In the second general approach to adaptive control, which is shown in Figure 4.2, we use an on-line system identification method to estimate the parameters of the plant and a"controller designer"module to subsequently specify the parameters of the controller Controller parameter Sy designer identification Controller (t r(t) controller plant F If the plant parameters change, the identifier will provide estimates of these and the controller designer will subsequently tune the controller. It is inherently assumed that we are certain that the estimated plant parameters are equivalent to the actual ones at all times (this is called the "certainty equivalence principle"). Then if the controller designer can specify a controller for each set of plant parameter estimates, it will succeed in controlling the plant. The overall approach is called"indirect adaptive control"since we tune the controller indirectly by first estimating the plant parameters(as opposed to direct adaptive control, where the controller parameters are estimated directly without first identifying the plant parameters). In Section 4.6 we explain how to use the on-line estimation techniques, coupled with a controller designer, to achieve indirect adaptive fuzzy control for nonlinear systems. We discuss two approaches, one based on feedback linearization and the other we name"adaptive parallel distributed compensation"since it builds on the parallel distributed compensator 4.2 Fuzzy Model Reference Learning Control (FMRLC) A"learning system"possesses the capability to improve its performance over time by interacting with its environment. A learning control system is designed so that its"learning controller"has the ability to improve the performance of the closed-loop system by generating command inputs to the plant and utilizing feedback information from the plant In this section we introduce the"fuzzy model reference learning controller"(FMRLC), which is a(direct)model reference adaptive controller. The term"learning"is used as opposed to"adaptive"to distinguish it from the approach to the conventional model reference adaptive controller for linear systems with unknown plant parameters. In particular, theIn the second general approach to adaptive control, which is shown in Figure 4.2, we use an on-line system identification method to estimate the parameters of the plant and a "controller designer" module to subsequently specify the parameters of the controller. Figure 4.2 indirect adaptive controls. If the plant parameters change, the identifier will provide estimates of these and the controller designer will subsequently tune the controller. It is inherently assumed that we are certain that the estimated plant parameters are equivalent to the actual ones at all times (this is called the "certainty equivalence principle"). Then if the controller designer can specify a controller for each set of plant parameter estimates, it will succeed in controlling the plant. The overall approach is called "indirect adaptive control" since we tune the controller indirectly by first estimating the plant parameters (as opposed to direct adaptive control, where the controller parameters are estimated directly without first identifying the plant parameters). In Section 4.6 we explain how to use the on-line estimation techniques, coupled with a controller designer, to achieve indirect adaptive fuzzy control for nonlinear systems. We discuss two approaches, one based on feedback linearization and the other we name "adaptive parallel distributed compensation" since it builds on the parallel distributed compensator. 4.2 Fuzzy Model Reference Learning Control (FMRLC) A "learning system" possesses the capability to improve its performance over time by interacting with its environment. A learning control system is designed so that its "learning controller" has the ability to improve the performance of the closed-loop system by generating command inputs to the plant and utilizing feedback information from the plant. In this section we introduce the "fuzzy model reference learning controller" (FMRLC), which is a (direct) model reference adaptive controller. The term "learning" is used as opposed to "adaptive" to distinguish it from the approach to the conventional model reference adaptive controller for linear systems with unknown plant parameters. In particular, the