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Kernel-based multi-step predictors for data-driven analysis and control of nonlinear systems through the velocity form
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We propose kernel-based approaches for the construction of a single-step and multi-step predictor of the velocity form of nonlinear (NL) systems, which describes the time-difference dynamics of the corresponding NL system and admits a highly structured representation. The predictors in turn allow to formulate completely data-driven representations of the velocity form. The kernel-based formulation that we derive, inherently respects the structured quasi-linear and specific time-dependent relationship of the velocity form. This results in an efficient multi-step predictor for the velocity form and hence for nonlinear systems. Moreover, by using the velocity form, our methods open the door for data-driven behavioral analysis and control of nonlinear systems with global stability and performance guarantees.
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Kernelized offset-free data-driven predictive control for nonlinear systems
Kernelized velocity-form models yield an offset-free data-driven predictive controller for nonlinear systems, learned by least squares and supported by feasibility and stability conditions.
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