Adaptive Control via Non-Convex Optimization

The coupling of process estimation and controller design has proved to be a natural way to proceed with the control of engineering systems. In adaptive control, well-known and efficient algorithms have been developed for linear systems. However, it has been observed that when the estimation problem is poorly conditioned, the process becomes unstable, at least locally. In control experiments, this is manifested as a “bursting” phenomenon where both the inputs and outputs have huge oscillations. Several authors have suggested coupling the estimation and controller design problem and solving it as a single nonlinear program. This problem is nonconvex and typically consists of a convex objective with bilinear equations. In this paper, we develop a global branch and bound optimization algorithm that follows the prototype of Horst [6] and exploits the NLP structure to address the stability problem. In addition to an exposition of the algorithm as well as development of stability and convergence results, the approach is applied to a small example in order to demonstrate how bursting has been eliminated.