Guaranteed-Cost Finite-Time Fuzzy Control for Temperature-Constrained Nonlinear Coupled Heat-ODE Systems

This paper investigates the guaranteed-cost finite-time fuzzy control problem subject to a temperature constraint for a class of coupled systems represented by nonlinear ordinary differential equations (ODEs) and a scalar nonlinear heat equation. Initially, a finite-dimensional nonlinear coupled system is derived by combining the slow system of heat equation with the original ODE system, which can be exactly represented by the Takagi–Sugeno fuzzy model. Meanwhile, the temperature constraint is transformed into the state constraint performed on the finite-dimensional coupled system. Then, a guaranteed-cost finite-time constrained fuzzy control design is developed in terms of a set of time-dependent differential linear matrix inequalities (LMIs) to make the closed-loop of the original ODE system finite-time quasi-contractively stable with an upper bound of quadratic cost function, while the temperature constraint is respected. Furthermore, by utilizing the time-convexity and LMI optimization techniques, a suboptimal controller is obtained by means of minimizing the guaranteed-cost bound. Finally, the proposed design method is applied to the control of a temperature constrained hypersonic rocket car.