Gain-scheduled controller design for discrete-time Linear Parameter Varying systems with multiplicative noises

Ku, Cheung-Chieh; Chen, Guan‐Wei

doi:10.1007/s12555-014-0433-5

Cited by 11 publications

(7 citation statements)

References 28 publications

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“…Based on the PDLF, several positive definite matrices can be assigned to satisfy the LMIs. In our previous works, 2,3,11 we have verified that the stability criterion derived via PDLF is less conservative than one derived via PILF. Although PDLF provides some relaxation in stability analysis of LPV systems, the complexity and difficulty of the derived stability criterion are increased due to the number of LMIs.…”

Section: Introductionmentioning

confidence: 56%

“…One can find the following first forward difference of V ( x ( k )) along the trajectory of ). Moreover, ϑ i ( k ) ϑ j ( k ) ≤ ϑ i ( k ) can be found from Reference 2 due to 0 ≤ ϑ i ( k ) ≤ 1.

\begin{array}{l} Δ V ((), x ((), k)) & = V ((), x ((), k + 1)) - V ((), x ((), k)) \\ = x {(k)}^{T} ((), {(R (α (k)))}^{T} boldP ((), boldR ((), α ((), k))) - boldP) x ((), k) \\ = \sum_{i = 1}^{N} \sum_{j = 1}^{N} \sum_{l = 1}^{N} \sum_{m = 1}^{N} ϑ_{i} ((), k) ϑ_{j} ((), k) ϑ_{l} ((), k) ϑ_{m} ((), k) x {(k)}^{T} ((), R_{ij}^{T} boldP R_{lm} - boldP) x ((), k) \\ \leq \sum_{i = 1}^{N} \sum_{j = 1}^{N} ϑ_{i} ((), k) ϑ_{j} ((), k) x {(k)}^{T} ((), R_{ij}^{T} boldP R_{ij} - boldP) x ((), k) \\ = \sum_{i = 1}^{N} ϑ_{i} ((), k) x {(k)}^{T} ((), R_{ii}^{T} boldP R_{ii} - boldP) x ((), k) + \sum_{i = 1}^{N} \end{array}

…”

Section: Stability Criterion For Lpv System With Pole‐assignment Consmentioning

confidence: 99%

“…Referring to References 2,15‐19, the PDLF is usually proposed to derive the relaxed stability criterion for LPV systems. The reason for reducing conservatism in solving stabilization problem of LPV system is several multiple positive definite matrices in PDLF.…”

Section: Relaxed Stability Criterion For Lpv Systems With Pole‐assignmentioning

confidence: 99%

“…For the error and property, robust control has been widely interested for the stability issues of time‐varying systems. Referring to the literature, 1‐4 the LPV system is consisted of several linear systems and a specific weighting function. The parameters in those linear systems are modeled via the two extremities of the known time‐varying region, and the specific weighting function can be constructed via the time‐varying behaviors.…”

Section: Introductionmentioning

confidence: 99%

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Gain‐scheduled controller design for linear parameter varying systems subject to pole assignment

Chang

Yen

et al. 2020

Optim Control Appl Methods

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Summary This paper addresses a pole‐assignment control problem for discrete‐time linear parameter varying (LPV) systems. Based on LPV modeling approach, time‐varying systems can be mathematically described via combining several linear systems and a specific weighting function. For the LPV systems, gain‐scheduled (GS) control scheme is applied to deal with stabilization problem subject to pole‐assignment constraint. Moreover, two cases of Lyapunov function are respectively employed to derive some sufficient conditions which belong to linear matrix inequality (LMI) problems. Solving those derived conditions, the corresponding GS scheduled controller can be designed such that the asymptotical stability and pole assignment of LPV systems are guaranteed. Finally, a controller problem of truck‐trailer system is used to demonstrate the applicability and effectiveness of the proposed design methods.

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Section: Introductionmentioning

confidence: 56%

\begin{array}{l} Δ V ((), x ((), k)) & = V ((), x ((), k + 1)) - V ((), x ((), k)) \\ = x {(k)}^{T} ((), {(R (α (k)))}^{T} boldP ((), boldR ((), α ((), k))) - boldP) x ((), k) \\ = \sum_{i = 1}^{N} \sum_{j = 1}^{N} \sum_{l = 1}^{N} \sum_{m = 1}^{N} ϑ_{i} ((), k) ϑ_{j} ((), k) ϑ_{l} ((), k) ϑ_{m} ((), k) x {(k)}^{T} ((), R_{ij}^{T} boldP R_{lm} - boldP) x ((), k) \\ \leq \sum_{i = 1}^{N} \sum_{j = 1}^{N} ϑ_{i} ((), k) ϑ_{j} ((), k) x {(k)}^{T} ((), R_{ij}^{T} boldP R_{ij} - boldP) x ((), k) \\ = \sum_{i = 1}^{N} ϑ_{i} ((), k) x {(k)}^{T} ((), R_{ii}^{T} boldP R_{ii} - boldP) x ((), k) + \sum_{i = 1}^{N} \end{array}

…”

Section: Stability Criterion For Lpv System With Pole‐assignment Consmentioning

confidence: 99%

Section: Relaxed Stability Criterion For Lpv Systems With Pole‐assignmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gain‐scheduled controller design for linear parameter varying systems subject to pole assignment

Chang

Yen

et al. 2020

Optim Control Appl Methods

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“…Many researchers have recently considered the problem of robust controller design on linear parameter varying or linear time invariant systems in the regular statespace form such as in [1][2][3][4][5][6][7][8][9][10][11][12][13][14], where the systems are common linear parameter varying (LPV) systems. Unlike the regular state-space forms, descriptor systems enable an expression which includes algebraic conditions on physical factors.…”

Section: Introductionmentioning

confidence: 99%

Gain scheduling LQI controller design for LPV descriptor systems and motion control of two-link flexible joint robot manipulator

Altun

2018

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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This paper proposes a gain scheduling linear quadratic integral (LQI) servo controller design, which is derived from linear quadratic regulator (LQR) optimal control, for non-singular linear parameter varying (LPV) descriptor systems. It is assumed that state space matrices are non-singular since many mechanical systems do not have any non-singular matrices such as the natural state space forms of robotic manipulator, pendulum and suspension systems. A controller design is difficult for the systems due to rational LPV case. Therefore, the proposed gain scheduling controller is designed without the difficulty. Accordingly, the motion control design is implemented for two-link flexible joint robotic manipulator. Finally, the control system simulation is performed to prove the applicability and performance.

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Stabilization and disturbance rejection with decay rate bounding in discrete‐time linear parameter‐varying systems via ℋ_∞gain‐scheduling static output feedback control

Sereni

Assunção

Teixeira

2022

Intl J Robust & Nonlinear

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The stabilization of discrete‐time linear parameter‐varying (LPV) systems via gain‐scheduling static output feedback (SOF) control is addressed in this article. We propose new sufficient linear matrix inequalities (LMI) conditions for synthesizing a gain‐scheduled SOF controller that ensures asymptotic stability and also imposes a lower bound on the closed‐loop decay rate. The SOF controller design is based on a two‐step method: a state‐feedback controller is obtained in a first‐stage design, which is then used as input information in the second stage for computing the desired gain‐scheduled SOF controller. The proposed LMI constraints are given in terms of the existence of affine parameter‐dependent Lyapunov functions, considering arbitrarily fast variation of the time‐varying parameters. An extension for coping with disturbance rejection is also proposed, in terms of the scriptH∞$$ {\mathcal{H}}_{\infty } $$ guaranteed cost optimization. Some numerical experiments are presented to illustrate the control synthesis procedure and its efficacy. Also, feasibility analyses are presented to compare and show the advantages of our results over other available strategies present in literature.

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Gain-scheduled controller design for discrete-time Linear Parameter Varying systems with multiplicative noises

Cited by 11 publications

References 28 publications

Gain‐scheduled controller design for linear parameter varying systems subject to pole assignment

Gain‐scheduled controller design for linear parameter varying systems subject to pole assignment

Gain scheduling LQI controller design for LPV descriptor systems and motion control of two-link flexible joint robot manipulator

Stabilization and disturbance rejection with decay rate bounding in discrete‐time linear parameter‐varying systems via ℋ_∞gain‐scheduling static output feedback control

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Gain-scheduled controller design for discrete-time Linear Parameter Varying systems with multiplicative noises

Cited by 11 publications

References 28 publications

Gain‐scheduled controller design for linear parameter varying systems subject to pole assignment

Gain‐scheduled controller design for linear parameter varying systems subject to pole assignment

Gain scheduling LQI controller design for LPV descriptor systems and motion control of two-link flexible joint robot manipulator

Stabilization and disturbance rejection with decay rate bounding in discrete‐time linear parameter‐varying systems via ℋ∞gain‐scheduling static output feedback control

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Stabilization and disturbance rejection with decay rate bounding in discrete‐time linear parameter‐varying systems via ℋ_∞gain‐scheduling static output feedback control