Multivariable state feedback for output tracking MRAC for piecewise linear systems with relaxed design conditions

Abstract

The adaptive state feedback control problem for multivariable piecewise linear systems with switched parameters is considered in this paper. A direct state feedback model reference adaptive control (MRAC) scheme is developed based on high frequency gain matrix decompositions. This scheme relaxes a key design condition, namely the high frequency gain matrices sharing a common L matrix in their LDS decompositions, required by an existing adaptive control scheme. Under the usual slow system parameter switching condition, closed-loop stability (signal boundedness) and small output tracking error in the mean square sense are achieved. The proposed scheme is simulated on linearized NASA GTM models to demonstrate its effectiveness in tracking performance improvement.