Multiple Model Reference Adaptive Control With Blending for Nonsquare Multivariable Systems

In this article, we develop a multiple model reference adaptive controller (MMRAC) with blending. The systems under consideration are nonsquare, i.e., the number of inputs is not equal to the number of states; multi-input, linear, time-invariant with uncertain parameters that lie inside of a known, compact, and convex set. Moreover, the full state of the plant is available for feedback. A multiple model online identification scheme for the plant's state and input matrices is developed that guarantees the estimated parameters converge to the underlying plant model under the assumption of persistence of excitation. Using an exact matching condition, the parameter estimates are used in a control law such that the plant's states asymptotically track the reference signal generated by a state-space reference model. The control architecture is proven to provide boundedness of all closed-loop signals and to asymptotically drive the state tracking error to zero. Numerical simulations illustrate the stability and efficacy of the proposed MMRAC scheme, even in the presence of noise. Statistical analysis is included to showcase the improvements of using multiple models.