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Boundary adaptive synchronization of networked PDEs with adaptive parameter estimators

IFAC-PapersOnLine 2016年第8期49卷 242-247页

作者： Demetriou, Michael A. Aerospace Engineering Program Mechanical Engineering Department Worcester Polytechnic Institute WorcesterMA01609 United States

This work considers the synchronization control of networked PDEs that have boundary observation and control. The PDEs are assumed identical, with information exchange dictated by a complete directed graph. Parametric uncertainties entering in the boundary, result in structured perturbation terms that may render the open loop system unstable. Additionally constant disturbance terms entering at the boundary are impeding state regulation. To address these parametric uncertainties, a precompensator is utilized to stabilize each networked PDE. Another component of the controller provides an on-line cancellation of the parametric uncertainties by attempting to cancel them through their adaptive estimate, and to attenuate the effects of boundary disturbances, their adaptive estimates are utilized in the controller. To provide a robustness in the adaptive estimation of the parametric uncertainties and the boundary disturbances, the standard adaptive laws are complemented with a consensus protocol term that penalizes the pairwise disagreement of the adaptive estimates. Finally, to enforce synchronization of all networked PDEs, a synchronization controller is included which utilizes only the outputs of all communicating PDE systems weighted by adaptive synchronization gains. These gains, derived from Lyapunov redesign methods, include a consensus term for added robustness and to enforce convergence. Simulation studies of five networked diffusion PDEs with boundary observation and control are included. © 2016

关键词： Adaptive control systems controllers Directed graphs Laws and legislation Networked control systems Parameter estimation Robustness (control systems) synchronization Uncertainty analysis Adaptive synchronizations Boundary stabilization Constant disturbances Distributed parameter systems Parametric uncertainties Structured perturbations synchronization control synchronization controllers

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Desynchronization and resynchronization of networked second order finite and infinite dimensional systems 54

Desynchronization and resynchronization of networked second ...

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54th IEEE Conference on Decision and Control (CDC)

作者： Demetriou, Michael A. Worcester Polytech Inst Dept Mech Engn Aerosp Engn Program Worcester MA 01609 USA

ISBN: (纸本)9781479978861

This work considers the synchronization of interconnected second order infinite dimensional systems. An output feedback based synchronization controller is designed in order to enhance a measure of synchronization amongst the infinite dimensional systems and when using the aggregate form of the networked systems, the choice of the optimal gains in the synchronization controllers reduces to the optimization of an associated quadratic index. A desynchronization action which takes the form of severing a link between any two connected systems is interpreted as a benign action which results in a delayed synchronization or convergence of the synchronization measure to a nonzero value. When the desynchronization action takes the form of sign reversal of a link between two connected systems, it is interpreted as a malicious adversarial action and which results in destabilization of the networked systems with an unbounded synchronization measure. The desynchronization action is viewed as a fault occurring in the networked system and an adaptive scheme is thus used to monitor these interconnected systems in order to detect the presence of the desynchronization action. In order to maintain the synchronization of the interconnected systems, an adaptive fault accommodating scheme is proposed which takes the form of control reconfiguration and which ensures the resynchronization of the interconnected systems. Both finite and infinite second order systems are considered and a numerical example with four interconnected cable PDEs is included to demonstrate the effectiveness of the desynchronization monitoring scheme and the subsequent resynchronization policy.

关键词： Distributed parameter systems synchronization controllers networked systems desynchronization

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Actuator location optimization in synchronization control of networked distributed parameter systems

Actuator location optimization in synchronization control of...

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American Control Conference

作者： Demetriou, Michael A. Worcester Polytech Inst Dept Mech Engn Worcester MA 01609 USA

ISBN: (纸本)9781479986842

This work examines the effects of actuator location in networked distributed parameter systems. In particular, the effects of the optimal actuator location for one networked system can impact the collective behavior of the networked systems. The actuator optimization cannot be performed on the individual networked systems, but must be considered for the aggregate of the networked systems. To tackle the actuator optimization problem, the networked systems are viewed collectively and with the implementation of a synchronization controller, the resulting closed-loop aggregate system is parameterized by the actuator location. Using different metrics for the success of synchronization, the resulting actuator optimization problem is recast as a minimization of a performance index. The solution to this optimization is expressed as the minimization of the trace of a location-parameterized Lyapunov operator. Simulation studies on seven networked diffusion partial differential equations in one spatial dimension reveal the effects of a correct actuator placement on synchronization.

关键词： Distributed parameter systems synchronization controllers networked systems actuator optimization

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Leader selection and optimal synchronization gains in synchronization control of networked distributed parameter systems 54

Leader selection and optimal synchronization gains in synchr...

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54th IEEE Conference on Decision and Control (CDC)

作者： Demetriou, Michael A. Worcester Polytech Inst Dept Mech Engn Worcester MA 01609 USA

ISBN: (纸本)9781479978861

This work is concerned with the optimization aspects of networked distributed parameter systems. It is assumed that the information exchange between the networked systems, each of which is governed by an evolution equation in an abstract space, is a priori given and the design objective is to choose the leader and the synchronization controllers so that all the followers track the leader in an appropriate norm, and that all networked system agree with each other. The optimization problem is formulated as a minimization problem of a quadratic index penalizing the distance from synchronization and the tracking errors. The optimal value of the quadratic index, as it is parameterized by the synchronization gains, is expressed in terms of the solution to an associated operator Lyapunov equation. Adding another level of optimization, one can optimally select the leader and the associated optimal synchronization gains. Such a leader selection reduces to zeroing a row of an associated gain matrix for the aggregate system. Numerical studies of four networked parabolic PDEs are presented to provide additional insight on the effects of optimal leader selection and optimal gain selection on the synchronization controller performance and the collective behavior of the networked PDE systems.

关键词： Distributed parameter systems synchronization controllers networked systems leader selection

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Adaptive output feedback synchronization of networked distributed parameter systems

Adaptive output feedback synchronization of networked distri...

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American Control Conference

作者： Demetriou, Michael A. Worcester Polytech Inst Dept Mech Engn Worcester MA 01609 USA

ISBN: (纸本)9781479932740

The optimization and adaptation of the synchronization gains for a class of networked systems is presented in which the state of each of the networked nodes is governed by a distributed parameter system. The design objectives aim at ensuring that all pairwise state differences of the networked systems converge to zero in an appropriate norm and that the states of these systems satisfy the control objective. The proposed static output feedback controllers thus contain a term that addresses the control objective and a consensus term that ensures synchronization. The synchronization gains of the resulting aggregate systems can be viewed as the strengths of the interconnections among the network nodes. Two different optimization schemes for the non-zero entries of the associated graph Laplacian are proposed. An alternate design proposes the on-line adjustment of the entries of the graph Laplacian matrix via an adaptation involving available output signals of the networked systems. The proposed results are demonstrated by a numerical example for a 1D partial differential equation.

关键词： Distributed parameter systems synchronization controllers networked systems gain adaptation

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