|Adaptive fuzzy control for nonlinear systems in controller canonical form has been employed for decades. The shortcoming is that not all nonlinear systems can be transformed into this form, in particular when the system in question is not SISO or part of the system is known. An adaptive control method for general nonlinear systems does not exist. However, TS fuzzy models can well approximate a large class of nonlinear systems. The goal of this research is to design adaptive fuzzy controllers for partially unknown systems in TS form.
Most of the works in the adaptive control literature treat the control problem of input-affine SISO nonlinear systems. There are two distinct approaches that have been formulated in the design of a fuzzy adaptive control system: direct and indirect schemes. In the direct scheme, the fuzzy system is used to approximate an unknown ideal controller. The indirect scheme uses fuzzy systems to estimate the plant dynamics and then synthesizes a control law based on these estimates. For both approaches, the parameters of the fuzzy systems are updated by a law derived from the Lyapunov
Consider a fuzzy system where part of the system matrices is unknown, but their norm is bounded. The goal is to design a stable state feedback regulator. Two cases can be distinguished, depending on whether the scheduling vector depends or does not depend on the states. Here it can be considered that the scheduling vector does not depend on the states and all states are measured.
1. investigate suitable stability criteria (probably Lyapunov approach)
2. regulator design
3. (possibly) regulator design for other forms of uncertainty (e.g., uncertainty also in the input)
4. (possibly) tracking control
5. design a controller for an overhead crane (application)