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Register a new userDistributed Control of Networked Dynamical Systems: Static Feedback, Integral Action and Consensus
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Martin Andreasson Martin Andreasson
Publication date
2013
fields
Informatics Engineering
and research's language is
English
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This paper analyzes distributed control protocols for first- and second-order networked dynamical systems. We propose a class of nonlinear consensus controllers where the input of each agent can be written as a product of a nonlinear gain, and a sum of nonlinear interaction functions. By using integral Lyapunov functions, we prove the stability of the proposed control protocols, and explicitly characterize the equilibrium set. We also propose a distributed proportional-integral (PI) controller for networked dynamical systems. The PI controllers successfully attenuate constant disturbances in the network. We prove that agents with single-integrator dynamics are stable for any integral gain, and give an explicit tight upper bound on the integral gain for when the system is stable for agents with double-integrator dynamics. Throughout the paper we highlight some possible applications of the proposed controllers by realistic simulations of autonomous satellites, power systems and building temperature control.
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This paper investigates the consensus problem of multiple uncertain Lagrangian systems. Due to the discontinuity resulted from the switching topology, achieving consensus in the context of uncertain Lagrangian systems is challenging. We propose a new adaptive controller based on dynamic feedback to resolve this problem and additionally propose a new analysis tool for rigorously demonstrating the stability and convergence of the networked systems. The new introduced analysis tool is referred to as uniform integral-L_p stability, which is motivated for addressing integral-input-output properties of linear time-varying systems. It is then shown that the consensus errors between the systems converge to zero so long as the union of the graphs contains a directed spanning tree. It is also shown that the proposed controller enjoys the robustness with respect to constant communication delays. The performance of the proposed adaptive controllers is shown by numerical simulations.
This paper provides a protocol to address the robust output feedback consensus problem for networked heterogeneous nonlinear negative-imaginary (NI) systems with free body dynamics. We extend the definition of nonlinear NI systems to allow for systems with free body motion. A new stability result is developed for the interconnection of a nonlinear NI system and a nonlinear output strictly negative-imaginary (OSNI) system. Also, a class of networked nonlinear OSNI controllers is proposed to achieve output feedback consensus for heterogeneous networked nonlinear NI systems. We show that in this control framework, the system outputs converge to the same limit trajectory. This consensus protocol is illustrated by a numerical example.
We here investigate secure control of networked control systems developing a new dynamic watermarking (DW) scheme. Firstly, the weaknesses of the conventional DW scheme are revealed, and the tradeoff between the effectiveness of false data injection attack (FDIA) detection and system performance loss is analysed. Secondly, we propose a new DW scheme, and its attack detection capability is interrogated using the additive distortion power of a closed-loop system. Furthermore, the FDIA detection effectiveness of the closed-loop system is analysed using auto/cross covariance of the signals, where the positive correlation between the FDIA detection effectiveness and the watermarking intensity is measured. Thirdly, the tolerance capacity of FDIA against the closed-loop system is investigated, and theoretical analysis shows that the system performance can be recovered from FDIA using our new DW scheme. Finally, experimental results from a networked inverted pendulum system demonstrate the validity of our proposed scheme.
Distributed linear control design is crucial for large-scale cyber-physical systems. It is generally desirable to both impose information exchange (communication) constraints on the distributed controller, and to limit the propagation of disturbances to a local region without cascading to the global network (localization). Recently proposed System Level Synthesis (SLS) theory provides a framework where such communication and localization requirements can be tractably incorporated in controller design and implementation. In this work, we derive a solution to the localized and distributed H2 state feedback control problem without resorting to Finite Impulse Response (FIR) approximation. Our proposed synthesis algorithm allows a column-wise decomposition of the resulting convex program, and is therefore scalable to arbitrary large-scale networks. We demonstrate superior cost performance and computation time of the proposed procedure over previous methods via numerical simulation.
This work is concerned with the design and effects of the synchronization gains on the synchronization problem for a class of networked distributed parameter systems. The networked systems, assumed to be described by the same evolution equation in a Hilbert space, differ in their initial conditions. The proposed synchronization controllers aim at achieving both the control objective and the synchronization objective. To enhance the synchronization, as measured by the norm of the pairwise state difference of the networked systems, an adaptation of the gains is proposed. An alternative design arrives at constant gains that are optimized with respect to an appropriate measure of synchronization. A subsequent formulation casts the control and synchronization design problem into an optimal control problem for the aggregate systems. An extensive numerical study examines the various aspects of the optimization and adaptation of the gains on the control and synchronization of networked 1D parabolic differential equations.
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