Exact Controllability for Time Varying Singular Distributed Parameter System in Hilbert Space

Ge, Zhaoqiang; Feng, Donghai

doi:10.1109/is3c.2012.197

Cited by 2 publications

(6 citation statements)

References 10 publications

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“…Remark 2: With the generalized operator semigroup theory and differential inequalities, Ge et. and his work team make several insight results on well-posedness of SDPSs [14], [15], [51]. The existence, uniqueness and constructive expression for the strong solution z d (ξ, t) in ( 5) can be found in ( [51], Thm.…”

Section: System Description and Problem Formulation A Problem Formula...mentioning

confidence: 99%

“…Remark 3: The learning systems (15) has infinite number of singular systems. The transformed systems (17) is the limited equivalence to singular systems (15), which consists of fast subsystems (the systems state is X k n1 (t)) and slow subsystems (the systems state is X k n2 (t)).…”

Section: B Systems Simplification Via the Separation Principlementioning

confidence: 99%

“…differential-algebraic equations was solved based on the Kronecker-Weierstrass form of the matrix pencil. Meanwhile, there are still also other research attentions on SDPSs, such as decoupling [11], controllability and observability [12], passivity criteria [13], exponential stability [14], solvability [15], and so forth.…”

Section: Introductionmentioning

confidence: 99%

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Mixed PD-Type Iterative Learning Control Algorithm for a Class of Parabolic Singular Distributed Parameter Systems

Dai

Zhou

2021

IEEE Access

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In this paper, the iterative learning control (ILC) problem is investigated for a class of time-invariant parabolic singular distributed parameter systems. Initially, the singular distributed parameter systems is decomposed into infinite number of singular systems based on the separation principle. Meanwhile, the slow-fast subsystems are introduced via singular value decomposition method. Then, a novel mixed PD-type ILC algorithm with finite dimension is designed for the low dimensional slow part and the corresponding convergence conditions are manifested. With the proposed controller, the output error of high dimensional fast complement can satisfy the given value instead of neglecting the effect of high dimensional modes. Furthermore, under the aforesaid ILC law and the appropriate number of the low dimensional slow part, the resulting tracking error of parabolic singular distributed parameter systems can converge to any small tracking accuracy. Finally, simulation results on the distributed building automatic temperature system verify the convergence and effectiveness of the mixed PD-type ILC algorithm.

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Section: System Description and Problem Formulation A Problem Formula...mentioning

confidence: 99%

Section: B Systems Simplification Via the Separation Principlementioning

confidence: 99%

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Mixed PD-Type Iterative Learning Control Algorithm for a Class of Parabolic Singular Distributed Parameter Systems

Dai

Zhou

2021

IEEE Access

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“…According to (7), we can prove that P is a mapping from ([0, ]; ) C T X to itself, and for arbitrary 12 ,…”

Section: Semilinear Singular Distributed Parameter Systemmentioning

confidence: 99%

“…The exact controllability concerning the infinite dimensional nonlinear systems were discussed in [2][3][4][5][6][7][8][9][10]. The exact controllability of the infinite dimensional linear singular systems were discussed in [11][12][13][14]. It is regrettably that the exact controllability of the infinite dimensional nonlinear singular systems was not discussed.…”

Section: Introductionmentioning

confidence: 99%

Mild Solution and Exact Controllability of Semilinear Singular Distributed Parameter Systems

2014

2014 International Conference on Automatic Control Theory and Application

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Mild solution and exact controllability of semilinear singular distributed parameter system are discussed in Hilbert space, some results are obtained by functional analysis and generalized operator semigroup. First, we study the classical solution concerning the homogeneous linear singular distributed parameter system by generalized operator semigroup. Second, the existence and uniqueness for the mild solution of semilinear singular distributed parameter system is proved. Third, a new result concerning the exact controllability of linear singular distributed parameter system is obtained. At last, the exact controllability for the semilinear singular distributed parameter system is discussed. This research is theoretical important for studying the controllability of nonlinear singular distributed parameter systems.

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Exact Controllability for Time Varying Singular Distributed Parameter System in Hilbert Space

Cited by 2 publications

References 10 publications

Mixed PD-Type Iterative Learning Control Algorithm for a Class of Parabolic Singular Distributed Parameter Systems

Mixed PD-Type Iterative Learning Control Algorithm for a Class of Parabolic Singular Distributed Parameter Systems

Mild Solution and Exact Controllability of Semilinear Singular Distributed Parameter Systems

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