Adaptive Tracking Control of Hybrid Switching Markovian Systems with Its Applications

Abstract

This paper focuses on the model reference adaptive tracking control problem of uncertain hybrid switching Markovian systems. The stochastic multiple piecewise Lyapunov function method is set up for designing a hybrid switching signal and a piecewise dynamic switching adaptive controller. The hybrid switching signal is presented to improve the adaptive tracking capability by providing plenty of adjusting time during the stochastic switching stage. A piecewise dynamic parameter projection adaptive control technique is developed, which provides more freedom in designing a model reference adaptive law. A set of piecewise dynamic switching adaptive controllers are designed such that all the signals of the tracking error system remain within a bounded region under the proposed hybrid switching signal, and the tracking error converges to a neighborhood of zero where the radius of the neighborhood can be made arbitrarily small by choosing the regulation parameters appropriately. Finally, the developed adaptive tracking control theory of uncertain hybrid switching Markovian systems is illustrated by using a numerical example and an application example of an electro-hydraulic model.