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Output Feedback Stabilization and Regulation of Nonlinear Systems
The problem of output regulation, the design feedback control laws so as to asymptotically track/reject exogenous inputs, is one of the defining problems in control theory. In the case of MIMO linear systems the problem was solved in fuIl generality several decades ago by introducing the celebrated "internal model principle." The latter claims that asymptotic regulation is achieved in presence of plant parameter variations “only if the controller utilizes feedback of the regulated variable, and incorporates in the feedback path a suitably reduplicated model of the dynamic structure of the exogenous signals which the regulator is required to process.”
The extension of the design techniques developed in the linear setting to nonlinear systems hides a lot of control challenges that make the nonlinear output regulation theory still an open research field. Design solutions proposed so far are limited to specific classes of nonlinear systems, mainly minimum-phase and without "extra" measurements besides the regulated variable. A “chicken-egg” dilemma arises in the design of the feedback control law and of the internal model whose "sequential" design, which is followed in the linear context, is not possible. The two units, rather, must be synergistically designed by adopting a mix of adaptive and identification tools. Furthermore, the quest for robustness is also a fundamental open research topic when designing nonlinear regulators to the point that, recently, it was shown that no finite dimensional robust asymptotic regulators exist if “unstructured” perturbations are considered.
Output regulation and internal model principle for linear systems
Fundamental tools: steady state, regulator equations, internal model property
Robust output regulation for nonlinear systems. Pre-processing and post-processing internal models. Wash out filters in the design of regulators in presence of extra measurements
The concept of robust minimum-phase and its use in the design of pre-processing regulators
The “chicken-egg” dilemma in the design of nonlinear post-processing regulators and the adoption of adaptive and identification tools for the synergistic design
Notions of robustness and the quest of robustness in nonlinear regulator design
Output regulation for hybrid systems: tools and main design solutions