A Chebyshev spectral method for time-varying two-point boundary-value and optimal control problems

Elnagar, Gamal N.; Zafiris, Vasilis

doi:10.1080/00207160412331296652

Cited by 5 publications

(4 citation statements)

References 4 publications

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“…Methods such as pseudo-spectral method, measure theoretical approaches, linearization methods, control parameterization methods, finite difference methods, and time-scaling transformation methods belong to this class (see previous studies [37][38][39][40][41][42][43][44][45][46][47] ). However, indirect methods are based on the Pontryagin minimum principle and Hamiltonian-Jacobi-Bellman equations, which can lead to a problem with initial and boundary conditions (see previous studies [48][49][50] ).…”

Section: Discretization Methodsmentioning

confidence: 99%

Optimal control approach for discontinuous dynamical systems

Skandari

Ghaznavi

2017

Optim Control Appl Methods

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Summary In this work, we consider a wide class of discontinuous dynamical systems, discontinuity of which is based on the sign (for short sgn) function. We propose a smooth optimal control problem to solve the main discontinuous system. By solving some numerical examples in mechanical engineering, we show the efficiency of our approach with respect to 2 smoothing methods for discontinuous systems.

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Section: Discretization Methodsmentioning

confidence: 99%

Optimal control approach for discontinuous dynamical systems

Skandari

Ghaznavi

2017

Optim Control Appl Methods

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“…The problem is to find the optimal control u(t) which minimizes Equation ( 42) subject to the constraints of Equations ( 41) and ( 43). The optimal control is (Elnagar and Zafiris, 2005;Elnagar and Razzaghi, 1997;Razzaghi, 1990) uðtÞ ¼ ÀwðtÞxðtÞ, ð44Þ…”

Section: Examplementioning

confidence: 99%

“…The Chebyshev spectral approximations (Elnagar and Zafiris, 2005) of the quadratic performance index J of order m ¼ 4, 6 are J 4 ¼ 0.48427022 and J 6 ¼ 0.48426764. In Table 4, we list the values of control variable u(t) and state variable x(t) obtained by the present method for N ¼ 10, 13, 15.…”

Section: Examplementioning

confidence: 99%

“…The computational methods for optimal control problems have been studied by several researchers. For example, you can see Wu et al (2008), El-Kady et al (2003, Salama (2006), Dooren and Vlassenbroeck (1982), Razzaghi and Elnegar (1994), Elnagar and Khamayseh (1997), Elnagar and Zafiris (2005), El-kady and Elbarbary (2002), Yousefi et al (2010), Marzban and Razzaghi (2003), Lakestani et al (2006), Elnagar et al (1995), Hager (1990), Polak et al (1993), Elnagar and Kazemi (1998), Elnagar and Razzaghi (1997), Marzban and Razzaghi (2004), Khellat (2009), Razzaghi and Marzban (2002), Razzaghi (2009), Razzaghi and Elnegar (1994) and references therein (see also Razzaghi and Sepehrian, 2004;Navabi et al, 2008;Yousefi et al, 2011;Baleanu et al, 2009;Agrawal, 2008;Agrawal and Baleanu, 2007).…”

Section: Introduction To the Problemmentioning

confidence: 99%

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Radial basis functions approach on optimal control problems: a numerical investigation

Rad

Kazem

Parand

2013

Journal of Vibration and Control

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A numerical method for solving optimal control problems is presented in this work. The method is based on radial basis functions (RBFs) to approximate the solution of the optimal control problems by using collocation method. We applied Legendre–Gauss–Lobatto points for RBFs center nodes to use numerical integration method more easily, then the method of Lagrange multipliers is used to obtain the optimum of the problems. For this purpose different applications of RBFs are used. The differential and integral expressions which arise in the system dynamics, the performance index and the boundary conditions are converted into some algebraic equations which can be solved for the unknown coefficients. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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Numerical methods based on extended one-step methods for solving optimal control problems

Salama

2006

Applied Mathematics and Computation

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A Chebyshev spectral method for time-varying two-point boundary-value and optimal control problems

Cited by 5 publications

References 4 publications

Optimal control approach for discontinuous dynamical systems

Optimal control approach for discontinuous dynamical systems

Radial basis functions approach on optimal control problems: a numerical investigation

Numerical methods based on extended one-step methods for solving optimal control problems

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