2021/01/07 by Joel A. Rosenfeld, Rosenfeld, Joel A., Benjamin P. Russo +3
Computer Science · Decision Sciences · Engineering · Physics and Astronomy · #46E22 #93-08 #Control Systems and Identification #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.2101.02646
openalex publication_date 2021/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Conventionally, data driven identification and control problems for higher\norder dynamical systems are solved by augmenting the system state by the\nderivatives of the output to formulate first order dynamical systems in higher\ndimensions. However, solution of the augmented problem typically requires\nknowledge of the full augmented state, which requires numerical differentiation\nof the original output, frequently resulting in noisy signals. This manuscript\ndevelops the theory necessary for a direct analysis of higher order dynamical\nsystems using higher order Liouville operators. Fundamental to this theoretical\ndevelopment is the introduction of signal valued RKHSs and new operators posed\nover these spaces. Ultimately, it is observed that despite the added\nabstractions, the necessary computations are remarkably similar to that of\nfirst order DMD methods using occupation kernels.\n