A Dynamic Neural Network-Based Sliding Mode Observer Method for a Class of Uncertain Dynamic Systems

A dynamic neural network (DNN)-based observer design is presented, which amalgamates an adaptive neural network-based technique with a finite-time sliding mode estimation method. The proposed observer design is motivated by practical quadrotor unmanned aerial vehicle tracking control applications, where direct sensor measurements of translational and rotational rates are not available for feedback. While sliding mode estimation strategies are well established as an effective means to compensate for bounded disturbances and dynamic model uncertainty, the proposed observer design employs a feedforward adaptive DNN-based estimation term in addition to a robust, high-gain feedback sliding mode element. The use of the DNN-based term in the estimator design is motivated by the desire to improve transient performance and reduce steady state error. In addition, the proposed sliding mode estimator design is proven to compensate for input-multiplicative parametric model uncertainty. To the best of the authors' knowledge, this is the first DNN-based sliding mode estimator result to rigorously prove asymptotic state estimation in the presence of parametric actuator uncertainty. A Lyapuov-based stability analysis is utilized to prove that the proposed DNN-based observer achieves asymptotic estimation of the quadrotor altitude and attitude rates in the presence of model uncertainty and bounded disturbances (e.g., sensor noise). Numerical simulation results are also provided to demonstrate the improved performance that is achieved by incorporating the adaptive DNN in the observer.