NARMAX l2 gain control: An approximate-inverse approach

This paper presents a proposal for a novel empirically based l₂ controller design technique for affine nonlinear autoregressive exogenous signal (NARMAX) characterisable plants. In single sensitivity cases, the method requires the use only of maximum likelihood NARMAX identification and a novel regularisation method which obtains stabilised inverses of the system. Proposals are given for extending the guarantees of the method to mixed sensitivity problems by a J-spectral factorisation approach using a novel Newton-iteration scheme based on reverse-time simulation and identification. The resulting approximate inverses are found to be usable in a similar way to the central controllers associated with H_∞ methods.