Discrete Takagi-Sugeno Fuzzy Models Applied to Control the Knee Joint Movement of Paraplegic Patients

Gaino, Ruberlei; Covacic, Márcio Roberto; Cardim, Rodrigo; Sanches, Marcelo Augusto Assunção; Carvalho, Aparecido Augusto de; Biazeto, Anderson Ross; Teixeira, Marcelo Carvalho Minhoto

doi:10.1109/access.2020.2971908

Cited by 9 publications

(10 citation statements)

References 27 publications

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“…e nonlinear function 􏽥 f 21 (x 1 ) is exactly represented by the convex combination of these two local models: [2,3,5,11,13]. Note that, from (26), α 1 ≥ 0, α 2 ≥ 0, and…”

Section: Knee Joint Modelmentioning

confidence: 99%

“…e mathematical model of the system, which relates the pulse width applied for the muscle to the torque generated at the knee joint, is presented in Section 4. e parameters of the system, presented in [2,3], were obtained experimentally. e parameters related to the shank-foot complex and their numerical values are given in Table 1.…”

Section: Numerical Model Of the Paraplegic Patientmentioning

confidence: 99%

“…e authors considered the leg mathematical model proposed by Ferrarin and Pedotti [1], with the parameter values given in [2,3]. e parameters B (viscous coefficient), J (inertial moment), τ (time constant), and G (static gain) of the shank-foot complex model have the nominal values given in [2,3], but with a 20% tolerance range around these nominal values, that is, these values are in the range between 80% and 120% of their nominal values.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, few articles have been published in this area, as, for instance, [12,13]. In [11] and subsequent articles [2,3,[14][15][16][17], published by our research group, some theories have been employed to control knee joint movement using neuromuscular electrical stimulation. In [18], an article was published describing control application in paraplegic patients.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robust T-S Fuzzy Control of Electrostimulation for Paraplegic Patients considering Norm-Bounded Uncertainties

Covacic

Teixeira

Carvalho

et al. 2020

Mathematical Problems in Engineering

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This manuscript presents a Takagi–Sugeno fuzzy control for a mathematical model of the knee position of paraplegic patients using functional electrical stimulation (FES). Each local model of the fuzzy system is represented considering norm-bounded uncertainties. After obtaining the model of FES with norm-bounded uncertainties, the fuzzy control strategy is designed through the solution of linear matrix inequalities (LMIs) using the conditions available in the literature, which consider these norm-bounded uncertainties. The strategy considers decay rate and constraints on the input signal. The model is simulated in the Matlab environment using the numerical parameters measured by experimental tests from a paraplegic patient.

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“…e nonlinear function 􏽥 f 21 (x 1 ) is exactly represented by the convex combination of these two local models: [2,3,5,11,13]. Note that, from (26), α 1 ≥ 0, α 2 ≥ 0, and…”

Section: Knee Joint Modelmentioning

confidence: 99%

Section: Numerical Model Of the Paraplegic Patientmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust T-S Fuzzy Control of Electrostimulation for Paraplegic Patients considering Norm-Bounded Uncertainties

Covacic

Teixeira

Carvalho

et al. 2020

Mathematical Problems in Engineering

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“…It has the capacity to supply currents with amplitudes of up to 140 mA, with a 1-mA step, pulse width (PW) from 0 to 500 μs, with a step of 1 μs, and frequency (F) from 20 to 300 Hz, with a step of 1 Hz. The stimulator has a currentbased output allowing its use in closed-loop control (Arcolezi et al 2019Nunes et al 2019;Gaino et al 2020;Teodoro et al 2020). The output stage of this stimulator is current, which is a great advantage for its use in control, as it makes it possible to control and predict the amount of current applied to the muscle, even if the coupling resistance and tissue impedance change.…”

Section: Test Platformmentioning

confidence: 99%

Identifying the knee joint angular position under neuromuscular electrical stimulation via long short-term memory neural networks

Arcolezi¹,

Nunes²,

Cerna³

et al. 2020

Res. Biomed. Eng.

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Purpose Recurrent neural networks (RNNs) offer a promising opportunity for identifying nonlinear systems. This paper investigates the effectiveness of the long short-term memory (LSTM) RNN architecture in the specific task of identifying the knee joint angular position under neuromuscular electrical stimulation (NMES). The standard RNN model referred to as SimpleRNN and the well-known multilayer perceptron (MLP) are used for comparison purposes. Methods Data from seven healthy and two paraplegic volunteers were experimentally acquired. These data were adequately scaled, encoded using three timestep values (1, 5, and 10), and divided into training, validation, and testing sets. These models were mainly evaluated using the root mean square error (RMSE) and training time metrics. Results The three NN models demonstrated very good fitting to data for all volunteers. The LSTM presented smaller RMSE for most of the individuals. This is even more notable when using 5 and 10 timesteps achieving half and one-third of the error from MLP and half of the error from the SimpleRNN. This higher utility comes with a substantial time-utility trade-off. Conclusion The results in this paper show that the LSTM worths deeper investigation to design control-oriented models to knee joint stimulation in closed-loop systems. Even though the LSTM takes more time for training due to a more complex architecture, time and computational costs could be increased if achieving better modeling of systems. Rather than mathematically modeling this system with several unique parameters per individual, the use of NNs is encouraged in this task where there exist high nonlinearities and time-varying parameters.

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Robust dynamic output‐feedback ℋ∞ control for uncertain Takagi–Sugeno time‐delay systems

Coşkun

2022

Math Methods in App Sciences

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This work deals with the problem of robust output‐feedback control for a class of uncertain Takagi–Sugeno (T‐S) fuzzy systems with state time‐varying delays. The system is described by a state‐space T‐S fuzzy model with time‐varying delays and norm‐bounded parameter uncertainties. A robust control strategy via Lyapunov–Krasovskii functionals for stability and performance conditions is derived. The T‐S fuzzy‐model‐based framework is employed in analysis, and formulations are performed based on the solution of a set of delay‐dependent linear matrix inequalities (LMIs). By solving the derived LMI conditions via a convex programming toolbox, a full‐order robust dynamic output‐feedback controller is designed. The obtained robust output‐feedback controller guarantees asymptotic stability of the closed‐loop system and provides an norm, that is, disturbance attenuation level, for all admissible uncertainties. In this sequel, three examples are given to reveal the effectiveness and merits of the proposed approaches.

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Discrete Takagi-Sugeno Fuzzy Models Applied to Control the Knee Joint Movement of Paraplegic Patients

Cited by 9 publications

References 27 publications

Robust T-S Fuzzy Control of Electrostimulation for Paraplegic Patients considering Norm-Bounded Uncertainties

Robust T-S Fuzzy Control of Electrostimulation for Paraplegic Patients considering Norm-Bounded Uncertainties

Identifying the knee joint angular position under neuromuscular electrical stimulation via long short-term memory neural networks

Robust dynamic output‐feedback ℋ∞ control for uncertain Takagi–Sugeno time‐delay systems

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