Bound Of Quadratic Cost Function Research Articles

Event-triggered feedback control for discrete-time piecewise-affine systems

ABSTRACTIn this paper, the problem of event-triggered control for discrete-time piecewise-affine system is investigated. An optimisation problem for minimising the upper bound of quadratic cost function for quantifying the control performance is formulated in the form of linear matrix inequalities (LMIs). The unique state-feedback control gain under the event-triggered strategy can be obtained by solving the LMIs optimisation problems. Comparisons by the simulations are given to demonstrate the advantages of the proposed approach, where the number of control input updates is reduced, while the control performance is still guaranteed.

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.

Guaranteed cost distributed fuzzy observer‐based control for a class of nonlinear spatially distributed processes

The guaranteed cost distributed fuzzy (GCDF) observer‐based control design is proposed for a class of nonlinear spatially distributed processes described by first‐order hyperbolic partial differential equations (PDEs). Initially, a T–S fuzzy hyperbolic PDE model is proposed to accurately represent the nonlinear PDE system. Then, based on the fuzzy PDE model, the GCDF observer‐based control design is developed in terms of a set of space‐dependent linear matrix inequalities. In the proposed control scheme, a distributed fuzzy observer is used to estimate the state of the PDE system. The designed fuzzy controller can not only ensure the exponential stability of the closed‐loop PDE system but also provide an upper bound of quadratic cost function. Moreover, a suboptimal fuzzy control design is addressed in the sense of minimizing an upper bound of the cost function. The finite difference method in space and the existing linear matrix inequality optimization techniques are used to approximately solve the suboptimal control design problem. Finally, the proposed design method is applied to the control of a nonisothermal plug‐flow reactor. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2366–2378, 2013