On the design of robustly performing adaptive controllers for partially modelled systems

The problem of designing robustly performant adaptive controllers with explicit incorporation of a representation for the model-process mismatch (MPM) is addressed in this paper. Global stability conditions are derived for a discrete-time pole-zero placement (PZP) adaptive controller, assuming a set membership statement for the process transfer function with uncertainty characterized by conic bounded operators. The overall system is decomposed into interconnected operators whose I/O properties are studied using the functional analysis approach pioneered by Zames [17]. Using the sector stability theorem [2] and the sectoricity properties of systems with cone-bounded uncertainties [3], frequency-domain measures quantifying the robustness/ performance tradeoff are derived. The effect of smoothing and antialiasing filters and the properties of various parameter adaptation algorithms (PAA) regarding this tradeoff are studied.