Optimal control problem for linear fractional-order systems

Кубышкин, В. А.; Postnov, S. S.

doi:10.1109/icfda.2014.6967412

Cited by 3 publications

(9 citation statements)

References 8 publications

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“…Consequently, the moment problem for Riemann-Liouville system differs from the problem for analogous Caputo system only by expressions (and values) for the moments. So, the theorems concerning correctness and solvability of the moment problem, proved for Caputo systems [5][6][7][8], will be valid also for analogous Riemann-Liouville systems. Thus, if there exists at least one nonzero moment in the set , = 1, , we have the following conditions for multidimensional Riemann-Liouville system:…”

Section: The Correctness and Solvability Of Moment Problemmentioning

confidence: 94%

“…Also we will compare obtained results with results described in [5,6,8] for system (1) with Caputo left-side derivative [9]:…”

Section: Problem Statementmentioning

confidence: 99%

“…It is known that optimal control problems in form of Problems 2 and 3 can be reduced to Problem 4 in case of integer-order systems with lumped parameters [4]. It was shown in [5][6][7][8] that the same is valid for Caputo systems. Below we will demonstrate that for Riemann-Liouville systems Problems 2 and 3 also can be reduced to Problem 4.…”

Section: The Moment Problemmentioning

confidence: 99%

“…As in case of integer-order systems, solutions (17) and (18) at = can be written in the form of expression (9) and, consequently, can be represented in the form of moment problem (in case of Caputo system it is demonstrated in detail in [5][6][7][8]). And in both of these solutions the components of matrix -exponent act as functions ( ).…”

Section: The Correctness and Solvability Of Moment Problemmentioning

confidence: 99%

“…Another effective and quite universal approach to the search of optimal control is moment method [4]. Based on these methods in [5][6][7][8] the approach was developed to investigation of optimal control problems for linear dynamic systems of fractional order with lumped parameters, described by equations with Caputo derivative. In [6,8] this approach was generalized on systems with distributed parameters, described by diffusion-like equation with Caputo time-derivative.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Control Problem Investigation for Linear Time-Invariant Systems of Fractional Order with Lumped Parameters Described by Equations with Riemann-Liouville Derivative

Кубышкин

Postnov

2016

Journal of Control Science and Engineering

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This paper studies two optimal control problems for linear time-invariant systems of fractional order with lumped parameters whose dynamics is described by equations which contain Riemann-Liouville derivative. The first problem is to find control with minimal norm and the second one is to find control with minimal control time at given restriction for control norm. The problem setting with nonlocal initial conditions is considered which differs from other known settings for integer-order systems and fractional-order systems described in terms of equations with Caputo derivative. Admissible controls are allowed to belong to the class of functions which are -integrable on half segment. The basic investigation approach is the moment method. The correctness and solvability of moment problem are validated for considered problem setting for the system of arbitrary dimension. It is shown that corresponding conditions are analogous to those derived for systems which are described in terms of equations with Caputo derivative. For several particular cases of one-and two-dimensional systems the posed problems are solved explicitly. The dependencies of basic values from derivative index and control time are analyzed. The comparison is performed of obtained results with known results for analogous integer-order systems and fractional-order systems which are described by equations with Caputo derivative.

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Section: The Correctness and Solvability Of Moment Problemmentioning

confidence: 94%

“…Also we will compare obtained results with results described in [5,6,8] for system (1) with Caputo left-side derivative [9]:…”

Section: Problem Statementmentioning

confidence: 99%