Robust Decoupling, Disturbance Rejection and Linearization of Unknown Nonlinear Systems

Multi-input multi-output (MIMO) systems are frequently encountered in energy systems, robotics, communications, cybersecurity and control engineering. They are difficult to control because of the existence of couplings between the inputs and outputs. These couplings are often nonlinear and unknown or unmodelled. In many such systems it is desirable to be able to independently control the outputs in a linear manner. Also there often are disturbance inputs from which the outputs must be protected, that is decoupled or made uncontrollable. This has led to a substantial amount of research effort directed at the decoupling, linearization and disturbance rejection problems for linear and nonlinear systems. Typically, most decoupling and linearization methods available in the literature require knowledge of a model of the system which is often unavailable. Moreover exact implementation of decoupling and disturbance controllers are fragile and therefore of limited applicability. In this paper we show how high-gain feedback can effectively and robustly reject disturbances, linearize and decouple an unknown nonlinear static multivariable system under fairly mild conditions. These conditions are that there should be at least as many inputs as outputs to be controlled, and that the unknown nonlinear system be left invertible, although knowledge of the left inverse is not needed. An illustrative example of a circuit where two coupled output voltages are to be controlled independently and linearly in the presence of sources which are disturbances, is solved using PSpice. Future research problems are discussed.