Parameter‐dependent preview control with robust tracking performance

Li, Li; Liao, Fang

doi:10.1049/iet-cta.2016.0361

Cited by 39 publications

(47 citation statements)

References 45 publications

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“…Define ΔV ( k ) = V ( k + 1) − V ( k ). Then, the following equality holds along the solution of system :

\begin{matrix} lefttrue \\ normalΔ V = \overset{true^}{x} {((), k + 1)}^{T} P (θ) \overset{true^}{x} (k) - \overset{true^}{x} {((), k)}^{T} P (θ) \overset{true^}{x} (k) + \overset{true^}{x} {((), k)}^{T} (Q_{1} (θ) + Q_{2} (θ)) \overset{true^}{x} (k) \\ - \overset{true^}{x} {((), k - d_{1})}^{T} Q_{1} (θ) \overset{true^}{x} (k - d_{1}) - \overset{true^}{x} {((), k - d_{2})}^{T} Q_{2} (θ) \overset{true^}{x} (k - d_{2}) + η {((), k)}^{T} \\ ({d_{1}}^{2} R_{1} (θ) + {d_{2}}^{2} R_{2} (θ)) η (k) - \sum_{l = 1}^{2} \sum_{j = k - d_{l}}^{k - 1} [d_{l} η {((), j)}^{T} R_{l} (θ) η (j)] . \end{matrix}

Using the Jensen inequality, the following can be obtained:

- \sum_{l = 1}^{2} \sum_{j =}

…”

Section: Derivation Of the Augmented Error Systemmentioning

confidence: 99%

“…This paper is focused on designing a static output feedback control law with a preview action for polytopic uncertain discrete‐time systems with a time‐varying delay. Unlike in the aforementioned works, the difference operator approach cannot be employed to derive an error system, due to the existence of the time‐varying delay term in this paper. To overcome this difficulty, the time‐varying term is eliminated by using the two‐term approximation method.…”

Section: Introductionmentioning

confidence: 99%

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Output feedback preview control for polytopic uncertain discrete‐time systems with time‐varying delay

Yuan

2019

Intl J Robust & Nonlinear

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Summary This paper considers the preview tracking control problem of polytopic uncertain discrete‐time systems with a time‐varying delay subject to a previewable reference signal. First, a model transformation is employed and a discrete‐time system with a time‐invariant delay and an external disturbance is obtained. The difference operator method can be extended to derive an augmented error system that includes future information on the reference signal. Then, a previewable reference signal is fully utilized through reformulation of the output equation while considering the output feedback. Based on the small gain theorem, a static output feedback controller with preview actions is designed such that the output can asymptotically track the reference signal. Finally, numerical simulation examples also illustrate the superiority of the desired preview controller for the uncertain system in the paper.

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“…Define ΔV ( k ) = V ( k + 1) − V ( k ). Then, the following equality holds along the solution of system :

\begin{matrix} lefttrue \\ normalΔ V = \overset{true^}{x} {((), k + 1)}^{T} P (θ) \overset{true^}{x} (k) - \overset{true^}{x} {((), k)}^{T} P (θ) \overset{true^}{x} (k) + \overset{true^}{x} {((), k)}^{T} (Q_{1} (θ) + Q_{2} (θ)) \overset{true^}{x} (k) \\ - \overset{true^}{x} {((), k - d_{1})}^{T} Q_{1} (θ) \overset{true^}{x} (k - d_{1}) - \overset{true^}{x} {((), k - d_{2})}^{T} Q_{2} (θ) \overset{true^}{x} (k - d_{2}) + η {((), k)}^{T} \\ ({d_{1}}^{2} R_{1} (θ) + {d_{2}}^{2} R_{2} (θ)) η (k) - \sum_{l = 1}^{2} \sum_{j = k - d_{l}}^{k - 1} [d_{l} η {((), j)}^{T} R_{l} (θ) η (j)] . \end{matrix}

Using the Jensen inequality, the following can be obtained:

- \sum_{l = 1}^{2} \sum_{j =}

…”

Section: Derivation Of the Augmented Error Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Output feedback preview control for polytopic uncertain discrete‐time systems with time‐varying delay

Yuan

2019

Intl J Robust & Nonlinear

Self Cite

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“…Remark It should be pointed out that a new approach for discrete‐time descriptor systems with time‐varying parameters is being proposed to derive the augmented error system. The classical difference operator methods in the work of Li and Liao are not applicable due to the appearance of time‐varying uncertainties. Unlike the work of Li and Liao, the state vector

\overset{x}{true} ((), k)

does not include the error vector e ( k ).…”

Section: Construction Of the Augmented Error Systemmentioning

confidence: 99%

“…Other works investigated the problem of stability analysis and optimal preview controller design for linear constant systems based on linear quadratic regulator theory. Several papers address the control of stochastic systems, delay systems, and uncertain systems . In recent years, a great deal of attention has been devoted to the incorporation of other theories and problems.…”

Section: Introductionmentioning

confidence: 99%

“…Several papers address the control of stochastic systems, 19,20 delay systems, 21 and uncertain systems. [22][23][24][25] In recent years, a great deal of attention has been devoted to the incorporation of other theories and problems. For example, in the nonlinear case, the problem of stability analysis and control design has been studied based on the differentiable mean value theorem.…”

Section: Introductionmentioning

confidence: 99%

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Output feedback preview tracking control for time‐varying polytopic descriptor systems

Yan

2019

Optim Control Appl Methods

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Summary This paper focuses on the problem of static output feedback preview tracking control for discrete‐time descriptor systems with time‐varying parameters subject to a previewable reference signal. First, an augmented error system including the information of the future reference signal is constructed based on the error system approach. Second, a preview control policy is constructed by integrating output feedback, preview action, and integral operation. Relying on the augmentation modeling technique, a linear preview control design problem is transformed into an equivalent augmented output‐feedback control design problem. New design conditions guaranteeing the existence of a stabilizing controller are recast as an LMI‐based feasibility problem. The proposed preview controller design method requires neither special constraints on the state‐space system matrices nor a high‐dimensional augmented error system. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

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Preview repetitive control for linear discrete‐time periodic systems

2021

Adaptive Control & Signal

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A discrete-time preview repetitive control (PRC) scheme was proposed for linear discrete-time periodic systems that were subjected to previewable reference signals. First, the state augmentation technique was used to derive an augmented system that included future information on previewable signals. Second, a two-dimensional (2D) model was developed for the augmented system so that the control and leaning actions can be adjusted preferentially by using control gains. Sufficient conditions that guarantee the closed-loop stability of the augmented 2D systems were derived, and the design of a periodic controller with preview action and repetitive control was proposed using the linear matrix inequality approach. Finally, the effectiveness of the proposed PRC was established by using two numerical simulation examples.

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Parameter‐dependent preview control with robust tracking performance

Cited by 39 publications

References 45 publications

Output feedback preview control for polytopic uncertain discrete‐time systems with time‐varying delay

Output feedback preview control for polytopic uncertain discrete‐time systems with time‐varying delay

Output feedback preview tracking control for time‐varying polytopic descriptor systems

Preview repetitive control for linear discrete‐time periodic systems

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