On Sign-Projected Gradient Flow-Optimized Extended-State Observer Design for a Class of Systems With Uncertain Control Gain

If one cannot obtain the accurate prior information of the controlled object in advance, it will take much effort to get good dynamic performance. To this end, this article proposes an online estimation method to deal with disturbances and uncertainties for a class of systems with uncertain control gain. Based on the extended-state observer scheme, the estimation problem of disturbance and uncertain control gain is transformed to the convex optimization problem and solved by the sign-projected gradient flow, then the estimation can be applied to compensate disturbance and design controller. Moreover, the exponential and ultimate boundedness is obtained for the derived closed-loop system, together with rigorous theoretical analysis and proof. Finally, both the numerical simulations and the experiment on a brushless dc motor demonstrate that the proposed design has a better tracking performance and stronger robustness to deal with disturbances and uncertainties compared with the existing methods.