Noncertainty-Equivalent Adaptive Missile Control Via Immersion and Invariance

This paper presents a new non certainty-equivalent adaptive control system for the control of a missile based on the immersion-and-invariance approach. The mathematical model of the missile represents the nonlinear longitudinal dynamics, and it is assumed that all the aerodynamic parameters (except the sign of a single control input gain) are not known. The objective here is to control the angle of attack of the missile. For the trajectory control of the angle of attack, a nonlinear non-certainty-equivalent adaptive control system is designed, and Lyapunov stability theory is used for stability analysis in the closed-loop system. The autopilot has a modular structure, which consists of a control module and a parameter estimator. In this non certainty-equivalent adaptive law, each estimated parameter is the sum of a partial estimate generated by an update law and a nonlinear function. For comparison, a traditional certainty-equivalent adaptive control system is also designed. A special feature of the designed non certainty-equivalent adaptive autopilot (unlike the certainty-equivalent adaptive systems) is that whenever the estimated parameters attain their true values, they remain frozen thereafter. Furthermore, it is shown that the trajectory of the closed-loop system, including the non certainty-equivalent adaptive law, is eventually confined to a manifold in the space of missile states and estimated parameters, and the autopilot asymptotically recovers the performance of a deterministic control system. Simulation results for the non certainty-equivalent adaptive and certainty-equivalent adaptive laws are presented. These results show that the designed autopilots accomplish trajectory control of the angle of attack despite uncertainties in the system parameters, but for properly chosen feedback and adaptation gains, the trajectory tracking performance is better with the non certainty-equivalent adaptive law