Fuzzy Control of Nonlinear Systems with General Performance Criteria
Xin Wang, E Yaz Edwin, James E. Long, Tim Miller · InTech eBooks · 2012
Fuzzy ControllersIn the following sections, we first introduce the Takagi-Sugeno fuzzy modelling for non-linear systems in both continuous time and discrete time.We then propose the general performance criteria in section 3.Then, the LMI control solutions are derived to characterize the optimal and robust fuzzy control of continuous time and discrete time non-linear systems, respectively.The inverted pendulum system control is used as an illustrative example to demonstrate the effectiveness and robustness of our proposed approaches.The following notation is used in this work: x ∈R n denotes n-dimensional real vector with norm x =( x T x) 1/2 where (.) T indicates transpose.A ≥ 0 for a symmetric matrix denotes a positive semi-definite matrix.L 2 and l 2 denotes the space of infinite sequences of finite dimensional random vectors with finite energy, i.e. Takagi-Sugeno system modelThe importance of the Takagi-Sugeno fuzzy system model is that it provides an effective way to decompose a complicated non-linear system into local dynamical relations and express those local dynamics of each fuzzy implication rule by a linear system model.The overall fuzzy non-linear system model is achieved by fuzzy "blending" of the linear system models, so that the overall non-linear control performance is achieved.Both of the continuous-time and the discrete-time system models are summarized below.