Fractional order optimal control problems with free terminal time

By Shakoor Pooseh, Ricardo Almeida, Delfim F. M. Torres. 2013

131 citations recorded by the source corpus.

We consider fractional order optimal control problems in which the dynamic control system involves integer and fractional order derivatives and the terminal time is free. Necessary conditions for a state/control/terminal-time triplet to be optimal are obtained. Situations with constraints present at the end time are also considered. Under appropriate assumptions, it is shown that the obtained necessary optimality conditions become sufficient. Numerical methods to solve the problems are presented, and some computational simulations are discussed in detail.

Subfields: Aerospace Engineering, Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/6266a7a8c750fdd0a4188a509d2123fdbc21e416

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Aerospace Engineering

1. Ricardo Almeida
2. Dumitru Băleanu

In Control and Systems Engineering

1. Dumitru Băleanu
2. Amin Jajarmi
3. Ricardo Almeida
4. Loïc Bourdin
5. Tugba Akman Yildiz
6. Burak Yıldız
7. Maïtine Bergounioux
8. Delfim F. M. Torres

In Modeling and Simulation

1. Amin Jajarmi
2. Dumitru Băleanu
3. Delfim F. M. Torres
4. Loïc Bourdin
5. Ricardo Almeida
6. Maïtine Bergounioux
7. Tugba Akman Yildiz
8. Burak Yıldız

Citations in the corpus

• A Caputo fractional derivative of a function with respect to another function (2016, background): “However, in the past decades, this subject has proven its applicability in many and different natural situations, such as viscoelasticity [11, 26], anomalous diffusion [14, 19], stochastic processes [9, 29], signal and image processing [31], fractional models and control [24, 32], etc.”
• New aspects of time fractional optimal control problems within operators with nonsingular kernel (2020, methodology): “As a different model, a free final time FOCP governed by a dynamical model involving integer and fractional order derivatives has been studied in [49].”
• Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints (2020, background): “We refer to [3, 4, 8, 32, 46] for previous numerical studies on fractional optimal control problems.”
• A discrete method to solve fractional optimal control problems (2014, background): “Sufficient and necessary conditions to obtain solutions for this problem were studied in [14].”