Fuzzy Control Systems: LMI-Based Design

Seidi, Morteza; Hajiaghamemar, Marzieh; Segee, Bruce

doi:10.5772/48529

Cited by 8 publications

(4 citation statements)

References 34 publications

(23 reference statements)

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“…In this section, the fourth order nonlinear benchmark of a single link robot with flexible joint, depicted in Figure 1, is considered [40], [41]. [41].…”

Section: Simulation Resultsmentioning

confidence: 99%

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LMI conditions for non-quadratic stabilization of T-S models with pole placement assignation

Cherifi¹,

Guelton²,

Arcese³

2015

2015 3rd International Conference on Control, Engineering &Amp; Information Technology (CEIT)

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This paper presents new non-Parallel-Distributed-Compensation (non-PDC) controllers design conditions for continuous-time Takagi-Sugeno (T-S) models with pole placement assignation. Based on the D-stability concept, a desired transient response may be obtained by placing the poles of the T-S closed-loop system in a specific region of the complex plan. After deriving standard non-quadratic D-stability conditions for the T-S closed-loop system, new relaxed LMI-based conditions are obtained from enhanced Fuzzy Lyapunov Functions (FLF), which involve a double sum fuzzy structure. The effectiveness of the proposed result is illustrated in simulation through the benchmark of a flexible robot with single joint.

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“…In this section, the fourth order nonlinear benchmark of a single link robot with flexible joint, depicted in Figure 1, is considered [40], [41]. [41].…”

Section: Simulation Resultsmentioning

confidence: 99%

“…[41]. From its nonlinear model [41] and applying the wellknown sector nonlinearity approach [3], the dynamics of this robot can be exactly described by the following fourth order T-S model [42]:…”

Section: Simulation Resultsmentioning

confidence: 99%

LMI conditions for non-quadratic stabilization of T-S models with pole placement assignation

Cherifi¹,

Guelton²,

Arcese³

2015

2015 3rd International Conference on Control, Engineering &Amp; Information Technology (CEIT)

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“…A sector nonlinearity approach is used to get a global sector in which the model 𝑥̇= 𝑓(𝑥(𝑡)) could fit. for each uncertain parameter, a nonlinear function 𝜙(𝑥): ℝ → ℝ is fitted in a sector (𝑏 1 , 𝑏 2 ) for all 𝑥 ∈ ℝ , 𝑦 = 𝑓(𝑥) stand between 𝑏 1 𝑥 and 𝑏 2 𝑥 [30]. This model approves the stability of 𝑓 under the control system law.…”

Section: Polytopic Lpv Model Alpv Formulationmentioning

confidence: 99%

Optimal Robust LPV Control Design for Novel Covid-19 Disease

Najarzadeh

Dehghani

Asemani

et al. 2021

JoC

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These days almost all countries around the world are struggling with coronavirus outbreak. If the governments and public health care systems don't take any action against this outbreak, it would have severe effects on human life, now and in the future. By doing so, there are several intervention strategies that could be implemented and as the result, the societies become more secure from the casualties of this virus. In this paper, we used a mathematical model of coronavirus epidemic transmission and by use of some LMIs, a robust LPV controller is designed which helps us to choose and use the intervention methods, effectively. By use of the proposed robust controller, the robustness and stability of the model against a wide range of uncertainties are approved. The final objective of this control design is to minimize the number of exposed and infected individuals in the compartmental model. In the end, it can be seen that the control strategies which are preventive action, good medical care, and sterilization of the environment, can highly reduce the negative effects of the coronavirus.

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“…We consider the single link flexible manipulator system S, also used in [8] and [17] whose dynamics are given by:…”

Section: A Single Link Flexible Joint Manipulatormentioning

confidence: 99%

Robust model predictive control for non-linear systems with input and state constraints via feedback linearization

Pant

Abbas

Mangharam

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Robust predictive control of non-linear systems under state estimation errors and input and state constraints is a challenging problem, and solutions to it have generally involved solving computationally hard non-linear optimizations. Feedback linearization has reduced the computational burden, but has not yet been solved for robust model predictive control under estimation errors and constraints. In this paper, we solve this problem of robust control of a non-linear system under bounded state estimation errors and input and state constraints using feedback linearization. We do so by developing robust constraints on the feedback linearized system such that the non-linear system respects its constraints. These constraints are computed at run-time using online reachability, and are linear in the optimization variables, resulting in a Quadratic Program with linear constraints. We also provide robust feasibility, recursive feasibility and stability results for our control algorithm. We evaluate our approach on two systems to show its applicability and performance. Abstract-Robust predictive control of non-linear systems under state estimation errors and input and state constraints is a challenging problem, and solutions to it have generally involved solving computationally hard non-linear optimizations. Feedback linearization has reduced the computational burden, but has not yet been solved for robust model predictive control under estimation errors and constraints. In this paper, we solve this problem of robust control of a non-linear system under bounded state estimation errors and input and state constraints using feedback linearization. We do so by developing robust constraints on the feedback linearized system such that the non-linear system respects its constraints. These constraints are computed at run-time using online reachability, and are linear in the optimization variables, resulting in a Quadratic Program with linear constraints. We also provide robust feasibility, recursive feasibility and stability results for our control algorithm. We evaluate our approach on two systems to show its applicability and performance.

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Fuzzy Control Systems: LMI-Based Design

Cited by 8 publications

References 34 publications

LMI conditions for non-quadratic stabilization of T-S models with pole placement assignation

LMI conditions for non-quadratic stabilization of T-S models with pole placement assignation

Optimal Robust LPV Control Design for Novel Covid-19 Disease

Robust model predictive control for non-linear systems with input and state constraints via feedback linearization

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