Solvability of the output regulation problem for switched non-linear systems

Xiao, Dong; Zhao, Jun

doi:10.1049/iet-cta.2011.0075

Cited by 16 publications

(7 citation statements)

References 16 publications

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“…Necessary and sufficient conditions for the output regulability of switched linear systems with arbitrary switching were derived in [15] using the CLF approach. This result was further extended by [16], [13] using the ADT technique with MLFs. One common limitation of these results is that the external signals (including the reference inputs and/or the disturbances) are assumed to be generated by a single neutrally stable exosystem.…”

Section: Introductionmentioning

confidence: 81%

“…when switching occurs (19) With the controller parametrization (10), it can be verified that conditions (13) and (14) lead to the system matrices of the above transformed closed-loop system as…”

Section: B Dilated Lmi Representations Of the Brlmentioning

confidence: 99%

“…Output regulation of various dynamical systems has been extensively studied in control community (see [9], [10], [11], [12], [13], [14] and the reference therein). This problem specifies the control task of achieving not only the overall closed-loop stability, but also the tracking and/or rejection of persistent references/disturbances generated by an exosystem [12].…”

Section: Introductionmentioning

confidence: 99%

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Almost output regulation of discrete-time switched linear systems

Yuan

Chen

2015

2015 American Control Conference (ACC)

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In this paper, we propose a new hybrid control approach for almost output regulation of a class of discretetime switched linear systems with average dwell time (ADT). Both controlled plant and exosystem are described by switched linear systems. The proposed hybrid controller is constructed as a switching impulsive system, where the controller states will undergo impulsive jumps at each switching instant. By using the ADT technique incorporated with multiple quadratic Lyapunov functions, the hybrid synthesis conditions for almost output regulation with asymptotic stability and weighted H∞ performance are formulated as a set of linear matrix equations and linear matrix inequalities (LMIs), which can be solved effectively. The proposed hybrid control method has been demonstrated through a numerical example.

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Section: Introductionmentioning

confidence: 81%

Section: B Dilated Lmi Representations Of the Brlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Almost output regulation of discrete-time switched linear systems

Yuan

Chen

2015

2015 American Control Conference (ACC)

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“…Similar to the work of Fan et al, 42 the time interval between 2 continuous triggering time instants will be a positive number related to δ i k and ||e γ i (t i k )||. If ||…”

Section: Theorem 1 Suppose That Assumptions 1 3 and 4 Hold Thenmentioning

confidence: 95%

“…Similar to the work of Fan et al, the time interval between 2 continuous triggering time instants will be a positive number related to

{normalδ}_{k}^{i}

and

‖ e_{γ_{i}} false(t_{k}^{i} false) ‖

. If

‖ \sum_{\begin{matrix} 0 \\ j \in {normalΦ}_{i} \\ \bar{N} + 1 \leq j \leq N \end{matrix}} a_{i j} false[e_{γ_{i}} false(t_{k}^{i} false) - e_{γ_{j}} false(t_{k}^{i} false) false] + \sum_{\begin{matrix} 0 \\ j \in {normalΦ}_{i} \\ 1 \leq j \leq \bar{N} \end{matrix}} a_{i j} false[e_{γ_{i}} false(t_{k}^{i} false) - \overset{e}{true} false(t_{k}^{i} false) false] ‖ \leq normalι ‖ e_{γ_{i}} false(t_{k}^{i} false) ‖

{normalτ}_{k}^{i} \geq \frac{1}{‖ S ‖} \ln false[\frac{θ_{i} n^{*} ‖ S ‖}{false(1 + θ_{i} n^{*} false) false(‖ S ‖ + normalι ‖ K ‖ false)} + 1 false] = normalς > 0

, where ς and ι are constants.…”

Section: Estimation Of Exogenous Signalmentioning

confidence: 99%

Cooperative output regulation of heterogeneous multiagent systems based on event‐triggered control with fixed and switching topologies

Jia

Zhao

2017

Intl J Robust & Nonlinear

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Summary This paper addresses the cooperative output regulation problem of multiagent systems with fixed and switching topologies. Each agent is a heterogeneous linear system, and the output of the exosystem can be available to only a subset of agents. For the agents that can directly access the exosystem, a common observer based on an event‐triggered strategy is constructed to estimate the exogenous signal for feedback control design. For the rest of the agents, estimators based on an event‐triggered mechanism to acquire the estimation value of the exogenous signal are designed under some essential assumptions. A decentralized event‐triggered formulation is considered first by applying a Lyapunov function for a fixed topology. Furthermore, a topology‐dependent triggering condition and the average dwell‐time switching law are deduced simultaneously by using multiple Lyapunov functions for switching topologies. Under communication constraints, we propose observer‐based and estimator‐based feedback controllers to solve the cooperative output regulation problem using available local information among agents. Two examples are finally provided to verify the effectiveness of the proposed theoretical results.

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Almost output regulation of switched linear dynamics with switched exosignals

Yuan

2017

Intl J Robust & Nonlinear

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Summary For systems with switched linear dynamics and affected by persistent switched exosignals, we propose a new hybrid control approach to achieve not only closed‐loop stability but also tracking and/or rejection of persistent references/disturbances generated by multiple exosystems, namely, output regulation. It is assumed that both controlled plant and exosystem are described by switched linear models. The proposed hybrid controller/output regulator is specified as a switching impulsive system, where the controller states will undergo impulsive jumps at each switching instant. Based on the average dwell time switching technique, it has been shown how to completely reduce the synthesis problem of the hybrid controller to a set of linear matrix equations and linear matrix inequalities. Both continuous‐time and discrete‐time cases are discussed. To demonstrate its usefulness, the proposed hybrid control method has been applied to solve the output regulation problem for a mechanical system. Copyright © 2017 John Wiley & Sons, Ltd.

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Solvability of the output regulation problem for switched non-linear systems

Cited by 16 publications

References 16 publications

Almost output regulation of discrete-time switched linear systems

Almost output regulation of discrete-time switched linear systems

Cooperative output regulation of heterogeneous multiagent systems based on event‐triggered control with fixed and switching topologies

Almost output regulation of switched linear dynamics with switched exosignals

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