Agile Missile Controller Based on Adaptive Nonlinear Backstepping Control

This paper deals with a nonlinear adaptive autopilot design for agile missile systems. In advance of the autopilot design, an investigation of the agile turn maneuver, based on the trajectory optimization, is performed to determine state behaviors during the agile turn phase. This investigation shows that there exist highly nonlinear, rapidly changing dynamics and aerodynamic uncertainties. To handle of these difficulties, we propose a longitudinal autopilot for angle-of-attack tracking based on backstepping control methodology in conjunction with the time-delay adaptation scheme.

💡 Research Summary

The paper addresses the challenging problem of autopilot design for the agile‑turn phase of high‑angle‑of‑attack missiles, a flight regime characterized by strongly nonlinear dynamics, rapidly varying aerodynamic coefficients, and significant uncertainties due to fuel consumption, mass shift, and roll‑pitch coupling. After a brief review of existing linear and nonlinear approaches, the authors first perform a trajectory‑optimization study to extract the time histories of key state variables (angle of attack, pitch rate, body‑axis velocities) during an aggressive 180° heading‑reversal maneuver. This analysis reveals steep variations in α and q, confirming the need for a control law that can cope with fast dynamics and parameter drift.

A nonlinear missile model is presented in the body frame, assuming a fixed 90° roll angle and neglecting gravity. The equations of motion (1)–(3) include longitudinal velocity u, vertical velocity w, pitch rate q, thrust T, and aerodynamic forces/moments expressed through dynamic pressure Q, reference area S, Mach number M, and control‑surface deflection δ. Mass, inertia, and center‑of‑gravity are modeled as linear functions of time to capture the boost‑phase mass loss.

The control design is built on a strict‑feedback (backstepping) structure. By defining the state vector x₁ = α (angle of attack) and x₂ = q (pitch rate) and introducing virtual control variables z₁, z₂, the authors derive recursive control laws that guarantee convergence of the tracking errors e₁ = x₁ – x₁d and e₂ = x₂ – x₂d in finite time, provided the system is exactly known. However, the presence of unknown additive terms Δ₁ and Δ₂—originating from aerodynamic perturbations, roll‑pitch coupling, and unmodeled dynamics—degrades performance.

To compensate these uncertainties, a time‑delay adaptation scheme is incorporated. The core idea, based on Youcef‑Toumi and Wu’s time‑delay control, is that a continuous function f(t) can be approximated by its delayed value f(t‑L) when the delay L is sufficiently small. By treating Δ₁(t) and Δ₂(t) as continuous, the authors estimate them as Δ̂₁(t) = Δ₁(t‑L) and Δ̂₂(t) = Δ₂(t‑L) using a first‑order lag (single‑lag) filter with a small time constant dτ (0.02 s in the simulations). These estimates are then injected into the backstepping control law, yielding a compensated input that remains continuous and smooth. Theoretical stability is established through two theorems, which show that the closed‑loop system is uniformly ultimately bounded and that the estimation error converges as dτ → 0.

Three simulation scenarios are presented using a high‑fidelity 6‑DOF nonlinear missile model. (1) Step‑command tracking demonstrates basic performance; with 30 % multiplicative aerodynamic uncertainties and additive roll‑coupling terms, the uncompensated controller exhibits noticeable steady‑state error, while the time‑delay‑adapted controller tracks the command with negligible error. (2) A realistic agile‑turn maneuver uses the angle‑of‑attack profile obtained from the earlier trajectory optimization as the reference. The adaptive controller follows the aggressive α trajectory accurately, despite rapid changes in q and the presence of mass‑inertia variation. (3) An end‑to‑end engagement scenario combines the agile turn with a terminal homing phase. After the turn, the autopilot switches from angle‑of‑attack control to body‑acceleration control via a simple blending logic and a PI outer loop. The missile successfully intercepts a target located in its rear hemisphere, confirming the controller’s robustness across flight phases.

Actuator dynamics are modeled as second‑order systems (natural frequency 180 rad/s, damping ratio 0.7) with saturation limits of ±30° and a rate limit of 450°/s. Controller gains are chosen as K₁=12, K₂=25, with PI gains P_K=0.0098 and I_K=0.34. The simulations show smooth control effort, no chattering, and satisfactory performance even under severe uncertainties.

In conclusion, the paper makes three principal contributions: (1) a detailed state‑behavior analysis of the agile‑turn phase obtained via trajectory optimization; (2) a novel adaptive nonlinear autopilot that merges backstepping with a practical time‑delay estimation scheme, enabling real‑time compensation of both multiplicative and additive uncertainties; (3) extensive 6‑DOF nonlinear validation that demonstrates the controller’s effectiveness in step response, aggressive maneuver tracking, and full‑mission engagement. The authors acknowledge that the accuracy of the time‑delay approximation depends on the chosen delay constant and that future work should address hardware‑in‑the‑loop testing, larger communication delays, and extension to full three‑axis (roll‑pitch‑yaw) integrated control.