Normal form and adaptive control of mimo non-canonical neural network systems

This paper presents a new study on adaptive control of multi-input multi-output (MIMO) neural network system models in a non-canonical form. Different from canonical-form nonlinear systems whose neural network approximation models have explicit relative degrees, non-canonical form nonlinear systems usually do not have such a feature, nor do their approximation models which are also in non-canonical forms. For adaptive control of non-canonical form neural network system models with uncertain parameters, this paper develops a new adaptive feedback linearization based control scheme, by specifying relative degrees and establishing a normal form of such systems, deriving a new system re-parametrization needed for adaptive control design, and constructing a stable controller for which an uncertain control gain matrix is handled using a matrix decomposition technique. System stability and tracking performance is analyzed. A detailed example with simulation results is presented to show the control design procedure and desired system performance.