Attitude tracking control of quadrotor unmanned aerial vehicle based on an adaptive predefined time value iteration approach

Zhixin Feng; Renming Yang; Zhixin Feng; Renming Yang

doi:10.3934/math.2026260

AIMS Mathematics

2026, Volume 11, Issue 3: 6297-6328. doi: 10.3934/math.2026260

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Attitude tracking control of quadrotor unmanned aerial vehicle based on an adaptive predefined time value iteration approach

Zhixin Feng ,
Renming Yang ^,

School of Information Science and Electrical Engineering, Shandong Jiaotong University, Jinan, 250357, Shandong, China

Received: 18 December 2025 Revised: 03 March 2026 Accepted: 05 March 2026 Published: 12 March 2026
MSC : 93C10, 93C40, 93D05, 93D21

This paper addresses the attitude tracking problem of quadrotor unmanned aerial vehicles (UAVs) by introducing a novel predefined-time stable adaptive value iteration (PTS-AVI) control scheme. Unlike conventional value iteration-based adaptive dynamic programming (Ⅵ-ADP) methods—where the running cost is independent of the value function—the proposed cost function explicitly incorporates the value function $ V $, thereby ensuring predefined-time stability (PTS) throughout both the training and deployment phases. This functional dependency was systematically addressed via an auxiliary time-scale partial differential equation (PDE) formulated in the $ s $-domain. To circumvent the need to solve the complex Hamilton–Jacobi–Bellman (HJB) equation directly, a parameter update method was employed to approximate its solution, yielding an optimal control policy that satisfies predefined-time stability criteria. In addition, a high-precision predefined-time disturbance observer was designed to estimate and compensate for unknown disturbances. Both theoretical analysis and simulation results confirmed that the proposed control scheme guarantees state convergence to equilibrium within a user-specified time, regardless of initial conditions. This work differs from existing studies by integrating predefined-time stability requirements into the Ⅵ-ADP formulation and coupling it with a predefined-time disturbance observer for attitude tracking.
- predefined-time stable,
- adaptive value iteration,
- unmanned aerial vehicle,
- adaptive dynamic programming,
- disturbance observer
Citation: Zhixin Feng, Renming Yang. Attitude tracking control of quadrotor unmanned aerial vehicle based on an adaptive predefined time value iteration approach[J]. AIMS Mathematics, 2026, 11(3): 6297-6328. doi: 10.3934/math.2026260

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Abstract

This paper addresses the attitude tracking problem of quadrotor unmanned aerial vehicles (UAVs) by introducing a novel predefined-time stable adaptive value iteration (PTS-AVI) control scheme. Unlike conventional value iteration-based adaptive dynamic programming (Ⅵ-ADP) methods—where the running cost is independent of the value function—the proposed cost function explicitly incorporates the value function $ V $, thereby ensuring predefined-time stability (PTS) throughout both the training and deployment phases. This functional dependency was systematically addressed via an auxiliary time-scale partial differential equation (PDE) formulated in the $ s $-domain. To circumvent the need to solve the complex Hamilton–Jacobi–Bellman (HJB) equation directly, a parameter update method was employed to approximate its solution, yielding an optimal control policy that satisfies predefined-time stability criteria. In addition, a high-precision predefined-time disturbance observer was designed to estimate and compensate for unknown disturbances. Both theoretical analysis and simulation results confirmed that the proposed control scheme guarantees state convergence to equilibrium within a user-specified time, regardless of initial conditions. This work differs from existing studies by integrating predefined-time stability requirements into the Ⅵ-ADP formulation and coupling it with a predefined-time disturbance observer for attitude tracking.

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