On fractional infinite-horizon optimal control problems with a combination of conformable and Caputo–Fabrizio fractional derivatives

On characterisations of the input to state stability properties for conformable fractional order bilinear systems

“…Over the past centuries, the fractional calculus, dealing with differential equations of fractional order, has attracted a major interest in various fields of science and engineering [4, 15, 21, 24, 25, 32, 36, 50]. During recent decades, many researchers from the control community have been actively exploring the possibility of extension/adaptation of various control methods from the integer setting into the fractional one.…”

On asymptotically stabilizing control of nonlinear fractional control systems using an optimization scheme

“…Theory and applications, modelling, design, structure and mathematics of neural networks (NNs) are important topics in enjoining, science, medicine, etc. In particular, the numerical solution of ordinary and partial differential equations (Kumar and Yadav, 2011), OC problems (Nazemi and Karami, 2017), mathematical programming problems (Nazemi, 2019) and numerical solution of fractional optimal control problems (FOCPs) and fractional differential equations (Ghasemi and Nazemi, 2018; Ghasemi et al, 2017, 2020; Kheyrinataj and Nazemi, 2020a, 2020b; Yavari and Nazemi 2019, 2020). Among the papers mentioned and in order to solve FOCPs, by using the perceptron NN’s ability in approximating a nonlinear function and the Grünwald–Letnikov approximation of Riemann–Liouville fractional derivatives (RLFDs), Ghasemi et al (2017) have contributed to presenting an indirect method for solving FOCPs.…”

“…Recently, Kheyrinataj and Nazemi (2020a) have proposed a higher order NN, namely the functional link NN, for the model of linear and nonlinear delay fractional OC problems with mixed control state constraints. Also Yavari and Nazemi (2020) have introduced a novel fractional infinite-horizon OC problem with a combination of conformable and Caputo–Fabrizio fractional derivatives and solve it using a network network scheme. Recently, Gasemi et al (2020) used the single layer Legendre NN to solve fractional OC problems with an application to fractional chaotic systems.…”

On fractional optimal control problems with an application in fractional chaotic systems using a Legendre collocation-optimization technique

“…There are many references in theory and applications, modeling, design, structure and mathematics of neural networks (see Daniel, 2013; Haykin, 1994; Müller et al, 2012; Tang et al, 2007). In particular, the numerical solution of ordinary and partial differential equations (Beidokhti and Malek, 2009; Kumar and Yadav, 2011; Shirvany et al, 2009), optimal control problems (Cheng et al, 2007; Effati and Pakdaman, 2013; Vrabie and Lewis, 2009), mathematical programming problems (Nazemi, 2011, 2012, 2013, 2014; Nazemi and Effati, 2013; Nazemi and Nazemi, 2014; Nazemi and Omidi, 2012, 2013; Nazemi and Sharifi, 2013) and numerical solution of FOCP and fractional differential equations (Ghasemi and Nazemi, 2018; Ghasemi et al, 2017; Jafarian et al, 2017; Kheyrinataj and Nazemi, 2020a, 2020b; Yavari and Nazemi, 2019, 2020; Zuniga-Aguilar et al, 2018). Among the papers mentioned and in order to solve FOCPs, by using perceptron neural network’s ability in approximating a nonlinear function and the Grunwald–Letnikov approximation of Riemann–Liouville fractional derivatives, Ghasemi et al (2017) contribute to presenting an indirect method for solving FOCPs.…”

“…Recently, Kheyrinataj and Nazemi (2020a) propose a higher order neural network, namely the functional link neural network, for the model of linear and nonlinear delay FOCPs with mixed control state constraints. Also Yavari and Nazemi (2020) introduce a novel fractional infinite horizon optimal control problem with a combination of conformable and Caputo–Fabrizio fractional derivatives and solve it using a network network scheme. In this paper, to reduce the complexity of some existing methods for solving FOCPs and to remove some disadvantages, a computational intelligence method based on single layer Legendre neural network is presented.…”