Optimal Attitude Regulation of Quadrotors With Prandtl–Ishlinskii Hysteresis: A Nash Equilibrium Solution

The presence of nonlinearities and actuator faults poses significant challenges to achieving optimal control of quadrotors. This article investigates an adaptive dynamic programming algorithm to solve the optimal attitude regulation problem of quadrotors with nonlinear hysteresis. The optimal regulation problem is modeled as a graphical game, and optimality is defined by the Nash equilibrium. A nonlinear hysteresis inverse model is first designed to compensate for the nonlinearity of the hysteresis. To eliminate matched disturbances caused by compensation errors, an integral sliding mode mechanism is proposed, improving fault tolerance. Through problem transformation, the Nash equilibrium is achieved by solving interconnected Hamilton–Jacobi–Bellman equations. A data-based policy iteration algorithm is then developed to numerically solve the approximate optimal solution using a least-squares approach. Finally, a quadrotor team is employed to verify the effectiveness of the proposed algorithm.