An embedding approach for the design of state-feedback tracking controllers for references with jumps

R.G. Sanfelice, J.J.B. Biemond, N. Wouw, van de, W.P.M.H. Heemels

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We study the problem of designing state-feedback controllers to track time-varying state trajectories that may exhibit jumps. Both plants and controllers considered are modeled as hybrid dynamical systems, which are systems with both continuous and discrete dynamics, given in terms of a flow set, a flow map, a jump set, and a jump map. Using recently developed tools for the study of stability in hybrid systems, we recast the tracking problem as the task of asymptotically stabilizing a set, the tracking set, and derive conditions for the design of state-feedback tracking controllers with the property that the jump times of the plant coincide with those of the given reference trajectories. The resulting tracking controllers guarantee that solutions of the plant starting close to the reference trajectory stay close to it and that the difference between each solution of the controlled plant and the reference trajectory converges to zero asymptotically. Constructive conditions for tracking control design in terms of LMIs are proposed for a class of hybrid systems with linear maps and input-triggered jumps. The results are illustrated by various examples
Originele taal-2Engels
Pagina's (van-tot)1585-1608
Aantal pagina's24
TijdschriftInternational Journal of Robust and Nonlinear Control
Volume24
Nummer van het tijdschrift11
DOI's
StatusGepubliceerd - 2014

Vingerafdruk

State feedback
Trajectories
Controllers
Hybrid systems
Dynamical systems

Citeer dit

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An embedding approach for the design of state-feedback tracking controllers for references with jumps. / Sanfelice, R.G.; Biemond, J.J.B.; Wouw, van de, N.; Heemels, W.P.M.H.

In: International Journal of Robust and Nonlinear Control, Vol. 24, Nr. 11, 2014, blz. 1585-1608.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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AU - Heemels, W.P.M.H.

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AB - We study the problem of designing state-feedback controllers to track time-varying state trajectories that may exhibit jumps. Both plants and controllers considered are modeled as hybrid dynamical systems, which are systems with both continuous and discrete dynamics, given in terms of a flow set, a flow map, a jump set, and a jump map. Using recently developed tools for the study of stability in hybrid systems, we recast the tracking problem as the task of asymptotically stabilizing a set, the tracking set, and derive conditions for the design of state-feedback tracking controllers with the property that the jump times of the plant coincide with those of the given reference trajectories. The resulting tracking controllers guarantee that solutions of the plant starting close to the reference trajectory stay close to it and that the difference between each solution of the controlled plant and the reference trajectory converges to zero asymptotically. Constructive conditions for tracking control design in terms of LMIs are proposed for a class of hybrid systems with linear maps and input-triggered jumps. The results are illustrated by various examples

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