Abstract
This paper proposes a general robust model predictive control (MPC) approach for the constrained Takagi-Sugeno (T-S) fuzzy model with additive bounded disturbances. We adopt the homogeneous polynomially parameter-dependent (HPP) Lyapunov matrix with the arbitrary complexity degree and the corresponding HPP control law for the controller design. By applying the Polya’s theorem and the extended nonquadratic boundedness property, a systematic approach to construct a set of sufficient conditions for assessing robust stability described by parameter-dependent linear matrix inequalities (LMIs) is established. The proposed approach is an improvement over existing approaches in terms of control performance and stabilizable model range. Numerical examples are provided to show the effectiveness of the proposed robust MPC approach.
Highlights
Takagi-Sugeno (T-S) fuzzy model has been widely used to approximate or even exactly represent nonlinear systems, whose basic idea is transforming the original system into a family of linear submodels [1]–[3]
Model predictive control (MPC), as a widespread control technique being implemented in a receding horizon fashion, has advantages in constraints handling for multivariable plants, such as distributed MPC [14], industrial hierarchical MPC [15], and stochastic MPC [16]
The stability analysis and control synthesis for T-S fuzzy model by MPC approaches have been studied with variety
Summary
Takagi-Sugeno (T-S) fuzzy model has been widely used to approximate or even exactly represent nonlinear systems, whose basic idea is transforming the original system into a family of linear submodels [1]–[3]. The work of [27] proposes a tube-based MPC for nonlinear continuous-time model, and the feedback control law is optimized off-line. This paper characterizes MPC synthesis, based on improving the Lyapunov function, for constrained T-S fuzzy model with the bounded disturbance. Some general results for the positiveness of polynomials with matrix-valued coefficients (based on Pólya’s theorem) is given in [35], where some complete characterization of the solution of parameter-dependent LMIs, usually arising in the robust stability analysis, is proposed. In [34], a general robust MPC approach for linear parameter varying (LPV) systems in the absence of bounded disturbance has been proposed, which can include many existing approaches with common quadratic Lyapunov matrices and state feedback laws (e.g., [24], [25]) as special cases. The timedependence of the MPC decision variables is often omitted for brevity
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