Adaptive Model Predictive Control with Generalized Orthonormal Basis Functions
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An adaptive model predictive control (MPC) method using models derived from orthonormal basis functions is presented. The defining predictor dynamics are obtained from state-space realizations of finite truncations of generalized orthonormal basis functions (GOBF). A structured approach to define multivariable system models with customizable, open-loop stable linear dynamics is presented in Chapter 2. Properties of these model objects that are relevant to the adaptation component of the overall scheme, are also discussed. In Chapter 3, non-adaptive model predictive control policies are presented with the definition of extended state representations through filter operations that enable output feedback. An infinite horizon set-point tracking policy which always exists under the adopted modeling framework is presented. This policy and its associated cost are included as the terminal stage elements for a more general constrained case. The analysis of robust stability guarantees for the non-adaptive constrained formulation is presented, under the assumption of small prediction errors. In Chapter 4, adaptation is introduced and the certainty equivalence constrained MPC policy is formulated under the same framework of its non-adaptive counterpart. Information constraints that induce the excitation of the signals relevant to the adaptation process are formulated in Chapter 5. The constraint generation leverages the GOBF model structure by enforcing a sufficient richness condition directly on the state elements relevant to the control task. This is accomplished by the definition of a selection procedure that takes into account the characteristics of the most current parameter estimate distribution. Throughout the manuscript, illustrative simulation examples are provided with respect to minimal plant models. Concluding remarks and general descriptions for potential future work are outlined in Chapter 6.