Output feedback control of nonlinear systems via deterministic learning theory

In this paper, a deterministic learning based output feedback controller is designed for a class of nonlinear systems. Firstly, with the appropriately designed observer and controller, it is shown that the state observation and control error converge to a small neighborhood of zero exponentially in finite time, and a partial persistent excitation (PE) condition is satisfied. Secondly, by imposing an auxiliary filter and constructing a new Lyapunov function, the accurate approximation of closed-loop control system is achieved. Then, it is obtained that the neural weight estimation errors also converge to a small neighborhood of zero. The uncertain dynamics along the periodic trajectory can be locally-accurately identified by the radial basis function (RBF) neural networks (NNs) and stored in a constant RBF NNs. The obtained knowledge of system dynamics can be reused in the constant weight observer and controller with good performance. Simulation studies show the effectiveness of our approach.