Intercalated Injection, Target Model Construction and H2 Performance of Retrospective Cost Adaptive Control

Abstract

This dissertation extends retrospective cost adaptive control (RCAC) by devel- oping a novel interpretation of RCAC, wherein the retrospective cost minimization uses intercalated injection between the controller numerator and denominator to fit a specific closed-loop transfer function to a target model. The target model thus incor- porates the modeling information required by RCAC. To demonstrate the effect of the target model on closed-loop performance, RCAC is applied to a collection of problems that demonstrate adaptive pole placement, where the target model is used to place closed-loop poles; adaptive PID control, where RCAC adaptively tunes PID gains; and LQG cost minimization, where the optimality and closed-loop frequency response of RCAC is compared with the performance of discrete-time LQG controllers. Next, RCAC is applied to plants that are difficult to control using fixed gain con- trollers, including an aircraft lateral dynamics model that has an unknown transition from minimum-phase to nonminimum-phase (NMP) dynamics, as well as plants with severely limited achievable gain and delay margin. xvi Methods are developed to control NMP plants without knowledge of the NMP zero. Specifically, a decentralized feedback-feedforward architecture as well as quasi- FIR controllers are considered, where the FIR controller operates in parallel with an internal model controller in order to follow commands for NMP plants without knowledge of the NMP zeros. Next, the following question is considered: Are all full-order dynamic compen- sators observer-based? It is shown that the only case where a dynamic compensator is not observer-based is the case where n is odd and the closed-loop spectrum has no real eigenvalues. Since this is the case, such controllers are necessarily suboptimal in the sense of LQG. This question is relevant to understanding the closed-loop pole locations arising from full-order RCAC compensators. Finally, retrospective cost model refinement (RCMR) is used to estimate parame- ters in a mass-spring-damper system and an aircraft lateral dynamics model. RCMR is compared to the extended Kalman filter (EKF) and the unscented Kalman fil- ter (UKF), and the ability to estimate parameters without knowledge of the noise characteristics using RCMR is demonstrated. RCMR is then paired with a forward- propagating Riccati-based controller for indirect adaptive control of the aircraft lateral dynamics model considered earlier.