Gravitational search algorithm-based fuzzy control for a nonlinear ball and beam system

Mahmoodabadi, Mohammad Javad; Danesh, Nasim

doi:10.1080/23307706.2017.1403864

Cited by 23 publications

(11 citation statements)

References 45 publications

(42 reference statements)

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“…For brevity, we define + ≜ (k + n + 1|k ), ≜ (k + n|k ), e ≜ e(k + n|k ), u ≜ u(k + n|k ), ≜ (k +n|k ) and + ≜ (k +n+1|k ) . According to the above discussion, for system (11) with hard constraints (4a) and (4b), the following online optimization problem is developed to solve the fuzzy MPC controller 40 :…”

Section: Problem Of Interestsmentioning

confidence: 99%

“…Definition 3 (ISS Lyapunov function 18 ). A quadratic function V ( (k)) = T (k)P (k) is called an ISS-Lyapunov function for system (11) if there exist  ∞ -function 1 , 2 , 3 and -function such that…”

Section: Problem Of Interestsmentioning

confidence: 99%

“…Substituting Based on (28) with noting system (11) and the definition (15), (17) is directly obtained. This completes the proof.…”

Section: ℜ Of the Tc Setmentioning

confidence: 99%

“…Lemma 3. For system (11), if there exist positive-definite matrices X r ≜ diag{X 1r , X 2r , X 3r }, X l t ≜ diag{X l 1t , X l 2t , X l 3t }, matrices A c,r , B c,r , C c,r , D c,r , O, and positive scalars̄, such that, for ∀r, t, i ∈ {1, 2, … ,m} and ∀ , , l ∈ {1, 2, … , L}, the following inequalities hold:…”

Section: ℜ Of the Tc Setmentioning

confidence: 99%

“…Theorem 2 (Stability). If the optimization problem P2 is feasible, then the closed-loop system (11) is ISS.…”

Section: Stability Analysis and Online Algorithmmentioning

confidence: 99%

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Dynamic output‐feedback fuzzy MPC for Takagi‐Sugeno fuzzy systems under event‐triggering–based try‐once‐discard protocol

Dong

Song

Wang

et al. 2019

Intl J Robust & Nonlinear

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Summary The fuzzy model predictive control (FMPC) problem is studied for a class of discrete‐time Takagi‐Sugeno (T‐S) fuzzy systems with hard constraints. In order to improve the network utilization as well as reduce the transmission burden and avoid data collisions, a novel event‐triggering–based try‐once‐discard (TOD) protocol is developed for networks between sensors and the controller. Moreover, due to practical difficulties in obtaining measurements, the dynamic output‐feedback method is introduced to replace the traditional state feedback method for addressing the FMPC problem. Our aim is to design a series of controllers in the framework of dynamic output‐feedback FMPC for T‐S fuzzy systems so as to find a good balance between the system performance and the time efficiency. Considering nonlinearities in the context of the T‐S fuzzy model, a “min‐max” strategy is put forward to formulate an online optimization problem over the infinite‐time horizon. Then, in light of the Lyapunov‐like function approach that fully involves the properties of the T‐S fuzzy model and the proposed protocol, sufficient conditions are derived to guarantee the input‐to‐state stability of the underlying system. In order to handle the side effects of the proposed event‐triggering–based TOD protocol, its impacts are fully taken into consideration by virtue of the S‐procedure technique and the quadratic boundedness methodology. Furthermore, a certain upper bound of the objective is provided to construct an auxiliary online problem for the solvability, and the corresponding algorithm is given to find the desired controllers. Finally, two numerical examples are used to demonstrate the validity of proposed methods.

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Section: Problem Of Interestsmentioning

confidence: 99%

Section: Problem Of Interestsmentioning

confidence: 99%

“…Substituting Based on (28) with noting system (11) and the definition (15), (17) is directly obtained. This completes the proof.…”

Section: ℜ Of the Tc Setmentioning

confidence: 99%

Section: ℜ Of the Tc Setmentioning

confidence: 99%

“…Theorem 2 (Stability). If the optimization problem P2 is feasible, then the closed-loop system (11) is ISS.…”

Section: Stability Analysis and Online Algorithmmentioning

confidence: 99%

See 3 more Smart Citations

Dynamic output‐feedback fuzzy MPC for Takagi‐Sugeno fuzzy systems under event‐triggering–based try‐once‐discard protocol

Dong

Song

Wang

et al. 2019

Intl J Robust & Nonlinear

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show abstract

Optimal PD-PD and State Feedback Control of Underactuated Ball and Beam System with Uncertainty and Disturbances

Sahu,

Gupta,

Wael

et al. 2024

Springer Proceedings in Mathematics &Amp; Statistics

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A PSO-optimized novel PID neural network model for temperature control of jacketed CSTR: design, simulation, and a comparative study

Chaturvedi,

Kumar,

Kumar

2023

Soft Comput

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This paper proposes a Particle Swarm Optimization (PSO) tuned novel Proportional Integral Derivative (PID) like neural network (PID-NN). The structure of proposed PID-NN is very simple having only 3 neurons in the hidden layer and a single output neuron. The proportional, integral, and derivative gains of the PID controller are represented by the three weights in the neural network's output layer, respectively. The suggested approach uses the PSO method to optimize the output layer weights, which correspond to PID gains. The non-linear Continuous Stirred Tank Reactor (CSTR) plant, one of the most popular chemical industry processes, is utilized to test the suggested approach. A jacketed CSTR's temperature is controlled via a Particle Swarm Optimization tuned PID like neural network (PSO-NN-PID) controller. In terms of time domain specifications, the performance of the PSO-based NN-PID controller, the back propagation-based NN-PID controller (BP-NN-PID), and the conventionally tuned PID controller are compared. Mean square error is the objective function used in PSO-NN-PID and BP-NN-PID to optimize PID settings. The results show that the overshoot decreases from 44.13% in case of Zeigler-Nichols tuned PID controller to 26.33% in case of BPNN-PID controller, and further reduces to 23.13% in case of proposed PSO-based NN-PID controller. The decrease in rise time is observed from 0.2727 seconds in case of BPNN tuned PID to 0.1283 seconds in case of proposed PSO-NN-PID controller.

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Gravitational search algorithm-based fuzzy control for a nonlinear ball and beam system

Cited by 23 publications

References 45 publications

Dynamic output‐feedback fuzzy MPC for Takagi‐Sugeno fuzzy systems under event‐triggering–based try‐once‐discard protocol

Dynamic output‐feedback fuzzy MPC for Takagi‐Sugeno fuzzy systems under event‐triggering–based try‐once‐discard protocol

Optimal PD-PD and State Feedback Control of Underactuated Ball and Beam System with Uncertainty and Disturbances

A PSO-optimized novel PID neural network model for temperature control of jacketed CSTR: design, simulation, and a comparative study

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