TY - JOUR

T1 - Non-periodic Multi-Rate Sampled-Data Fuzzy Control of Singularly Perturbed Nonlinear Systems

AU - Xu, Jing

AU - Niu, Yugang

AU - Lam, Hak-Keung

PY - 2022/12/23

Y1 - 2022/12/23

N2 - Choosing adequate sampling frequencies in sensors has a considerably positive impact on the two-time scale fuzzy logic controller design. Motivated by this concept, this paper addresses the fuzzy-PDC-based control synthesis for a singularly perturbed nonlinear systems (SPNS) under a non-periodic multi- rate sampling mechanism, which also provides guidance on the reasonable choice of maximum allowable sampling time intervals (MASTIs) for multi-rate sensors. First, the sampled SPNS is converted into a continuous-time Takagi-Sugeno fuzzy singularly perturbed model (TSFSPM) with slow and fast time-varying delays. Then, an ε-dependent Lyapunov-Krasovskii functional of order n is proposed to derive the sufficient conditions for stabilizing a multi-rate sampled TSFSPM under a two-time- scale PDC control. Given the slow MASTI, an efficient LMI- based design is proposed to recast the ε-dependent stabilization conditions as a set of ε-independent linear matrix inequalities that are easily solved. On this basis, the upper bound of singular perturbation parameter ε, i.e. ε∗, should be determined to compute the fast MASTI for the possibly slow sampling of fast states. The optimal match of (ε∗,n) is detected for a trade-off among the closed-loop stability, the controller performance and the sensor cost. The superiority of the obtained results is shown in an example of a flexible joint inverted pendulum system.

AB - Choosing adequate sampling frequencies in sensors has a considerably positive impact on the two-time scale fuzzy logic controller design. Motivated by this concept, this paper addresses the fuzzy-PDC-based control synthesis for a singularly perturbed nonlinear systems (SPNS) under a non-periodic multi- rate sampling mechanism, which also provides guidance on the reasonable choice of maximum allowable sampling time intervals (MASTIs) for multi-rate sensors. First, the sampled SPNS is converted into a continuous-time Takagi-Sugeno fuzzy singularly perturbed model (TSFSPM) with slow and fast time-varying delays. Then, an ε-dependent Lyapunov-Krasovskii functional of order n is proposed to derive the sufficient conditions for stabilizing a multi-rate sampled TSFSPM under a two-time- scale PDC control. Given the slow MASTI, an efficient LMI- based design is proposed to recast the ε-dependent stabilization conditions as a set of ε-independent linear matrix inequalities that are easily solved. On this basis, the upper bound of singular perturbation parameter ε, i.e. ε∗, should be determined to compute the fast MASTI for the possibly slow sampling of fast states. The optimal match of (ε∗,n) is detected for a trade-off among the closed-loop stability, the controller performance and the sensor cost. The superiority of the obtained results is shown in an example of a flexible joint inverted pendulum system.

M3 - Article

SN - 1063-6706

JO - IEEE Transactions on Fuzzy Systems

JF - IEEE Transactions on Fuzzy Systems

ER -