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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.

Synthesis of the Quadratic Near-optimal Closed of a Linear System with Disturbances

Pełczewski J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2002

Vol. 50, Nr 2

153--159

The paper deals with the synthesis procedure of a closed-loop quadratic, near-optimal control of a linear, time-invariant system, subject to known, deterministic, external disturbances. On the basis of the approximate, open-loop control obtained for that system by application of Legendre polynomials method the state-feedback matrix and the input signal vector were found.