the authors parameterize upper bounds of the target accel-

eration and then develop the resulting parameter adaptive

laws, t hus handling the target maneuver. As such, the con-

trol saturation an d the speed of the parameter adaptation

are two fundamental concerns in adaptive control design

[8, 9, 10]. To address these two concerns, in [11], a set of

relative-state-dependent basis functions is selected to rep-

resent the target acceleration , and then a weight vector

adaptive law is derived using optimal modiﬁcation tech-

nique. Alth ough th e adapti ve guid anc e laws work well in

the above-mentioned sce nar i os, they have three drawbacks

herein: 1) the guidance performanc e heavily depends on

the convergence of adapti ve parameters, while these pa-

rameters are easily prone to diverge wh en the jerk of the

maneuverable target is considerable; 2) the robustness to

the target maneuver relies on the parameterization of the

target maneuver, while it is very h ar d to accurately pa-

rameterize the target maneuver under study; 3) the order

of the closed-loop guidance system will inevitably increase

as the dimension of the adaptive parameters grows.

The sliding mode control is used to suppress the ef-

fect of t h e target maneuver in [12, 13]. In [14], the high-

order sliding mode control is adopted to estimate and to

compensate for t he e↵ect of the target maneuver. In this

regard, the sl i di n g mode guidance laws are upper-bound-

dependent. For the UMTI, the upper bounds of the target

acceleration are required to be chosen relatively big for

the sake of completely canceling the adverse e↵ects of the

target maneuver. Consequently, the resulting control is

conservati ve and may induce severe chattering due t o var-

ious kinds of modeling imperfections [15]. As another way,

a smooth sliding mo d e guidanc e law is proposed in [16], in

which an adaptive law is us ed to estimate th e upper bound

of the target maneuver. However, the adaptive parameter

may di verge under the situation of control s at ur at i on.

In [17], the high-gain control is used to ensure input-to-

state stability for a closed-l oop LOS rate dynamics, and

thereby the residual error of the LOS rate can be made

suﬃciently smal l in the presence of the target maneuver.

In [18], a ﬁnite-time guidance is proposed to nullify the

LOS rate, and the convergence boundary layer is theoret-

ically analyzed. The guidance pe rf or manc e of the high-

gain control, however, may det e ri or at e due to measure-

ment noise when the system bandwidth is excessively en-

larged. In fact, it is diﬃcult to make a reason abl e trade-o↵

between the disturbance suppression and the noise attenu-

ation without the priori information of the evasive strategy

of the target.

Following the technical route of the MS-GLs, a ro-

bust ﬁnite-time guidan ce (RFTG) law is presented in this

paper. An integrated continuous ﬁnite-time disturbance

observer (CFTDO)/bounded continuous ﬁnite-time stabi-

lizer (BCFTS) strategy is proposed. The CFTDO is de-

signed to estimate the disturbances that are the e↵ects

of the target maneuvers by making the observation-error

dynamics behave as a second-order homogeneous system.

The BCF TS uses a typical ﬁrst-order homogeneous system

to specify the ﬁnite-time stability of the nominal guid-

ance system in consideration. Both the CFTDO and the

BCFTS are based on non-smooth yet continuous feedback

contr ol. Such non-smo ot h feedback control has a favor-

able characteristic: its equivalent control gain increases

as the feedback error decreases. In contrast to existing

smooth feedback controls, the non -s mooth feedback con-

trol may have better convergence and robustness [19, 20]

and is suitable to be applied to the UMTI. Given these

virtues, a fe w guidance laws based on the non-smooth

feedback control have been designed. For example, the

ﬁnite-time convergence of the LOS rate is realized in [12],

but the e↵e ct of the t ar get maneuver is suppressed using

the convent i on al sliding mode control; in [21], using the

high-gain control, the authors present a guidance law with

ﬁnite-time input-to-state stability (FTISS). Note that the

robustness of these two guidance laws is routinely guar an -

teed by the sliding mode control or the high-gain control.

As discussed previously, these two control methods have

their own drawbacks when adopted in the UMTI.

To address the preceding drawbacks, the int egr at ed

strategy is put forward with two key ideas: 1) the e↵ect of

the target maneuver is modeled as the disturbance and is

estimated using the CFTDO; 2) the design of the BCFTS

is coupled wi t h that of the CFTDO. An unique charac-

teristic of this integrate d strategy is that it can explic-

itly d eal with the interplay between the CFTDO and the

BCFTS. This characterist i c is di↵erent from the existing

ﬁnite-time disturbance observer-based control methodolo-

gies (e.g., [22, 23, 24, 25, 26]), which d es ign the observer

and the ﬁnite-time controller in a decoupled fashion: they

are based on a zero-observation-error assumption. How-

ever, the observation errors cannot be perfectly canceled

in practi c e, especial l y concerning the UMT I. Nevertheless,

the proposed RFTG law can avoid such a restricted as-

sumption bec aus e of the integrated design adopted herein.

In addition, the proposed integrated strategy has sev-

eral appreciable advantages in the current scenari o. The

BCFTS, which uses the control saturation to quickly sta-

bilize the LOS rate, can take advantage of the limit of

the maneuver capability of the interceptor. Regarding the

CFTDO, it can rapidly estimate the disturbance of i n-

terest without su↵ering from the parameter convergence

issues. Through cooperation between the BCFTS and the

CFTDO, the resultant RFTG law is independent of both

the explicit maneuver models and the upper bounds of

the target maneuver s. Further, the RFTG law can guar-

antee locally FTISS in the presence of bounded derivative

of the disturbance, implying the LOS rate can b e rendered

within a bounded error as q u ickly as possible. Numerical

comparison results demonstrate the proposed RFTG law

can guarant ee the high-precision miss-distance.

This paper is organized as follows. We begin by formu-

lating a new short-range interception problem. In partic-

ular, a notion of the unpredictable evasive strategies is in-

troduced. The next section pre sents the robust ﬁnite-time

guidance law. Then, the convergence analysis of the LO S

2