Gain-scheduled control of the ONR UCAV       Gain-scheduled control of the ONR UCAV       Gain-scheduled control of the ONR UCAV

Introduction


The dynamics of Unmanned Combat Air Vehicles (UCAVs) undergoing aggressive maneuvers are highly nonlinear and time-varying. One approach towards modeling UCAVs involves linearizing the dynamics of the UCAV around various points in the flight envelope. Then, the composite model of the UCAV can be given as a linear parameter-dependent model, with the parameters being the flight conditions. A comprehensive effort towards identifying such models is currenly being undertaken at Texas A & M University

We describe here research efforts towards a systematic design procedure for controller synthesis for the linear parameter-dependent ONR UCAV models. Traditional techniques for controller synthesis consist of designing a single controller that is intended to function across varying flight conditions. These include constant state-feedback, as well as the celebrated LQR/LQG and H-infinity controllers. While these control techniques can be sometimes proven to work (i.e., stabilize the system or provide acceptable performance), they can be quite conservative, especially when the flight conditions vary considerably.

Gain-scheduled controller design offers the potential much more aggressive control design. The basic idea is to synthesize a series of dynamic controllers, one for each linearized model of the UCAV around a flight condition, and then "schedule" these controllers according to the actual flight condition. An ad hoc implementation of such a scheme is not guaranteed to work; however, it is possible to develop a gain-scheduling scheme, using Lyapunov functions, that is guaranteed to work across various flight regimes.

Another advantage of an approach based on Lyapunov functions is that it can be extended to handle constraints other than mere stability. Stability requires the Lyapunov function to decrease along the trajectories of the parameter-varying system. Additional constraints on the Lyapunov function can be used to design controllers with guaranteed performance. Examples of performance measures are the energy in the state vector, and peak values of signals of interest; in several instances, it is desirable that these performance measures be small. And gain-scheduled controllers that minimize upper bounds on these performance measures can be designed.

The technical details behind synthesizing improved gain-scheduled controllers can be found in the following reports and publications, and the references therein:

  • F. Wang and V. Balakrishnan, ``Improved Stability Analysis and Gain-Scheduled Controller Synthesis for Parameter-Dependent Systems''. In Proc. IEEE Conf. on Decision and Control, pages 1771--1776, Tampa, FL, December 1998.

  • V. Balakrishnan and F. Wang. `` Efficient Computation of a Guaranteed Lower Bound on the Robust Stability Margin of Uncertain Systems''. In Proc IEEE Conf. on Decision and Control, pages 4406-4407, Tampa, FL, December 1998.

  • V. Balakrishnan and F. Wang. `` Efficient Computation of a Guaranteed Lower Bound on the Robust Stability Margin of Uncertain Systems''. In IEEE Trans. Aut. Contr., AC-44(11):2185--2190, January 1999.

  • F. Wang and V. Balakrishnan, `` Robustness analysis and gain-scheduled controller synthesis for rational parameter-dependent uncertain systems using parameter-dependent Lyapunov functions''. In the Proc. IEEE Conf. on Decision and Control, December 1999.

  • F. Wang and V. Balakrishnan, `` Improved Stability Analysis and Gain-Scheduled Controller Synthesis for Parameter-Dependent Systems''. Submitted to the IEEE Trans. AC, September 1999

    • Gain-scheduled controllers for some UCAV models

    We present the application of gain-scheduled controller design techniques on the models for UCAVs developed at Texas A & M University: 
    Professor Venkataramanan Balakrishnan ragu@ecn.purdue.edu
    This document was last modified March 20, 2001.