Constrained parameterized optimal control of switched systems based on continuous Hopfield neural networks

Kahloul, Ahmed Anis; Sakly, Anis

doi:10.1007/s40435-016-0287-1

Cited by 4 publications

(3 citation statements)

References 29 publications

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“…Proof of Theorem 1. Taking into consideration the dynamics of the identification error ∆ presented in (7), one may propose an energetic function depending on the deviation between the state ζ and ζ as well as the deviation between the weights estimated with the identifier and the actual values of the approximation.…”

Section: Ric(p α):=Pmentioning

confidence: 99%

“…Here ∆ is the tracking error already, for which its dynamics has been defined in (7). The symbol • 2 2,P represents the weighted l 2 norm of finite-dimensional vectors with the positive definite and symmetric matrix P ∈ R 2×2 .…”

Section: Ric(p α):=Pmentioning

confidence: 99%

“…In particular, differential neural networks (DNNs) have been used for a long time as efficient modeling strategies of dynamic systems with uncertain mathematical models that are affected by perturbations and modeling inaccuracies. Notice that DNN based models could be well fitted to represent the VOR dynamics [6,7]. Still, the selection of activation functions could be a matter of discussion, considering that sigmoidal or other monotonical functions may not capture the complex electrophysiological VOR response.…”

Section: Introductionmentioning

confidence: 99%

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Differential Neural Network-Based Nonparametric Identification of Eye Response to Enforced Head Motion

et al. 2022

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Dynamic motion simulators cannot provide the same stimulation of sensory systems as real motion. Hence, only a subset of human senses should be targeted. For simulators providing vestibular stimulus, an automatic bodily function of vestibular–ocular reflex (VOR) can objectively measure how accurate motion simulation is. This requires a model of ocular response to enforced accelerations, an attempt to create which is shown in this paper. The proposed model corresponds to a single-layer spiking differential neural network with its activation functions are based on the dynamic Izhikevich model of neuron dynamics. An experiment is proposed to collect training data corresponding to controlled accelerated motions that produce VOR, measured using an eye-tracking system. The effectiveness of the proposed identification is demonstrated by comparing its performance with a traditional sigmoidal identifier. The proposed model based on dynamic representations of activation functions produces a more accurate approximation of foveal motion as the estimation of mean square error confirms.

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Section: Ric(p α):=Pmentioning

confidence: 99%

Section: Ric(p α):=Pmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Differential Neural Network-Based Nonparametric Identification of Eye Response to Enforced Head Motion

et al. 2022

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Hybrid Approach for Constrained Optimal Control of Nonlinear Switched Systems

Kahloul

Sakly

2020

J Control Autom Electr Syst

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This paper examines the problem of the optimal control of nonlinear switched systems under mixed constraints. The solution to this problem consists mainly in determining two major factors; on the one hand, we need to determine the optimal control input, and on the other one, we have to find out the best switching instants that lead to minimizing a particular functional cost. In order to reach this objective, we use a hybrid approach that consists in dividing the problem in two stages. In the first one, we employ the method of Lagrange multipliers while considering the Karush-Kuhn-Tucker (KKT) conditions. This method must be accompanied by the bang-bang control. This combination of these optimization methods enables us to obtain the optimal control input while respecting the simultaneously imposed constraints on the state and the input. In the second stage, a metaheuristic method is used to define the optimum switching instants, and this is what we call the particle swarm optimization (PSO). In order to approve this approach, different examples are applied in this study.

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Multistability of switched neural networks with sigmoidal activation functions under state-dependent switching

Guo

Wang

2020

Neural Networks

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Constrained parameterized optimal control of switched systems based on continuous Hopfield neural networks

Cited by 4 publications

References 29 publications

Differential Neural Network-Based Nonparametric Identification of Eye Response to Enforced Head Motion

Differential Neural Network-Based Nonparametric Identification of Eye Response to Enforced Head Motion

Hybrid Approach for Constrained Optimal Control of Nonlinear Switched Systems

Multistability of switched neural networks with sigmoidal activation functions under state-dependent switching

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