A tutorial and overview of retrospective cost adaptive control

The goal of this paper is to provide a tutorial on retrospective cost adaptive control (RCAC). RCAC is a discrete-time adaptive control technique that is applicable to stabilization, command following, and disturbance rejection. RCAC is based on the concept of retrospectively optimized control, where past controller coefficients used to generate past control inputs are re-optimized in the sense that if the reoptimized coefficients had been used over a previous window of operation, then the performance would have been better. Unlike signal processing applications such as estimation and identification, it is impossible to change past control inputs, and thus the re-optimized controller coefficients are used only to generate the next control input. This paper presents a tutorial on the algorithmic details of RCAC including the construction of the retrospective cost, the role of the target model, and the effect of tuning parameters. Numerical examples are given to illustrate each of these choices as well as the performance of RCAC for command following and disturbance rejection under minimal modeling of the plant dynamics and exogenous inputs. Properties of the closed-loop system are also compared to features of discrete-time, high-authority LQG controllers.