Stability and Control Design  for Time-Varying Systems with Time-Varying Delays using a Trajectory-Based Approach

Mazenc, Frédéric; Malisoff, Michael; Niculescu, Silviu–Iulian

doi:10.1137/15m1027838

Cited by 36 publications

(27 citation statements)

References 36 publications

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“…Now, consider t i ∈ T . Taking a time-derivative of (50) for t ∈ (t i ,t i+1 ) and using integrations by parts jointly with (22)- (23) and Lemma 4, one getṡ…”

Section: Stability Analysis -Proof Of Theoremmentioning

confidence: 99%

“…By contrast with previous works accounting explicitly for the delay (that is, without recasting it as a disturbance) and assuming thaṫ D(t) ≤ 1 for t ≥ 0 (see [5] [14] [36]), we allow the delay to be such thatḊ(t) > 1 on some interval of time. A delay of this type, considered for the first time in preliminary study [9] in a prediction design context, is also considered in [25] and [23], but, in these papers the delay is supposed to be equal to a function of class C 1 plus a small discontinuous part, treated as a disturbance. We do not impose such an assumption; in other words, we consider delays with more general types of discontinuities, covering the case where they have large discontinuous jumps.…”

Section: Introductionmentioning

confidence: 99%

“…We follow our preliminary study [9] which, as a first step, considered the delay function to be continuously differentiable, which is a demanding assumption from a practical point of view, and apply the novel time-varying version of Halany inequality proposed in [23] to address delay jumps. In this paper, as a result, the delay is only assumed to be piecewise continuously differentiable, encompassing potential sudden delay jumps and discontinuities, which are quite common, e.g., in the context of networks and communication protocols.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust compensation of a chattering time-varying input delay with jumps

2018

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We investigate the design of a prediction-based controller for a linear system subject to a time-varying input delay, not necessarily First-In/First-Out (FIFO). This means that the input signals can be reordered. The feedback law uses the current delay value in the prediction. It does not exactly compensate the delay in the closed-loop dynamics but does not require to predict future delay values, contrary to the conventional prediction technique. Modeling the input delay as a transport Partial Differential Equation, we prove asymptotic stabilization of the system state, that is, robust delay compensation, providing that the average L 2-norm of the delay time-derivative over some time-window is sufficiently small and that the average time between two discontinuities (average dwell time) is sufficiently large.

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“…Now, consider t i ∈ T . Taking a time-derivative of (50) for t ∈ (t i ,t i+1 ) and using integrations by parts jointly with (22)- (23) and Lemma 4, one getṡ…”

Section: Stability Analysis -Proof Of Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust compensation of a chattering time-varying input delay with jumps

2018

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“…Our results on delay margin focused on the use of LTI controller. For some nonlinear feedback controllers, such as adaptive controllers [13,14], and nonlinear controllers [15,16], the delay margin can be made infinite. Because these controllers are not easy to implement, it is still desired to study LTI controllers.…”

Section: Introductionmentioning

confidence: 99%

Achievable delay margin using LTI control for plants with unstable complex poles

Zhang

2018

Sci. China Inf. Sci.

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We consider the achievable delay margin of a real rational and strictly proper plant, with unstable complex poles, by a linear time-invariant (LTI) controller. The delay margin is defined as the largest time delay such that, for any delay less than this value, the closed-loop stability is maintained. Drawing upon a frequency domain method, particularly a bilinear transform technique, we provide an upper bound of the delay margin, which requires computing the maximum of a one-variable function. Finally, the effectiveness of the theoretical results is demonstrated through a numerical example.Keywords delay margin, systems with time-delay, time-invariant systems, unstable complex poles, frequency domain method CitationJu P J, Zhang H S. Achievable delay margin using LTI control for plants with unstable complex poles. Sci China Inf Sci, 2018, 61(9): 092203, https://doi.

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“…Predictor‐based controls for linear systems with input delays were developed in other works . For nonlinear systems with time‐varying input delays, as well as wave actuator dynamics with moving boundaries, predictor controls have also been achieved. The implementation and approximation issues of predictor‐feedback law can be found in the work of Karafyllis and Krstic …”

Section: Introductionmentioning

confidence: 99%

Inverse optimal control for strict‐feedforward nonlinear systems with input delays

Cai

Lin

Liu

et al. 2018

Intl J Robust & Nonlinear

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We consider inverse optimal control for strict-feedforward systems with input delays. A basic predictor control is designed for compensation for this class of nonlinear systems. Furthermore, the proposed predictor control is inverse optimal with respect to a meaningful differential game problem. For a class of linearizable strict-feedforward system, an explicit formula for compensation for input delay, which is also inverse optimal with respect to a meaningful differential game problem, is also acquired. A cart with an inverted pendulum system is given to illustrate the validity of the proposed method. KEYWORDSactuator delay, explicit formula, inverse optimality, predictor feedback, strict-feedforward systems 2976

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Stability and Control Design for Time-Varying Systems with Time-Varying Delays using a Trajectory-Based Approach

Cited by 36 publications

References 36 publications

Robust compensation of a chattering time-varying input delay with jumps

Robust compensation of a chattering time-varying input delay with jumps

Achievable delay margin using LTI control for plants with unstable complex poles

Inverse optimal control for strict‐feedforward nonlinear systems with input delays

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