On the solution of fuzzy fractional optimal control problems with the Caputo derivative

Alinezhad, Masoud; Allahviranloo, Tofigh

doi:10.1016/j.ins.2017.08.094

Cited by 26 publications

(6 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Also, it can improve the robustness and reduce, or even eliminate, chattering phenomena [40,41]. Fractional calculus was used in the control of singular perturbed systems [42], solving optimal control problems [43], tracking control of legged robots [44], fault diagnosis and classification [45], and formation control of multi-agent systems [46]. Besides, fractional-order disturbance observer, which is derived from the integer-order type, was applied to synchronization of two uncertain fractional-order chaotic systems [47].…”

Section: Related Workmentioning

confidence: 99%

Finite-time disturbance reconstruction and robust fractional-order controller design for hybrid port-Hamiltonian dynamics of biped robots

Farid,

Ruggiero

2021

Preprint

View full text Add to dashboard Cite

In this paper, disturbance reconstruction and robust trajectory tracking control of biped robots with hybrid dynamics in the port-Hamiltonian form is investigated. A new type of Hamiltonian function is introduced, which ensures the finite-time stability of the closed-loop system. The proposed control system consists of two loops: an inner and an outer loop. A fractional proportional-integral-derivative filter is used to achieve finite-time convergence for position tracking errors at the outer loop. A fractional-order sliding mode controller acts as a centralized controller at the inner-loop, ensuring the finite-time stability of the velocity tracking error. In this loop, the undesired effects of unknown external disturbance and parameter uncertainties are compensated using estimators. Two disturbance estimators are envisioned. The former is designed using fractional calculus. The latter is an adaptive estimator, and it is constructed using the general dynamic of biped robots. Stability analysis shows that the closed-loop system is finite-time stable in both contact-less and impact phases. Simulation studies on two types of biped robots (i.e., two-link walker and RABBIT biped robot) demonstrate the proposed controller's tracking performance and disturbance rejection capability.

show abstract

Section: Related Workmentioning

confidence: 99%

Finite-time disturbance reconstruction and robust fractional-order controller design for hybrid port-Hamiltonian dynamics of biped robots

Farid,

Ruggiero

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Later, various authors have studied the theoretical and numerical aspects of the optimal control problems for fractional ordinary differential equations. We refer to previous studies [20][21][22] for some relevant articles for the underlying problems. For the control problems governed by fractional PDEs on bounded domains, the work of Mophou et al is worth mentioning.…”

Section: Introductionmentioning

confidence: 99%

Well‐posedness, optimal control and discretization for time‐fractional parabolic equations with time‐dependent coefficients on metric graphs

Mehandiratta

Mehra

Leugering

2022

Asian Journal of Control

View full text Add to dashboard Cite

We study distributed optimal control problems governed by time‐fractional parabolic equations with time dependent coefficients on metric graphs, where the fractional derivative is considered in the Caputo sense. Using the Galerkin method and compactness results, for the spatial part, and approximating the kernel of the time‐fractional Caputo derivative by a sequence of more regular kernel functions, we first prove the well‐posedness of the system. We then turn to the existence and uniqueness of solutions to the distributed optimal control problem. By means of the Lagrange multiplier method, we develop an adjoint calculus for the right Caputo derivative and derive the corresponding first order optimality system. Moreover, we propose a finite difference scheme to find the approximate solution of the state equation and the resulting optimality system on metric graphs. Finally, examples are provided on two different graphs to illustrate the performance of the proposed difference scheme.

show abstract

“…Ghomanjani (2016) applied the Bezier Curves Method for solving FOCP. Alinezhad and Allahviranloo (2017) presented an extension to Fractional Optimal Control Problems withmodeled ambiguity consideringthe fuzzy method associated with the Caputo sense. Jajarmi et al (2018) proposed an iterative approach for solving FOCP taking into accountexternal persistent disturbances.…”

Section: Introductionmentioning

confidence: 99%

Solution of Fractional Optimal Control Problems by using orthogonal collocation and Multi-objective Optimization Stochastic Fractal Search

2021

View full text Add to dashboard Cite

In this contribution the solution of Fractional Optimal Control Problems (FOCP) by using the Orthogonal Collocation Method (OCM) and the Multi-objective Optimization Stochastic Fractal Search (MOSFS) algorithm is investigated. For this purpose, three classical case studies on engineering are considered. Initially, the concentration profiles of laccase enzyme production process are analyzed to evaluate the influence of fractional order. Then, two classical FOCP (Catalyst Mixing and Batch Reactor) are solved by using the association between OCM and MOSFS approachesthrough the formulation and solution of a multi-objective optimization problem. The results indicate that the variation of the fractional order impliesdifferent values for the original objective function. In addition, physicallyincoherent profiles can be obtained by considering the fluctuation of the fractional order. Finally, the proposed MOSFS is considered as apromising methodology to solve multi-objective optimization problems.

show abstract

On the solution of fuzzy fractional optimal control problems with the Caputo derivative

Cited by 26 publications

References 22 publications

Finite-time disturbance reconstruction and robust fractional-order controller design for hybrid port-Hamiltonian dynamics of biped robots

Finite-time disturbance reconstruction and robust fractional-order controller design for hybrid port-Hamiltonian dynamics of biped robots

Well‐posedness, optimal control and discretization for time‐fractional parabolic equations with time‐dependent coefficients on metric graphs

Solution of Fractional Optimal Control Problems by using orthogonal collocation and Multi-objective Optimization Stochastic Fractal Search

Contact Info

Product

Resources

About