Data-based constrained H∞ optimal control for unknown nonlinear systems via adaptive dynamic programming

Peyman Ahmadi, Aref Shahmansoorian and Mehdi Rahmani

International Journal of Systems Science, 2026, vol. 57, issue 3, 868-882

Abstract: This paper introduces a method for designing the $ H_\infty $ H∞ optimal control for unknown continuous-time nonlinear polynomial systems with input constraints. The problem is formulated as a two-player zero-sum game, in which the Nash condition holds. Initially, the zero-sum game is relaxed to a sum of squares (SOS)-based policy iteration (PI) problem. Adaptive dynamic programming (ADP) is then employed to enhance the proposed approach in systems with inaccurate models. Moreover, the proposed model-free control approach can apply asymmetric constraints on the control input using the concept of inverse optimal control (IOC). This approach does not rely on computationally expensive numerical solutions for model approximation methods. Instead, it introduces an ADP-based sum-of-squares programming, which is computationally tractable. The stability of the proposed control scheme is theoretically guaranteed using the Lyapunov technique, and its performance and effectiveness are illustrated through two numerical examples.

Date: 2026
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DOI: 10.1080/00207721.2025.2515224

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