Robust finite-time guidance against maneuverable targets with unpredictable evasive strategies

TL;DR: Based on homogeneity technique, the local finite-time input-to-state stability is established for the closed-loop guidance system, thus implying the proposed RFTG law can quickly render the LOS rate within a bounded error throughout intercept.

About: This article is published in Aerospace Science and Technology.The article was published on 2018-06-01 and is currently open access. It has received 9 citations till now. The article focuses on the topics: Observer (quantum physics) & Guidance system.

Summary

1. Introduction

• Interception of a maneuverable target is one of essential questions in the study of homing guidance.
• This new guidance problem is referred to as Unpredictable Maneuverable Target Interception (UMTI) herein; that is, the interceptor cannot predict the evasive strategy of the target.
• The CFTDO is designed 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.
• Note that the robustness of these two guidance laws is routinely guaranteed 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.

2. Problem formulation

• The design and analysis of the RFTG law is based on the following assumptions: Assumption 1. a M and a T are acceleration of the interceptor and the target, respectively.
• $ represents the deterministic yet unknown maneuvers, such as an artificial-intelligence model and an eventtrigger-based model.
• A specific target maneuver model concerning (6) is given in Section 5.1 to assess the guidance performance of the proposed guidance law.

3. Robust finite-time guidance design

• The RFTG law is presented: first, the CFTDO is designed to estimate the e↵ect of the target maneuvers; second, the integrated CFTDO/BCFTS strategy is proposed to robustly stabilize the LOS rate.
• If = ↵, this integrated CFTDO/BCFTS strategy has two advantages.
• The disturbances must be completely canceled by the observer in finite time, and then the finite-time controller is designed based on this zeroobservation-error assumption.
• From the perspective of guidance performance, the RMP-GLs can achieve various optimal performance needs, while, except terminal constraints, the MS-GLs cannot attain other guidance performance needs.
• Furthermore, by examining the function ( ,!, d̂ T ), the non-smooth feedback control c 1 r|!|↵ sgn(!) can lead to a large magnitude of the guidance command and likely cause the control saturation to happen at the start of the intercept.

4. Convergence analysis of LOS rate

• This section presents the main theoretical results of the proposed RFTG law.
• Then, the zero solution of the closed-loop guidance system (17) is locally finite-time stable.
• Next, the authors establish the corresponding convergence of the LOS rate.
• The objective of dealing with the control saturation in these two guidance laws is to enable the adaptive laws to work so that the parameters of the target maneuvers can be e↵ectively estimated.
• Admittedly, a number of assumptions are made for the system states in Theorem 3.

5. Simulations

• Numerical comparison results for the RFTG law and the other three guidance laws are presented.
• In the simulation, the interceptor’s initial position is set at the origin, its initial velocity is 1000m/s, and its initial flight path angle is 50 deg.
• In addition, the divergence of the AGL that begins at approximately 5 s is caused by the parameter adaption.
• Figure 1d depicts the flight trajectories, and, correspondingly, table 1 gives the homing accuracy of the four guidance laws, demonstrating homing precision of the RFTG law is better than that of the other three in the presence of the target maneuver.
• As described in Figs. 3c and 3d, the LOS rate in Case 7 is quickly nullified after the sudden change of the target maneuver at 5 s, while the LOS rate in Case 8 is stabilized through a relative large transient period due to the control saturation, which is the adverse impact of the large magnitude of the target acceleration.

6. Conclusion

• The integrated continuous finite-time disturbance observer /bounded continuous finitetime stabilizer strategy is proposed to approach the problem of intercepting a maneuvering target with an unpredictable evasive strategy.
• The local FTISS of the proposed RFTG law is established in the case of the bounded derivative of the e↵ect of the target maneuver.
• Numerical comparisons demonstrate the favorable guidance performance of the RFTG law in terms of the homing accuracy and the estimation of the e↵ect of the target maneuver.
• Furthermore, the RFTG law can e↵ectively stabilizes the LOS rate in the presence of the control saturation, and achieve the high-precision miss-distances in the four typical cases of the unpredictable maneuverable target interception.

Figures

Fig. 1. Simulation results for MS-GLs.

Fig. 2. Simulation results for Cases 1, 2, 3 and 4.

Table 1. Summary of homing accuracy

Fig. 3. Simulation results for Cases 5, 6, 7 and 8.

Frequently asked questions

Q1. What have the authors contributed in "Robust finite-time guidance against maneuverable targets with unpredictable evasive strategies" ?

This paper presents a robust finite-time guidance ( RFTG ) law to a short-range interception problem. By robustly stabilizing a line-of-sight rate, this paper proposes an integrated continuous finite-time disturbance observer/bounded continuous finite-time stabilizer strategy. Moreover, convergence properties of the LOS rate in the presence of control saturation are discussed. 

Q2. What are the design tools for the UMTI?

The design tools mainly consist of adaptive control, sliding mode control, high-gain control, etc. In [7],Preprint submitted to Aerospace Science and Technology April 3, 2018the authors parameterize upper bounds of the target acceleration and then develop the resulting parameter adaptive laws, thus handling the target maneuver. 

Q3. What are the conditions needed to achieve intercept?

To achieve intercept, three conditions are needed: ! = 0, sin(M )a Msin( T )a T , and ṙ0 < 0, where ṙ 0 is the initial interceptor-target range rate. 

Q4. What is the objective of the two guidance laws?

The objective of dealing with the control saturation in these two guidance laws is to enable the adaptive laws to work so that the parameters of the target maneuvers can be e↵ectively estimated. 

Q5. What are the fundamental concerns in adaptive control design?

As such, the control saturation and the speed of the parameter adaptation are two fundamental concerns in adaptive control design [8, 9, 10]. 

Q6. What is the auxiliary signal in the fast adaptive guidance law?

A fast adaptive guidance law in [11] induces an auxiliary signal to prevent the control saturation from destroying the parameter adaptation. 

Q7. how is the zero solution of the observation-error dynamics?

0. Using LaSalle’s invariance theorem, the zero solution of the observation-error dynamics (13) is globally asymptotically stable. 

Q8. What is the initial position of the interceptor?

In the simulation, the interceptor’s initial position is set at the origin, its initial velocity is 1000m/s, and its initial flight path angle is 50 deg. 

Q9. What is the LOS rate in Case 7?

As described in Figs. 3c and 3d, the LOS rate in Case 7 is quickly nullified after the sudden change of the target maneuver at 5 s, while the LOS rate in Case 8 is stabilized through a relative large transient period due to the control saturation, which is the adverse impact of the large magnitude of the target acceleration. 

Q10. What is the LOS rate of the closed-loop CFTDO?

Using the RFTG law (10), together with = ↵, the closed-loop closed-loop LOS rate dynamics are given by!̇ = c 1 |!|↵ sgn(!) + e d ,ė! 

Q11. What are the drawbacks of adaptive guidance laws?

Although the adaptive guidance laws work well in the above-mentioned scenarios, they have three drawbacks herein: 1) the guidance performance heavily depends on the convergence of adaptive parameters, while these parameters are easily prone to diverge when 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 hard to accurately parameterize 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.