Distributed Saturated Control for a Class of Semilinear PDE Systems: An SOS Approach

Pitarch, José Luis; Rakhshan, Mohsen; Mardani, Mohammad Mehdi; Shasadeghi, Mokhtar

doi:10.1109/tfuzz.2017.2688379

Cited by 31 publications

(23 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One effective way for chattering reduction is replacing the discontinuous function ( ) sgn ⋅ with continuous functions [39,45]. Fuzzy logic controllers are widely utilized to stabilize the systems during recent years [28,27,38,30,11,40,7,17]. In this paper, the fuzzy mechanism fs u is employed and incorporated into Equation 20 Letting σ and fs u be the input and the output variables of the FAPISMC, respectively, the instinctive rules can be written as:…”

Section: Control Problemmentioning

confidence: 99%

Fuzzy-Logic-Based Adaptive Proportional-Integral Sliding Mode Control for Active Suspension Vehicle Systems: Kalman Filtering Approach

Zare¹,

Mardani²,

Vafamand

et al. 2019

ITC

Self Cite

View full text Add to dashboard Cite

This paper deals with the problem of synthesizing a fuzzy-logic-based adaptive proportional-integral sliding mode control (FAPISMC) for active suspension systems based on Kalman filtering approach. To improve the performance of the controller and eliminate the effect of the chattering, the switching input is designed based on the fuzzy-logic-based approach with a minimum number of rules. In order to facilitate the stability analysis, the estimation of the state variables is used in designing the sliding surface platform. Furthermore, the gain of the controller is updated by an adaptive law to avoid any pre-knowledge of the disturbance amplitude. Subsequently, the proposed approach is more implementable in real-world processes. Finally, in order to illustrate the effectiveness and merits of the proposed approach, a suspension system is considered and simulated by the real-time hardware-in-the-loop (HiL). In this example, a quarter-car model of suspension systems is considered. Then, the obtained real-time results are compared with the linear quadratic regulator approach.

show abstract

Section: Control Problemmentioning

confidence: 99%

Fuzzy-Logic-Based Adaptive Proportional-Integral Sliding Mode Control for Active Suspension Vehicle Systems: Kalman Filtering Approach

Zare¹,

Mardani²,

Vafamand

et al. 2019

ITC

Self Cite

View full text Add to dashboard Cite

show abstract

“…If A(x) and P(x) are constant matrices, then the design procedure is turned to the existing LMI-based sliding mode controller [7] as a special case. However in this theorem, the procedure of designing P(x) is not given.…”

Section: Remarkmentioning

confidence: 99%

“…However, by developing the polynomial models, another alternative numerical approach can be considered. Furthermore, the polynomial systems can be directly stabilized through the SOS-based approaches; meanwhile, to apply the LMI-based methods the polynomial systems must be locally represented by Takagi-Sugeno (TS) fuzzy systems [7,8]. Furthermore, the polynomial systems can be directly stabilized through the SOS-based approaches; meanwhile, to apply the LMI-based methods the polynomial systems must be locally represented by Takagi-Sugeno (TS) fuzzy systems [7,8].…”

Section: Introductionmentioning

confidence: 99%

Sum‐of‐Squares‐Based Finite‐Time Adaptive Sliding Mode Control of Uncertain Polynomial Systems With Input Nonlinearities

Mardani¹,

Vafamand²,

Zeini³

et al. 2017

Asian Journal of Control

Self Cite

View full text Add to dashboard Cite

This paper proposes a novel adaptive sliding mode control (ASMC) for a class of polynomial systems comprising uncertain terms and input nonlinearities. In this approach, a new polynomial sliding surface is proposed and designed based on the sum-of-squares (SOS) decomposition. In the proposed method, an adaptive control law is derived such that the finite-time reachability of the state trajectories in the presence of input nonlinearity and uncertainties is guaranteed. To do this, it is assumed that the uncertain terms are bounded and the input nonlinearities belong to sectors with positive slope parameters. However, the bound of the uncertain terms is unknown and adaptation law is proposed to effectively estimate the uncertainty bounds. Furthermore, based on a novel polynomial Lyapunov function, the finite-time convergence of the sliding surface to a pre-chosen small neighborhood of the origin is guaranteed. To eliminate the time derivatives of the polynomial terms in the stability analysis conditions, the SOS variables of the Lyapunov matrix are optimally selected. In order to show the merits and the robust performance of the proposed controller, chaotic Chen system is provided. Numerical simulation results demonstrate chattering reduction in the proposed approach and the high accuracy in estimating the unknown parameters.

show abstract

“…In the TS fuzzy model, the nonlinear system is split into local linear subsystems called fuzzy rules. Then, by fuzzy blending of the local fuzzy rules, the overall fuzzy model will be achieved [12], [13]. Compared to the linear modeling techniques, the fuzzy model-based controller design procedure for TS fuzzy model is as simple as linear one; meanwhile, the performance of the fuzzy model-based controllers is significantly better.…”

mentioning

confidence: 99%

“…Compared to the linear modeling techniques, the fuzzy model-based controller design procedure for TS fuzzy model is as simple as linear one; meanwhile, the performance of the fuzzy model-based controllers is significantly better. Therefore, numerous fuzzy control methods such as state feedback controller [14], fuzzy observer-based controller [15], output feedback controller [16], distributed sampled-data fuzzy controller [17], and distributed fuzzy polynomial controller [13], have been investigated in the literature. During the recent years, the linear matrix inequality (LMI) approaches are distinguished to construct a systematic, simple, and effective way to analyze the stability and stabilization of DC MGs with CPLs [9], [11].…”

mentioning

confidence: 99%

Design of Quadratic D-Stable Fuzzy Controller for DC Microgrids With Multiple CPLs

Mardani

Vafamand

Khooban

et al. 2019

IEEE Trans. Ind. Electron.

Self Cite

View full text Add to dashboard Cite

The DC microgrid (MG) system has several advantages over the AC one. Therefore, it recently became a preferred architecture in numerous industrial applications. Many loads in DC MGs are electronically regulated and they challenge the stability of the system due to their constant power load (CPL) behavior. This paper proposes a systematic and simple approach to design an improved state feedback controller for the power buffer that can stabilize the DC MGs with multiple CPLs. Based on the so-called sector nonlinearity approach, the nonlinear DC MG with several CPLs is exactly represented in a Takagi-Sugeno (TS) fuzzy model. Then, by employing the quadratic D-stability theory, the sufficient conditions to guarantee the stability and transient performance of the closed-loop system are obtained in terms of linear matrix inequalities (LMIs), such that the decay rate and oscillatory behavior of the closedloop DC MG system are guaranteed to lie inside a predefined region. The LMI conditions can be numerically solved by utilizing the YALMIP toolbox in the MATLAB. Finally, to illustrate the merits and implementation validity of the proposed approach, some hardware-in-the-loop (HiL) real-time simulation (RTS) results on a DC MG, which feeds two CPLs, are presented. In comparison with the state-of-the-art techniques, the RTS results indicate the simplicity, validity, and better performance of the proposed approach. According to the results, one can conclude that the proposed approach not only theoretically assures the stability but also guarantees the fast convergence and less oscillatory response of the DC MGs with multiple CPLs.

show abstract

Distributed Saturated Control for a Class of Semilinear PDE Systems: An SOS Approach

Cited by 31 publications

References 37 publications

Fuzzy-Logic-Based Adaptive Proportional-Integral Sliding Mode Control for Active Suspension Vehicle Systems: Kalman Filtering Approach

Fuzzy-Logic-Based Adaptive Proportional-Integral Sliding Mode Control for Active Suspension Vehicle Systems: Kalman Filtering Approach

Sum‐of‐Squares‐Based Finite‐Time Adaptive Sliding Mode Control of Uncertain Polynomial Systems With Input Nonlinearities

Design of Quadratic D-Stable Fuzzy Controller for DC Microgrids With Multiple CPLs

Contact Info

Product

Resources

About