Intermittent Control of Unstable Multivariate Systems with Uncertain System Parameters

Abstract

Multivariable intermittent control (MIC) combines stability with flexibility in the control of unstable systems. Using an underlying continuous-time optimal control design, MIC uses models of the physical system to generate multivariate open-loop control signals between samples of the observed state. Using accurate model values of physical system parameters, stability of the closed loop system is not dependent upon sample interval. Here we consider the sensitivity of MIC to inaccurate model values of system parameters. The high dimensionality of multiple parameters combined with an unstable open loop system ensures the ratio of hyper-volumes containing good to bad parameter combinations resembles a "needle in a haystack". Is this sensitivity a problem or an asset? Prediction error between open loop and observed states provides the basis for triggering a sampling event but is also sensitive to inaccurate model values. Investigation of the mapping between prediction error and model values of physical parameters illustrates the value of prediction error to identify combinations of parameters giving stable closed loop control with low state error, similar to that provided by accurate values. Sensitivity of prediction error to model inaccuracy is potentially an asset facilitating adaptation and supporting the rationale for MIC to combine control with flexibility.