A performance bound for nonlinear control systems

This research focuses on the control of a nonlinear system whose output is subject to an additive disturbance. The main interest is in the investigation of controllers that reduce the effect of the disturbance on the system output. Usually, it is not possible to construct a controller that completely eliminates the effects of the disturbance. It is then of interest to find how well the "best" controller can attenuate the effect of the disturbance. The main result of this dissertation is a performance bound, that provides an estimate of the best disturbance attenuation that can be achieved for a given system, using a causal controller that renders the system internally stable.; An approximate right inverse of a nonlinear system {dollar}Sigma{dollar} is introduced to facilitate the derivation of the performance bound and the development of nonlinear controllers. An approximate right inverse is constructed to be stable and causal for implementation purposes. The difference between an approximate right inverse and a right inverse is that the right inverse may not be both stable and causal. The role of an approximate right inverse is to approximate a disturbed signal with a signal in the image of the system {dollar}Sigma .{dollar} An approximate right inverse can be constructed for any system {dollar}Sigma .{dollar}; The calculation of the performance bound involves an optimization process of finding a global maximum of a non-convex function. For several cases, a nonlinear programming algorithm is developed to handle the optimization. To demonstrate the application of this performance bound, it is calculated for three practical systems: (1) the voltage control of a permanent magnet stepper motor; (2) the longitudinal control of an aircraft; and (3) the multivariable process control of a regulator that regulates the liquid level in a pressurized tank.