This dissertation extends retrospective cost adaptive control (RCAC) by broadening its applicability to nonlinear systems. Specifically, we consider command following and disturbance rejection for uncertain Hammerstein systems.
All real-world control systems must operate subject to constraints on the allowable control inputs. We use convex optimization to perform the retrospective input optimization, provided the saturation levels are known. The use of convex optimization bounds the magnitude of the retrospectively optimized input and thereby influences the controller update to satisfy the control bounds. We demonstrate this technique on illustrative numerical examples involving single and multiple inputs. In particular, this technique is applied to a multi-rotor helicopter with constraints on the total thrust magnitude and inclination of the rotor plane.
We develop RCAC for uncertain Hammerstein systems with odd, even, or arbitrary nonlinearities by constructing auxiliary nonlinearities to account for the non-monotonic input nonlinearities. The purpose of the auxiliary nonlinearities is to ensure that RCAC is applied to a Hammerstein system with a globally nondecreasing composite input nonlinearity. We assume that the linear plant is either asymptotically stable or minimum-phase, and only one Markov parameter of the linear plant is known. The input nonlinearity is uncertain. The required modeling information for the input nonlinearity includes the intervals of monotonicity as well as values of the nonlinearity that determine overlapping segments of the range of the nonlinearity within each interval of monotonicity.
Although RCAC is able to tune the linear controller to the command signal and nonlinear characteristics of the plant, the ability of the linear controller to produce accurate command following is limited by the distortion introduced by the nonlinearities. The linear controller structure of RCAC is replaced by a NARMAX (nonlinear ARMAX) controller structure, where the basis functions in the NARMAX controller are chosen by the user, and the controller coefficients appear linearly. To account for the case in which the input nonlinearity is uncertain, we investigate the performance of retrospective cost adaptive NARMAX control (RCNAC) in the case of uncertainty, an approximate input nonlinearity, called the ersatz nonlinearity, can be used by RCANC for adaptation.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/100042/1/yanjin_1.pd
