Modified optimal energy and initial memory of fractional continuous-time linear systems

Abstract

Fractional systems with Riemann-Liouville derivatives are considered. The initial memory value problem is posed and studied. We obtain explicit steering laws with respect to the values of the fractional integrals of the state variables. The Gramian is generalized and steering functions between memory values are characterized.

Numerical approximations of fractional derivatives with applications

“…This is a recent and promising research subject, under strong current research (see, e.g. , and references therein). Here we show how to use expansions to transform a fractional problem into a classical one, where we can benefit from the vast number of techniques available in the field.…”

“…The fractional calculus of variations consists of the study of dynamic optimization problems in which the objective functional or constraints depend on derivatives and/or integrals of non-integer order. This is a recent and promising research subject, under strong current research (see, e.g., [14,20,21] and references therein). Here we show how to use expansions to transform a fractional problem into a classical one, where we can benefit from the vast number of techniques available in the field.…”

A Rational Approximation Method of Fractional Order Differentiators and Integrators Based On Joint Optimal Criterion

“…In fact, many scientific areas currently are paying attention to these concepts, such as signal process, stochastic processes, vibration suppression, automatic control and so on [1][2][3][4][5][6][7][8]. Hence, their analog and digital implementations are important research topics.…”

Pontryagin maximum principle for fractional ordinary optimal control problems

“…However, its consideration is not new. The first to introduce the initial condition in the study of fractional problems of the calculus of variations were Almeida and Torres ,theorem 6.4 and Mozyrska and Torres in the context of fractional optimal control, where is interpreted as an initial memory value. Several physical interpretations of this condition are demonstrated in .…”