An alternate approach to the fixed terminal point regulator problem

Rekasius, Z.

doi:10.1109/tac.1964.1105700

Cited by 59 publications

(33 citation statements)

References 1 publication

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“…Theorem 2 [7] . Consider the linear system (1) with (A, B) reachable, A control law 0 v minimizing the criteria (17) and driving system (1) to 0 F z t at 0 F t for an initial bounded condition z(0) is given by (with 0 …”

Section: Continuous Control Part Designmentioning

confidence: 99%

Sliding Mode Control Algorithm Design for a Class of Unmatched Uncertain System

Zhao

Zhang

et al. 2011

2011 Fourth International Symposium on Parallel Architectures, Algorithms and Programming

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An Integral sliding mode control algorithm for a class of unmatched uncertain system is proposed in this paper. In order to make that the perturbation is minimal, the perturbation is provided into two parts by projection matrix----the matched and unmatched perturbation. It is also shown that when the minimum is attained and the resulting perturbation is not amplified. The controller design uses integral sliding mode concept and optimal control to ensure finite-time convergent in the effect of the unmatched uncertainty. The time convergence is chosen in advance. Simulation studies demonstrate that the proposed controller is robust with respect to the perturbation. An illustrative example of an aircraft control shows the applicability of the method.

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Section: Continuous Control Part Designmentioning

confidence: 99%

Sliding Mode Control Algorithm Design for a Class of Unmatched Uncertain System

Zhao

Zhang

et al. 2011

2011 Fourth International Symposium on Parallel Architectures, Algorithms and Programming

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“…The main disadvantage of open-loop controllers is that they do not produce asymptotic stability (and render the system unstable) if there is any uncertainty or disturbance in the system. A closed-loop continuous time optimal controller can be found in [55] which combines a continuous optimal state feedback with a time varying feedback that drives the trajectories to zero in finite time. This is a feedback form but any uncertainty or disturbances appearing in the system would render the trajectories only asymptotically stable and not finite time stable.…”

Section: B Synthesismentioning

confidence: 99%

“…Interestingly, the optimal controller proposed in [55] is a good example of a state and time dependent finite time stable controller where it was shown that finite time stability holds for the nominal system under appropriate optimality conditions. For the case when disturbances are present, however, the optimal time-varying controller can only coincide with traditional LQR control at best as discussed in [55]. Hence, proving robustness of finite time stable controllers is a theoretical challenge for which various analysis methods outlined in the previous section can be employed.…”

Section: Robustness Guaranteesmentioning

confidence: 99%

Robust finite time stability and stabilisation: A survey of continuous and discontinuous paradigms

Oza

Orlov

Spurgeon

2014

2014 13th International Workshop on Variable Structure Systems (VSS)

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The aim of this paper is to provide a survey of the tools for analysis and synthesis of finite time stable controllers. The paper analyses the literature in continuous and discontinuous finite time stabilisation in a unified way covering both the fundamentals as well as the latest techniques available in this non-linear control paradigm. The contribution of the paper lies in its exposition of the robustness properties that continuous and discontinuous controllers guarantee. Some open problems are identified which are relevant to both the theory and practice of finite time stabilisation.

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“…After tj (t > tj) 8(t) will be removed. In this case, Uo will have two dynamics [25]: U = { -r™z(t)+rT8(t)fo rO:S;t:S;tj (24) o -rTMz(t) for t > tj.…”

Section: Initial Condition 8(0) Of 8(t) Is Selected In Order To Satismentioning

confidence: 99%

“…+ Uo + U dis (25) In order to reject the perturbation 13 (.) for t > 0, U dis is synthesised using the integral sliding mode concept [29], [31].…”

Section: Initial Condition 8(0) Of 8(t) Is Selected In Order To Satismentioning

confidence: 99%

Higher order sliding mode controller for driving steering vehicle wheels: Tracking trajectory problem

Manceur

Menhour

2013

52nd IEEE Conference on Decision and Control

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A higher order sliding controller scheme for a steering vehicle control is proposed in this paper. Since the sys tem is uncertain, to overcome the constraint on the knowledge of the vehicle model, local models related to some operating points have been used to synthesis a nominal fuzzy type-2 global model.The controller is based on the integral sliding mode concept and it is composed of two parts. The first one leads to achieve finite time stabilization of the sliding manifold and its derivatives, it has two dynamics: a robust feedback and a forcing term. The second part has to reject the system uncertainties and noises.As a result, a higher order sliding mode is established and the time convergence is chosen in advance. Promising results have been obtained using real data acquired by a laboratory vehicle. I. INTRODUCTIONThe design of robust vehicle controllers remains an inter esting research topic and has received more attention during the last decades. This, to design the driving aid systems and increase the road safety. The development of such systems, requires the knowledge of the models able to represent the behaviors of the vehicle. Unfortunately, a such requirement is ensured partially and the known nonlinear vehicle models are only used for simulations tests but not for control design. To overcome the models knowledge constraints, several solutions are propose: fuzzy systems [26], [28], [6], [20], switched systems [4], [15], [8] and LPV systems [2]. The first problem addressed in this work is related to the design of a global vehicle model which will be used to develop a robust vehicle controller. In fact, several vehicle controllers based on simple vehicle models are proposed [1], [24], [7], [23]. These controllers are developed to accomplish some maneuvers: platooning [24], stop-and-go control [17], [13], steering and braking control [23], coupled longitudinal and lateral vehicle control [21]. Unfortunately, in major part of these works, simple vehicle models are used in the design controllers procedure. Consequently, the performances and the validity domain of such controllers depend strongly of the vehicle models. To overcome the constraint on the knowledge of the vehicle model, some local vehicle linear models have been used to obtain a nominal type-2 fuzzy model.The second problem treated in this work concerns the design of a robust steering vehicle control using the type-2 fuzzy vehicle model. The proposed steering vehicle control uses higher order sliding mode approach [5], [12]. The sliding mode control (SMC) is among a widely used method because of its simplicity and robustness [30]. However, because of the

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An alternate approach to the fixed terminal point regulator problem

Cited by 59 publications

References 1 publication

Sliding Mode Control Algorithm Design for a Class of Unmatched Uncertain System

Sliding Mode Control Algorithm Design for a Class of Unmatched Uncertain System

Robust finite time stability and stabilisation: A survey of continuous and discontinuous paradigms

Higher order sliding mode controller for driving steering vehicle wheels: Tracking trajectory problem

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