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Research Papers

Robust Distributed Model Predictive Control of Constrained Continuous-Time Nonlinear Systems Using Two-Layer Invariant Sets

[+] Author and Article Information
Xiaotao Liu

Department of Mechanical Engineering,
University of Victoria,
Victoria, BC V8W 2Y2, Canada
e-mail: xtliu@uvic.ca

Yang Shi

Department of Mechanical Engineering,
University of Victoria,
Victoria, BC V8W 2Y2, Canada
e-mail: yshi@uvic.ca

Daniela Constantinescu

Department of Mechanical Engineering,
University of Victoria,
Victoria, BC V8W 2Y2, Canada
e-mail: danielac@uvic.ca

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 2, 2015; final manuscript received February 10, 2016; published online March 30, 2016. Assoc. Editor: Fu-Cheng Wang.

J. Dyn. Sys., Meas., Control 138(6), 061004 (Mar 30, 2016) (7 pages) Paper No: DS-15-1254; doi: 10.1115/1.4032829 History: Received June 02, 2015; Revised February 10, 2016

This paper introduces a robust distributed model predictive control (DMPC) strategy for constrained continuous-time nonlinear systems coupled through their cost functions. In the proposed technique, all the subsystems receive the assumed control trajectories of their neighbors and compute their controls by optimizing local cost functions with coupling terms. Provided that the initial state is feasible and the disturbances are bounded, a two-layer invariant sets-based controller design ensures robustness while appropriate tuning of the design parameters guarantees recursive feasibility. This paper first derives sufficient conditions for the convergence of all the subsystem states to a robust positive invariant set. Then, it exploits the κδ controllability set to propose a less conservative robust model predictive control (MPC) strategy that permits the adoption of a shorter prediction horizon and tolerates larger disturbances. A numerical example illustrates that the designed algorithm leads to stronger cooperation among subsystems compared to an existing robust DMPC technique.

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References

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Figures

Grahic Jump Location
Fig. 1

State trajectories of agent 3 with the DMPC proposed in this paper and in Ref. [19]

Grahic Jump Location
Fig. 2

Control trajectories of agent 3 with the DMPC proposed in this paper and in Ref. [19]

Grahic Jump Location
Fig. 3

Difference between states of agent 3 under decentralized and DMPC

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