Predefined-time stabilization of high order systems

Jiménez‐Rodríguez, Esteban; Sánchez‐Torres, Juan Diego; Gómez‐Gutiérrez, David; Loukianov, Alexander G.

doi:10.23919/acc.2017.7963865

Cited by 14 publications

(12 citation statements)

References 23 publications

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“…Defining the tracking error variables x 1 = q − q d , x 2 =̇q −̇q d and u = , the mechanical model (14) can be rewritten in the state-space form (10), with f (t, x 1 ,…”

Section: Application: Predefined-time Tracking Of Fully-actuated mentioning

confidence: 99%

“…Thus, the problem of tracking the position q to q d is equivalent to stabilize the system (10). In this sense, the controller (11) developed in the last section constitutes a predefined-time tracking position controller for fully-actuated mechanical systems modeled by (14).…”

Section: Application: Predefined-time Tracking Of Fully-actuated mentioning

confidence: 99%

“…Even so, the term dΦ m 1 ,q 1 (x 1 ;T c 1 ) dx 1 , which produces theoretically infinite signals whenever the system solutions cross the axis x 1 = 0 unless = 0 (see (6)), is also present in the controller. (ii) In fact, the stability analysis in [9,10] assumes implicitly that the system solutions do not cross the axis x 1 = 0 before = 0. However, this assumption does not hold in general.…”

Section: Remarkmentioning

confidence: 99%

See 2 more Smart Citations

Variable Structure Predefined‐Time Stabilization of Second‐Order Systems

Jiménez‐Rodríguez¹,

Sánchez‐Torres

Gómez‐Gutiérrez

et al. 2018

Asian Journal of Control

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A controller that stabilizes second-order vector systems in predefined-time is introduced in this paper. That is, for second-order systems a controller is designed such that the trajectories reach the origin in a time defined in advance. The proposed controller is a variable structure controller that first drive the system trajectories to a linear manifold in predefined time and then drives the system trajectories to a non-smooth manifold with the predefined-time stability property, in predefined time also; this is done in order to avoid the differentiability problem that inherently appears when stabilizing high-order systems in finite time under the block control principle technique. The proposal is applied to the predefined-time exact tracking of fully actuated mechanical systems. As an example, the proposed solution is applied to a two-link planar manipulator, and numerical simulations are conducted to show its performance.

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“…Defining the tracking error variables x 1 = q − q d , x 2 =̇q −̇q d and u = , the mechanical model (14) can be rewritten in the state-space form (10), with f (t, x 1 ,…”

Section: Application: Predefined-time Tracking Of Fully-actuated mentioning

confidence: 99%

Section: Application: Predefined-time Tracking Of Fully-actuated mentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

See 1 more Smart Citation

Variable Structure Predefined‐Time Stabilization of Second‐Order Systems

Jiménez‐Rodríguez¹,

Sánchez‐Torres

Gómez‐Gutiérrez

et al. 2018

Asian Journal of Control

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show abstract

“…Especially, a note on predefined-time stability in [11] pointed that the predefined-time stability of system can be guaranteed without the exponential term. This result allows a construction of the predefined-time stabilizing controller with only polynominal term (instead of the exponential one) and its Lyapunov characterization analysis is perfect, but this class of predefined-time stability function [11,12,13,14] may not consider if system can reach and stay in the neighborhood of equilibrium point within predefined time. The related researchers study a reconstruction method of controller in Definition 3.1 of [8] to make system convergence to the equilibrium point theoretically, but it seems that the actual characterization of the equilibrium point will be different from the description in [8] by considering the analysis and simulation in this paper.…”

Section: Introductionmentioning

confidence: 99%

On Parameter Selection of Nonsingular Predefined-time Terminal Sliding Mode With the Fixed-time Convergence Guarantee

Yan

2020

Preprint

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This paper study the parameter selection of predefined-time sliding mode and try to design a general nonsingular predefinedtime terminal sliding mode. 1). On parameter selection: Some existing predefined-time sliding modes are designed to focus on the reaching time and ignore the characterization of the equilibrium point i.e. xe = 0. In actual engineer, the system can only converge to a small neighborhood near the equilibrium point because of the existence of uncertainty i.e. xe → 0. The actual equilibrium point should be deduced by taking the limit but not directly solve the equilibrium point. Hence, the actual selection of exponential term is suggested to be not 1 to make system convergence to the equilibrium point within predefined time.2). On singularity-avoidance: Based on the exponential feature of predefined-time stability systems, a mathematic concept of switching sliding mode [1] is applied in the design of nonsingular predefined-time terminal sliding mode. However, this class of sliding mode switching method will cause a singular problem, which can be described as control input u → ∞ if the system state x → 0 and any-order time derivative of x is not 0. Hence, a non-singular selection condition for each recursive sliding mode surface is explored in this paper to realize the global finiteness of control input. In addition, an unnecessary chattering of control input will also be caused by the sliding mode switching frequency, and a novel switching condition will be applied in the controller to reduce this chattering. Simulations will be carried out to validate the effect of the novel nonsingular predefined-time sliding mode control method to some extent.

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“…"Fixed-time" stabilization 13,[21][22][23][24][25] further requires that this finite terminal time should be bounded by a constant independent of the initial conditions. Further requiring that this fixed terminal time should be possible to be arbitrarily picked (ie, prescribed) by the designer yields the stronger notion of "prescribed-time" stabilization, [26][27][28][29][30][31][32][33][34][35] that is, prescribed-time stabilization requires that the convergence not just be over a finite time interval, but that the length of the time interval be a parameter that can be arbitrarily prescribed by the control designer independent of initial condition and system dynamics. This prescribed-time stabilization notion can be viewed in the physical context of controls applications such as autonomous vehicle rendezvous, missile guidance, and so on, wherein the state convergence control objective is inherently formulated over a time horizon of predefined length.…”

mentioning

confidence: 99%

Adaptive output‐feedback stabilization in prescribed time for nonlinear systems with unknown parameters coupled with unmeasured states

Krishnamurthy

Khorrami

Krstić

2020

Adaptive Control & Signal

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Summary The prescribed‐time output‐feedback stabilization (ie, regulation of the state and control input to zero within a “prescribed” time picked by the control designer irrespective of the initial state) of a general class of uncertain nonlinear strict‐feedback‐like systems is considered. Unlike prior results, the class of systems considered in this article allows crossproducts of unknown parameters (without any required magnitude bounds on unknown parameters) and unmeasured state variables in uncertain state‐dependent nonlinear functions throughout the system dynamics. We show that prescribed‐time output‐feedback stabilization (ie, both prescribed‐time state estimation and prescribed‐time regulation) is achieved through a novel output‐feedback control design involving specially designed dynamics of an adaptation state variable and a high‐gain scaling parameter in combination with a temporal transformation and a dual high‐gain scaling based observer and controller design. While standard dynamic adaptation techniques cannot be applied due to crossproducts of unknown parameters and unmeasured states, we show that instead, the dynamics of the high‐gain scaling parameter and adaptation parameter can be designed with temporal forcing terms to ensure that unknown parameters in system dynamics are dominated by a particular fractional power of the high‐gain scaling parameter and the adaptation parameter after a subinterval (of unknown length) of the prescribed time interval. We show that the control law can be designed such that the system state and input are regulated to zero in the remaining subinterval of the prescribed time interval.

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Predefined-time stabilization of high order systems

Cited by 14 publications

References 23 publications

Variable Structure Predefined‐Time Stabilization of Second‐Order Systems

Variable Structure Predefined‐Time Stabilization of Second‐Order Systems

On Parameter Selection of Nonsingular Predefined-time Terminal Sliding Mode With the Fixed-time Convergence Guarantee

Adaptive output‐feedback stabilization in prescribed time for nonlinear systems with unknown parameters coupled with unmeasured states

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