ADAPTIVE TRACKING CONTROL OF HYBRID SWITCHING MARKOVIAN SYSTEMS WITH ITS APPLICATIONS

This paper focuses on the model reference adaptive tracking control problem of un-certain 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 adap-tive 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 de-signing 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 regula-tion 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.