Inverse optimal incremental control of nonlinear jump-diffusion systems

Yuanhong Ren, Dingli Hua, Mingxuan Shen and Guangchen Zhang

Applied Mathematics and Computation, 2026, vol. 508, issue C

Abstract: In this study, we address the challenge of solving the inverse optimal incremental control problem for nonlinear jump-diffusion systems by proposing an innovative inverse optimal incremental controller framework. A pivotal aspect of our approach lies in the novel utilization of an auxiliary incremental controller as a cornerstone for constructing the inverse optimal controller. This design not only ensures that the resultant controller is optimal in the sense of minimizing a meaningful cost functional but also imparts upon the closed-loop jump-diffusion system the property of incremental global K∞-exponential stability. This dual capability of achieving optimality and robust stability underscores the significance and novelty of our proposed controller design. Leveraging our inverse incremental controller design, we derive a comprehensive set of conditions that guarantee the inverse incremental H∞ control of nonlinear jump-diffusion systems. Simultaneously, we develop a methodology for estimating the incremental Hamilton-Jacobi inequality (iHJI), which serves as a cornerstone for validating the controller's performance. We present two illustrative engineering examples, showcasing the practical implications and robustness of our approach.

Keywords: Nonlinear jump-diffusion systems; Inverse incremental controller; Incremental H∞ control (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:508:y:2026:i:c:s0096300325003698

DOI: 10.1016/j.amc.2025.129643

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