Novel closed-loop controllers for fractional linear quadratic time-varying systems

Malmir, Iman

doi:10.3934/naco.2022032

Cited by 7 publications

(2 citation statements)

References 47 publications

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“…where bϕ in (35) is the product operational matrix of b ϕ . There are significant differences between bSC and bSL , for more detailed information, see [27]. For the equivalent term of c(t){∂ γ x(y, t)/∂t γ },…”

Section: Definition 23 Polynomials Expansionsmentioning

confidence: 99%

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Simulating two-dimensional optimal control problem of fractional partial differential equations

Malmir

2023

ACSE

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In this work, a novel method for simulating the fractional twodimensional linear-quadratic optimal control problem of fractional partial differential equations is introduced. Here, the fractional two-dimensional optimal control problems are transformed into a quadratic programing framework by which we can use many quadratic programming solvers. There is no need to find the optimality conditions and no need to use any multiplier. The optimal control problem involves a two-dimensional performance index and the control of problem depends on both spatial and temporal variables. Some illustrative examples with complicated and challenging situations are investigated.

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Section: Definition 23 Polynomials Expansionsmentioning

confidence: 99%

“…The shifted Legendre polynomials given by ( 8) form an orthogonal basis with respect to the weight functions ς SL (t) = 1 and the shifted Chebyshev polynomials given by ( 9) form an orthogonal basis with respect to ς SC (t) = 1/ 1 − (2t − 1) 2 . As another property of the many properties of these polynomials given in [27], we know for m ≥ 1 and τ ∈…”

mentioning

confidence: 99%