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Fixed terminal time fractional optimal control problem for discrete time singular system

Chiranjeevi Tirumalasetty, Devarapalli Ramesh, Babu Naladi Ram, Vakkapatla Kiran Babu, Rao R. Gowri Sankara, Garcìa Màrquez Fausto Pedro

Archives of Control Sciences

2022

Vol. 32, No. 3

489--506

This paper presents the formulation and numerical simulation for linear quadratic optimal control problem (LQOCP) of free terminal state and fixed terminal time fractional order discrete time singular system (FODSS). System dynamics is expressed in terms of Riemann-Liouville fractional derivative (RLFD), and performance index (PI) in terms of state and costate. Because of its complexity, finding analytical and numerical solutions to singular system (SS) is difficult. As a result, we use coordinate transformation to convert FODSS to its corresponding fractional order discrete time nonsingular system (FODNSS). After that, we obtain the necessary conditions by employing a Hamiltonian approach. The relevant conditions are solved using the general solution approach. For the analysis of formulation and solution algorithm, a numerical example is illustrated. Results are obtained for various 𝛼 values. According to state of the art, this is the first time that a formulation and numerical simulation of free terminal state and fixed terminal time optimal control problem (OCP) of FODSS is presented.

On optimal control problem subject to fractional order discrete time singular systems

Chiranjeevi Tirumalasetty, Biswas Raj Kumar, Devarapalli Ramesh, Babu Naladi Ram, García Márquez Fausto Pedro

Archives of Control Sciences

2021

Vol. 31, No. 4

849--863

In this work, we present optimal control formulation and numerical algorithm for fractional order discrete time singular system (DTSS) for fixed terminal state and fixed terminal time endpoint condition. The performance index (PI) is in quadratic form, and the system dynamics is in the sense of Riemann-Liouville fractional derivative (RLFD). A coordinate transformation is used to convert the fractional-order DTSS into its equivalent non-singular form, and then the optimal control problem (OCP) is formulated. The Hamiltonian technique is used to derive the necessary conditions. A solution algorithm is presented for solving the OCP. To validate the formulation and the solution algorithm, an example for fixed terminal state and fixed terminal time case is presented.