Global stabilization of linear systems via bounded controls

Zhou, Bin; Duan, Guang‐Ren

doi:10.1016/j.sysconle.2008.08.002

Cited by 38 publications

(32 citation statements)

References 19 publications

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“…Similar to the work of Zhou and Duan, it is straightforward to show that there exists a state transformation y = Tx , where T is a nonsingular constant matrix, such that

\begin{matrix} right {\dot{y}}_{m - i} & left = - S (ω) y_{m - i} + \sum_{j = 0}^{i - 1} (\prod_{l = 0}^{j} k_{m - l}) y_{m - j} + u + d & right \\ right {\dot{y}}_{m} & left = - S (ω) y_{m} + u + d, \end{matrix}

where i =1,…, m −1. The control law is chosen as

u = - {normalΣ}_{m} false(y_{m} + {normalΣ}_{m - 1} false(y_{m - 1} + {normalΣ}_{m - 2} false(y_{m - 2} + … {normalΣ}_{1} false(y_{1} false) false) false) false) - Sat false(\overset{d}{true} false),

where

\overset{d}{true}

is obtained from (9), Sat(·) is a saturation function defined

Sat false(\overset{d}{true} false) = ({, \begin{matrix} array \hat{d}, & array if ‖ \hat{d} ‖ \leq d_{M} + d_{R M} / k_{d} \\ array \frac{\hat{d}}{‖ \overset{}{d}} \end{matrix})

…”

Section: Nested Saturation Control For Multiple Vector Integratorsmentioning

confidence: 91%

Nested saturation control of multiple vector integrators and its application to motion control of UAVs

Xie

Veitch

2019

Intl J Robust & Nonlinear

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Summary This paper presents two nested input saturation control schemes for a special class of multiple vector integrators with bounded additive disturbances. The considered systems originate from the motion control of rotary‐wing unmanned aerial vehicles (UAVs). The first scheme is based on a feedforward form, which requires state transformation and can be applied to stabilize arbitrary order vector integrator systems. The second scheme is constructed with original state variables using a new approach, applied here to double vector integrator systems. The capability of handling external disturbance using the two schemes is also analyzed. The two schemes are applied to design motion controllers for rotary‐wing UAVs and simulation results are provided to show the performances of two controllers.

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“…Similar to the work of Zhou and Duan, it is straightforward to show that there exists a state transformation y = Tx , where T is a nonsingular constant matrix, such that

\begin{matrix} right {\dot{y}}_{m - i} & left = - S (ω) y_{m - i} + \sum_{j = 0}^{i - 1} (\prod_{l = 0}^{j} k_{m - l}) y_{m - j} + u + d & right \\ right {\dot{y}}_{m} & left = - S (ω) y_{m} + u + d, \end{matrix}

where i =1,…, m −1. The control law is chosen as

u = - {normalΣ}_{m} false(y_{m} + {normalΣ}_{m - 1} false(y_{m - 1} + {normalΣ}_{m - 2} false(y_{m - 2} + … {normalΣ}_{1} false(y_{1} false) false) false) false) - Sat false(\overset{d}{true} false),

where

\overset{d}{true}

is obtained from (9), Sat(·) is a saturation function defined

Sat false(\overset{d}{true} false) = ({, \begin{matrix} array \hat{d}, & array if ‖ \hat{d} ‖ \leq d_{M} + d_{R M} / k_{d} \\ array \frac{\hat{d}}{‖ \overset{}{d}} \end{matrix})

…”

Section: Nested Saturation Control For Multiple Vector Integratorsmentioning

confidence: 91%

Nested saturation control of multiple vector integrators and its application to motion control of UAVs

Xie

Veitch

2019

Intl J Robust & Nonlinear

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“…Note that the global stabilization of linear control system and Lyapunov equation are usually required to be solved under some assumptions either on the controllability assumption of the normal control system or on the special spectral property of the system matrix A, which turns out to be very restrictive in practice [3,5,9,12]. Moreover, the system considered in this paper is subjected to time-varying delay, which is any continuous function belonging to a given interval, but not necessary to be differentiable.…”

Section: Using Proposition 22 and Newton-leibniz Formula For Estimatmentioning

confidence: 99%

“…This realization, together with the prevalence of hard constraints in control applications, has consequently fostered a large and growing body of research work on control of systems subject to input constraints. Examples include results on constrained optimal quadratic control [6,7], model predictive control [8] and feedback stabilization [9][10][11][12]. The GSP for linear systems without delays has been solved in existing literature, whereas a solution to the linear systems with time delay is not known to our knowledge.…”

Section: Introductionmentioning

confidence: 99%

Global stabilization of linear time-varying delay systems with bounded controls

Phát

Niamsup

2015

Applied Mathematics Letters

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“…In the literature, the nested-saturation based control design is known as an effective technique to design controllers for linear systems subject to input saturation. Generally, for system (1) with d(t) = 0, there are several different nestedsaturation based design methods, such as Bateman and Lin (2003), Raptis, Valavanis, andMoreno (2011), Teel (1992), Zhou and Duan (2009), etc. When these methods are used to design a nested-saturation based controller for system (1), it is found that all of such controllers exhibit the property that the saturation levels change in a non-increasing pattern.…”

Section: Problem Statementmentioning

confidence: 99%

Robust control of multiple integrators subject to input saturation and disturbance

Ding

Zheng

2014

International Journal of Control

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This paper is concerned with the problem of robust stabilisation of multiple integrators systems subject to input saturation and disturbance from the viewpoint of state feedback and output feedback. First of all, without considering the disturbance, a backstepping-like method in conjunction with a series of saturation functions with different saturation levels is employed to design a nested-saturation based state-feedback controller with pre-chosen parameters. On this basis, taking the disturbance into account, a sliding mode disturbance observer (DOB) is adopted to estimate the states and the disturbance. Then, by combining the above state-feedback controller and the estimated states together, a composite controller with disturbance compensation is developed. With the removal of the non-increasing restriction on the saturation levels, the controller design becomes very flexible and the convergence performance of the closed-loop system is much improved. Meanwhile, with the aid of the estimated values by the DOB, we obtain not only the output-feedback control scheme but also the better disturbance rejection property for the closed-loop system. A simulation example of a triple integrators system is presented to substantiate the usefulness of the proposed technique.

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Global stabilization of linear systems via bounded controls

Cited by 38 publications

References 19 publications

Nested saturation control of multiple vector integrators and its application to motion control of UAVs

Nested saturation control of multiple vector integrators and its application to motion control of UAVs

Global stabilization of linear time-varying delay systems with bounded controls

Robust control of multiple integrators subject to input saturation and disturbance

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