Optimal sampling in nonlinear systems using the Koopman operator
DOI:
https://doi.org/10.17979/ja-cea.2026.47.13670Keywords:
Optimal sampling, Optimal control theory, Applications of nonlinear analysis and design, Networked systemsAbstract
This article designs optimal sampling patterns for the design of quadratic regulators with free final time for nonlinear systems. The nonlinear systems are represented using the Koopman operator, which allows the use of previous results for linear systems to solve the problem of determining the optimal sampling. When the Koopman linearization is closed, the representation of the nonlinear system as a finite-dimensional linear system is exact. If the linearization is infinite, it is truncated to a finite value in order to design suboptimal patterns for the nonlinear system through its approximate linearized version and the previous results for linear systems. The basic theory is presented, along with the results obtained for some examples.
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Copyright (c) 2026 Asier Ibeas, Pedro Balaguer, José Carlos Alfonso
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