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Adaptive dwell-time switching in unfalsified control

We examine a data-dependent dwell-time switching algorithm in which the dwell-time is constrained to grow in proportion to the reciprocal of an adaptively-computed hysteresis variable ĥ(t) that converges to zero. This is in contrast to the Morse-Mayne-Goodwin (MMG) hysteresis switching algorithm in which usually a fixed hysteresis constant h > 0 is used. The algorithm is proved to be globally stabilizing assuming feasibility and τc-cost-detectability. It has the attractive property that the gap between optimal and achieved unfalsified performance levels are at each time bounded above by the current value of the hysteresis variable ĥ(t), thereby ensuring asymptotically optimal performance. A simulation example demonstrating this performance improvement is presented.