L₁ adaptive controller for MIMO systems with unmatched uncertainties using modified piecewise constant adaptation law

This paper presents the L₁ adaptive controller for a class of multi-input multi-output (MIMO) systems with both matched and unmatched nonlinear uncertainties. A modification of the piecewise constant adaptive law is introduced based on the history of the past samples. Compared with the standard L₁ adaptive law with piecewise constant adaptive law, here the performance bounds decay much faster as the sample period decreases, yielding better performance at a given sample period, or less stringent requirements on the computation and measurement frequency for a given performance level. Simulation results verify the theoretical findings.