×

Distributed receding horizon control for multi-vehicle formation stabilization. (English) Zbl 1103.93031

Summary: We consider the control of interacting subsystems whose dynamics and constraints are decoupled, but whose state vectors are coupled non-separably in a single cost function of a finite horizon optimal control problem. For a given cost structure, we generate distributed optimal control problems for each subsystem and establish that a distributed receding horizon control implementation is stabilizing to a neighborhood of the objective state. The implementation requires synchronous updates and the exchange of the most recent optimal control trajectory between coupled subsystems prior to each update. The key requirements for stability are that each subsystem not deviate too far from the previous open-loop state trajectory, and that the receding horizon updates happen sufficiently fast. The venue of multi-vehicle formation stabilization is used to demonstrate the distributed implementation.

MSC:

93B51 Design techniques (robust design, computer-aided design, etc.)
93D09 Robust stability
93C95 Application models in control theory
93C15 Control/observation systems governed by ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Acar, L., Boundaries of the receding horizon control for interconnected systems, Journal of Optimization Theory and Applications, 84, 2, 251-271 (1995) · Zbl 0822.93009
[2] Bertsekas, D. P.; Tsitsiklis, J. N., Parallel and distributed computation: Numerical methods (1997), Athena Scientific
[4] Chen, H.; Allgöwer, F., A quasi-infinite horizon nonlinear model predictive scheme with guaranteed stability, Automatica, 14, 10, 1205-1217 (1998) · Zbl 0947.93013
[11] Mayne, D. Q.; Rawlings, J. B.; Rao, C. V.; Scokaert, P. O.M., Constrained model predictive control: Stability and optimality, Automatica, 36, 789-814 (2000) · Zbl 0949.93003
[12] Michalska, H.; Mayne, D. Q., Robust receeding horizon control of constrained nonlinear systems, IEEE Transactions on Automatic Control, 38, 1623-1632 (1993) · Zbl 0790.93038
[15] Ren, W.; Beard, R. W., A decentralized scheme for spacecraft formation flying via the virtual structure approach, AIAA Journal of Guidance, Control and Dynamics, 27, 1, 73-82 (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.