Passivity-based Robust Design of Proportional-Derivative Navigation Guidance Law

Abstract

This article proposes a robust augmented proportional navigation guidance (PNG) law synthesis based on the passivity approach and applied to missiles whose ∞ight control dy- namics are represented by a second-order model with bounded parametric uncertainties. Instrumental in designing the proposed guidance law is an appropriate subsystem decom- position that enables passivation by both feedback and feedforward control. L2 stability of the missile-target closed-loop system is then inferred by the application of the passivity theorem and the extension of the Kalman-Yakubovich-Popov lemma to linear-time varying systems, thus ensuring robust stability of the null miss distance when the maneuvering target acceleration is in L2. Numerical simulations demonstrate the efiectiveness of the proposed guidance law. proposed. Uncertainties in the target and in the ∞ight control system of the missile are taken into account in the guidance synthesis by means of a parameter adaptation scheme. The ∞ight control dynamics are modeled as a second-order state-space form to which is added exogenous disturbances representing approxi- mation errors due to the use of curve fltting techniques in the modeling of the aerodynamic coe-cients. The guidance law proposed in, 4 although proven efiective by means of numerical simulations that show reduced miss distances as compared with PNG and sliding mode guidance laws, is relatively complex, showing little physical insight. Building upon previous results obtained by the authors in, 5 we propose in this article a robust augmented proportional navigation guidance law for the interception of maneuvering targets with acceleration in L2. Our proposed law is labeled proportional-derivative navigation guidance or PDNG. The pursuer dynamics is modeled as a second-order linear uncertain system, with parametric uncertainties expressed in polytopic form, whereas the missile-target relative kinematics is represented by a double integrator mapping the missile-target relative lateral accelerations to the miss distance. The terminal guidance law is obtained by a passivation of the missile-target closed-loop dynamics, which is represented by a linear, parameter-uncertain, time-varying model. This model is expressed in a suitable feedback subsystem decomposition. The time dependence arises from the fact that the PNG law is equivalent to an output feedback whose gains are functions of the time to go. The robust strict passivity property is obtained by output feedback and robust feedforward control laws whose parameters are tuned by applying an extension of the Kalman-Yakubovich- Popov (KYP) lemma to linear-time varying systems 6 and leveraging previous results obtained by the authors