Adaptive Control of MIMO Systems Using Sparsely Parameterized Controllers

In applications, it is usually desirable to implement the simplest controller in terms of signal interconnections and controller order. In accordance with this goal, this paper presents an adaptive output-feedback control technique for MIMO systems, where the order and structure of each SISO entry of the controller can be assigned an arbitrary parameterization. The first parameterization is based on a MIMO input-output model of fixed window length. The second parameterization constrains all SISO entries of each row of the controller to have the same denominator of specified order; the third parameterization constrains all SISO entries of the controller to have the same denominator of specified order; and the fourth parameterization allows complete flexibility in setting the structure and order of each SISO entry of the controller. PID, infinite impulse-response, finite impulse-response, and sparsely parameterized controllers can be specified as special cases. This paper 1) defines the regressor structure for each parameterization; 2) enumerates the number of updated coefficients of each parameterization; 3) provides bounds on the McMillan degree of each parameterization; and 4) provides numerical examples to illustrate the relative effectiveness of each parameterization.