A novel tensor product model transformation-based adaptive variable universe of discourse controller

In this paper, a tensor product (TP) model transformation-based variable universe of discourse (VUD) controller is presented for a class of under-actuated nonlinear systems. First, the under-actuated nonlinear system is transformed into a parameter-varying weighted polytopic system by TP model transformation. Next, the VUD approach is extended to the TP model case; in this model, the gains of the error and error derivative in the VUD are calculated by linear matrix inequalities rather than traditional linear methods, such as the linear quadratic regulator or the Lyapunov equation. The TP model transformation-based VUD (TPVUD) is augmented with a σ-adaptive strategy to improve the controller׳s performance. To demonstrate the advantages of the developed control method, numerical simulations are carried out on a parallel-type double inverted pendulum and an aeroelastic wing system. Moreover, experimental results are employed to test the effectiveness of TPVUD on a laboratory-scale three-dimensional (3-D) crane system.