Optimal preview control: A review

Birla, Nidhika; Swarup, Akhilesh

doi:10.1002/oca.2106

Cited by 99 publications

(81 citation statements)

References 63 publications

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“…It is well known that every system has certain limitations or constraints that can be avoided by suitably utilizing the additional information or the preview information of the signals. Thus, the field of preview control has attracted researchers and scientists for its applications in varied areas, for instance, flight control, autonomous vehicle guidance, robotics, and signal processing . The error signal e ( k ) is defined as

e ((), k) = y ((), k) - r ((), k) .

In this paper, our objective is to design a preview control law in such a manner that the output y ( k ) tracks the reference signal r ( k ) even in the presence of model uncertainty or unknown disturbances, namely,

\lim_{k \to \infty} e ((), k) = \lim_{k \to \infty} ((), y ((), k) - r ((), k)) = 0 .

Consider an interconnection system consisting of

S_{1}

and

S_{2}

S_{1} : η ((), k) = normalT ((), σ ((), k)); S_{2} : σ ((), k) = normalΔ ((), η ((), k)),

where the forward

S_{1}

is a known linear time‐invariant system with the operator T mapping σ ( k ) to η ( k ), and the feedback

S_{2}

is an unknown linear time‐varying system with the operator

normalΔ \in D = ({}, normalΔ : {‖normalΔ‖}_{\infty} \leq 1)

and η ( k ) ∈ R η , σ ( k ) ∈ R σ .…”

Section: Problem Formulation and Basic Assumptionsmentioning

confidence: 99%

“…Its current control action is obtained at each sampling instant by solving a finite‐time domain open‐loop optimal control problem . In a preview control problem, if the future information of the reference signals or the disturbances is available, then we can fully utilize the future information about reference signals or disturbances to improve the performance of the transient responses . The classical method of preview control is to construct an error system by applying the difference operator to the equation of the state and error vectors, by which the tracking control problem is transformed into a regulator problem.…”

Section: Introductionmentioning

confidence: 99%

“…In preview control, most control methods are based on linear quadratic control theory . These methods, however, do not consider the unknown disturbances effect on the system when designing a preview controller.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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e ((), k) = y ((), k) - r ((), k) .

\lim_{k \to \infty} e ((), k) = \lim_{k \to \infty} ((), y ((), k) - r ((), k)) = 0 .

Consider an interconnection system consisting of

S_{1}

and

S_{2}

S_{1} : η ((), k) = normalT ((), σ ((), k)); S_{2} : σ ((), k) = normalΔ ((), η ((), k)),

where the forward

S_{1}

is a known linear time‐invariant system with the operator T mapping σ ( k ) to η ( k ), and the feedback

S_{2}

is an unknown linear time‐varying system with the operator

normalΔ \in D = ({}, normalΔ : {‖normalΔ‖}_{\infty} \leq 1)

and η ( k ) ∈ R η , σ ( k ) ∈ R σ .…”

Section: Problem Formulation and Basic Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Yuan

2019

Intl J Robust & Nonlinear

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show abstract

“…Optimal control problems have been widely studied since the 1950s, with sustained efforts to promote practical applications (e.g., ). In this section, we present the design of EPTOS control for typical servo systems characterized by an integrator cascaded with an inertia block:

({, \begin{matrix} \dot{y} = v, \\ \dot{v} = a \cdot v + b \cdot sat (u), \end{matrix})

where y is the output position (measurable), v represents the velocity signal, and u is the control input of the plant.…”

Section: Expanded Proximate Time‐optimal Servomechanism Controlmentioning

confidence: 99%

Expanded proximate time‐optimal servo control of permanent magnet synchronous motor

Lü

Cheng

2015

Optim Control Appl Methods

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Summary This paper extends the existing proximate time‐optimal servomechanism control methodology to the more typical second‐order servo systems with a damping element. A parameterized design of expanded proximate time‐optimal servomechanism control law with a speed‐dependent linear region is presented for rapid and smooth set‐point tracking using a bounded input signal. The control scheme uses the time‐optimal bang‐bang control law to accomplish maximum acceleration or braking whenever appropriate and then smoothly switches into a linear control law to achieve a bumpless settling. The closed‐loop stability is analyzed, and then the control scheme is applied to the position–velocity control loop in a permanent magnet synchronous motor servo system for set‐point position regulation. Numerical simulation has been conducted, followed by experimental verification based on a TMS320F2812 digital signal controller board. The results confirm that the servo system can track a wide range of target references with superior transient performance and steady‐state accuracy. Copyright © 2015 John Wiley & Sons, Ltd.

show abstract

“…Its current control action is obtained at each sampling instant by solving a finite‐time domain open‐loop optimal control problem . In a preview control problem, if the future information of the reference signals or the disturbances is available, then we can fully utilize the future information about reference signals or disturbances to improve the performance of the transient responses . As it is well known, every system has certain limitations or constraints that can be avoided by suitably utilizing the additional information or the preview information of the signals.…”

Section: Introductionmentioning

confidence: 99%

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.

show abstract

Optimal preview control: A review

Cited by 99 publications

References 63 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

Expanded proximate time‐optimal servo control of permanent magnet synchronous motor

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

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