Learning from neural control of general Brunovsky systems

In this paper, we investigate deterministic learning from adaptive neural control of general Brunovsky systems, in which the affine terms are unknown functions of system states. We firstly present an extension of a recent result on stability analysis of linear time varying (LTV) systems. We then analyze the difficulties caused by the unknown affine term in deterministic learning for general Brunovsky systems. By taking a state transformation, the closed-loop control system is transformed into a LTV form for which exponential stability can be guaranteed when the PE condition is satisfied. Consequently, locally-accurate approximation of the closed-loop control system dynamics can be achieved along a periodic orbit of closed-loop signals. Simulation studies are included to demonstrate the effectiveness of the approach