A} {\|P(z) M_l(z)
G_d(z)\|_A\over\|P(z) M_l(z) G_f(z)\|_A}\tag 2$$ and then proves (in
Theorem 1) that problem (2) is equivalent to the minimization problem
$$μ= \min_{P(z)\in A} \|P(z) M_l(z) G_d(z)\|_A,\quad \text{s.t.
}\|P(z) M_l(z) G_f(z)\|_A= 1.\tag 3$$ The Theorem 2 shows that problem
(3) can be solved by means of a certain mixed 0-1 type integer linear
programming problem. Some simulation examples are also given.
rv: Yang En-Hao (Guangzhou)