Linear Systems, Adaptive Drive Failure Compensation Control

This paper studies adaptive actuator failure compensation control for liner time-invariant system with uncertain actuator failures and unknown parameters. Actuator failures in control systems may cause severe system performance deterioration and even lead to catastrophic closed-loop system instability. For example, many aircraft accidents were caused by operational failures (such as rudder and elevator) in the control surfaces. For system safety and reliability, such actuator failures must be appropriately accommodated. Actuator failure compensation is an important and challenging problem for control systems research not only on the theoretical but also on the practical significance. Despite substantial progress in the area of actuator failures compensation, there are still many important problems to be solved, in particular those involving system uncertainties. The main difficulty is that the actuator failures are uncertain in nature, very often it is impossible to predict in advance which actuators may fail during system operation, when the actuator failures occur, what type and what value of the actuator failures are. It may also be impractical to determine such actuator failure parameters after a failure occurs. It is appealing to develop control schemes that can accommodate actuator failures without explicit knowledge of the occurrences of actuator failures and the actuator failure values. Adaptive control, which is capable of accommodating system parametric, structural, and environmental uncertainties, is a suitable choice for such actuator failures compensation schemes.This paper includes the following two parts:First, adaptive actuator failure compensation control for multivariable systems with unmolded dynamicsConsider the following MIMO system with unmodeled dynamicsy(t) = G0(s)(IM + vAm(s))u(t) (0.0.1)where y G RM is the plant output vector, u G RN is the plant input vector. G0(s) e RMxN is the transfer function matrix, s is the Laplace transform variable or the differential operator. Am(s) G RMxN is the unmodeled dynamic, n > 0 is the magnitude of the unmodeled dynamics. We assume that the N inputs can be separated into M groups. Each group contains n^ inputs,witVi r> ■ ^> 1 i — 1 ? ? ? A/f anrl \ A n- — TVVV Hjli. I b i ^_<sub> A., If ----- .1. , , 1VJL , dlx\A /,-'_<sub>1 ... *f ' v% ----- -i *Consider the case that any actuator may fail during system operation, but at least one actuator in each group does not fail. The actuator failures are characterized asUij(t) = Uij, t>tijy ie{l,...,M}, j G {1,2, ...,rii}, (0.0.2)where the failed actuators u^, constant value ?y and the failure time instant Uj are all unknown.A more general failure model isuij0 + ]Tdijkfijk{t), t >je{i,2,...,m}, (0.0.3)for some unknown constants Uij0 and d^ , and known and bounded scalar signals fijk, i = 1, ? ? ? , M, j = 1, ■ ? ? , ni: k = 1, ? ? ? , n,-,-, and ni-7- > 1. We have?i(*) = [?n (*),..-, ?ini(*)]r = Ui(*) + at(?i-t;i(<)), (0.0.4)where Vi(t) = [vn(t),..., Vini(t)]T is a to be designed control input vector for group i andUi --= [un,..., uini]T, o{1 if the jth actuator in group i has faild,i.e. Uij(t) = iiij, since