In this paper, a robust continuous guidance law with terminal angle constraint for intercepting maneuvering targets in the presence of autopilot lag is proposed and its finite-time stability is proved. First, assuming that the missile autopilot is sufficiently fast, a composite fast nonsingular terminal sliding mode guidance (CFNTSMG) law is presented. The proposed guidance law is obtained through a combination of fast nonsingular terminal sliding mode control theory and generalized disturbance observer (GDOB). The presented guidance law requires no priori information on target maneuver, which is estimated and compensated online by GDOB. Moreover, no discontinuous term exists in CFNTSMG law and therefore chattering is eliminated effectively. Next, viewing the missile autopilot as an uncertain second-order system, an integrated guidance and control dynamics is formulated and the systematic step-by-step backstepping technique is used to derive a new robust guidance law, which not only holds the advantages of CFNTSMG law, but also is insensitive to autopilot lag. At each backstepping step, novel continuous virtual/real control laws using finite-time control approach are designed and tracking differentiator is used to overcome the ‘explosion of complexity’ problem encountered with traditional backstepping method. Theoretical analysis and numerical simulations demonstrate the effectiveness of the proposed method.

Robust terminal angle constraint guidance law with autopilot lag for intercepting maneuvering targets

This paper proposes a new three-dimensional integrated guidance and control (IGC) scheme for intercepting maneuvering targets based on backstepping technique, nonlinear disturbance observer (NDOB) and nonlinear differentiator. To this end, a realistic six degree-of-freedom model, considering aerodynamic uncertainties, cross-coupling effects, model uncertainties and target maneuvers, is constructed first. In order to achieve precise interception, a multivariable NDOB is designed based on second-order sliding mode technique to estimate the lumped uncertainties in finite time. By virtue of the proposed adaptive law, the upper bounds of the lumped uncertainties and their gradients are not required in NDOB design. Using the reconstructed information, a robust IGC law is then synthesized following a backstepping-like way. At each step of backstepping design, a nonlinear differentiator is adopted to avoid analytical differentiation of the virtual control laws and therefore the associated problem of ‘explosion of terms’ is completely addressed. Detailed stability analysis shows that the line-of-sight (LOS) angular rates will converge to zero asymptotically. Finally, the IGC algorithm is tested through numerical simulations against a maneuvering target.

Three-dimensional multivariable integrated guidance and control design for maneuvering targets interception

This paper presents a new composite robust controller for a class of uncertain nonlinear systems through backstepping method and disturbance observer (DOB) technique. By designing a generalized disturbance observer (GDOB), the mismatched/matched uncertainty is estimated and compensated at each backstepping step. By virtue of the proposed GDOB, the proposed controller only requires the lumped uncertainties are differentiable and the higher-order derivatives are bounded. With the help of GDOB, the high-gain backstepping controller is also avoided completely. Asymptotical stability of the closed-loop system is established using direct Lyapunov method. An illustrative example of missile autopilot design is given and simulations are carried out to validate the proposed method.

Robust backstepping control for a class of nonlinear systems using generalized disturbance observer

Summary
This paper presents a robust impact angle constraint guidance law for maneuvering target interception in the presence of autopilot dynamics and input saturation. The presented guidance law is designed on the basis of a combination of adaptive backstepping control technique and higher-order sliding mode differentiator. Different from existing impact angle constraint guidance law using sliding mode control, the line-of-sight angular rate and impact angle tracking error are regulated by two different virtual control laws. Because the future course of action of the target, an independent entity, cannot be predicted beforehand, adaptive laws are introduced in guidance law derivation for disturbance rejection. Unlike dynamic surface control approach, higher-order sliding mode differentiator is adopted here as an alternative way to obtain the derivatives of the virtual control laws, thus leading to the exact tracking performance of backstepping control. Detailed stability analysis shows that both the line-of-sight angular rate and impact angle error can be stabilized in a small region around zero asymptotically. Simulation results explicitly show that accurate interception is achieved with a wide range of impact angles. Copyright © 2017 John Wiley & Sons, Ltd.

Adaptive backstepping impact angle control with autopilot dynamics and acceleration saturation consideration

This paper has proposed two continuous composite finite-time convergent guidance laws to intercept maneuvering targets in the presence of autopilot lag: one is for hit-to-kill and the other is for zeroing the line-of-sight (LOS) angular rate. More specifically, the nonlinear disturbance observer (NDOB) is used to estimate the lumped uncertainty online while the finite-time control technique is used to fulfill the design goal in finite time. The key feature in derivation of the proposed guidance law is that two integral-type Lyapunov functions are used to avoid analytic differentiation of virtual control law encountered with traditional backstepping. The finite-time stability of the closed-loop nonlinear observer-controller system is established using finite-time bounded (FTB) function and Lyapunov function methods. Numerical simulations with some comparisons are carried out to demonstrate the superiority of the proposed method.

Continuous composite finite-time convergent guidance laws with autopilot dynamics compensation.

Taking into consideration both the autopilot dynamics and uncertainties, this paper proposes a finite time convergent guidance law for homing missile to intercept a maneuvering target Firstly, an exact observer (differentiator) is employed to estimate the target maneuvers in finite time Then, a finite time convergent guidance law is designed based on the existing finite time sliding-mode control theory It is proved that the line-of-sight (LOS) angular rate converges to zero in finite time under the proposed guidance law Compared with the existing finite time guidance laws, this guidance law can compensate for the effects of the autopilot dynamics and uncertainties, and the information used for feedback control is much easier to obtain Finally, simulation results show that our scheme, as a finite time convergent algorithm, has strong robustness to bounded disturbances

Han Yan

Papers

A guidance law with finite time convergence considering autopilot dynamics and uncertainties