Multiple Model Adaptive Control with Blending in State Space - Lovi, Alex (University of Waterloo, 2025)
Adaptive Control (AC) provides a systematic framework for handling uncertainty in linear and non-linear systems. Single-model adaptive schemes such as Model Reference Adaptive Control (MRAC) and Adaptive Pole Placement Control (APPC) face inherent limitations when applied to systems with large parametric uncertainty, such as slow convergence rates and limited noise robustness. This has motivated researchers to investigate multiple-model strategies that employ several candidate plants to represent different regions of the operating space. In this thesis, we develop Multiple-Model Adaptive Control (MMAC) methodologies based on the blending of signals from multiple fixed models. We consider uncertain plants with known, compact, convex polytopic uncertainty. Our starting point is the design of a Multiple-Model Parameter Identification (MMPI) scheme that quickly and robustly identifies the uncertain plant parameters. In combination with a Model Reference Control (MRC) framework, this leads to a Multiple-Model Reference Adaptive Control (MMRAC) with blending for Linear, Time-Invariant (LTI), non-square (different number of inputs and outputs), multi-input systems, with full-state feedback. Under an exact matching condition, the parameter estimates are used to design a control input such that the plant states asymptotically track the reference signal generated by a state-space reference model. A procedure is provided to select the corner models based solely on the polytopic uncertainty. The proposed MMRAC guarantees the boundedness of all closed-loop signals and the asymptotic convergence of the state-tracking error to zero. Statistical analysis demonstrate improved tracking speed and robustness to noise compared with single-model approaches. The combination of MMPI with pole-placement techniques, allowed us to develop Multiple-Model Adaptive Pole Placement Control (MMAPPC) for LTI, square (same number of inputs and outputs), multivariable systems with full-state feedback, and for with LTI, Single-Input, Single-Output (SISO) systems via an intermediate state estimation step. The resulting controller again ensures the boundedness of all closed-loop signals, while also asymptotically placing the closed-loop eigenvalues at designer-specified locations. Statistical analysis shows a clear increase in robustness to noise relative to single-model schemes. These improvements were validated in the context of motion control of lateral vehicle dynamics, where multiple-model schemes consistently outperformed single-model approaches, including cases with slowly time-varying unknown parameters.
Keywords: Adaptive Control; Multiple Model; Polytopic Uncertainty; Uncertain Systems; Model Reference Adaptive Control; Pole Placement Adaptive Control