Deterministic learning from NN output feedback control of Brunovsky systems

Recently, a deterministic learning theory was presented in which an appropriately designed adaptive neural controller can learn the system internal dynamics while attempting to control a class of nonlinear systems. In this paper, we investigate deterministic learning from adaptive neural network (NN) control of Brunovsky systems by using only output measurements. A high-gain observer (HGO) is first adopted to accurately estimate the derivatives of the system output. Then, an adaptive output feedback NN controller is proposed to guarantee that the output tracking error is small and bounded. The difficulty caused by the unknown affine term in deterministic learning is analyzed, the measures to eliminate peaking phenomenon associated with the use of HGO is proposed. When a partial persistent excitation (PE) condition is satisfied, tracking to an output recurrent reference trajectory and the exponential stability of the linear time-varying (LTV) system can be guaranteed. Locally accurate identification of the unknown closed-loop system dynamics can be achieved along a periodic orbit of closed-loop estimated signals. Consequently, learning from NN output feedback control of Brunovsky system is implemented. A neural learning control scheme is proposed which can effectively recall and reuse the learned knowledge to achieve the well output tracking performance. It simplifies the controller design, saves the computing time and decreases amounts of output actuators in practical implementation.