Control of constrained nonlinear uncertain discrete-time systems via robust controllable sets: a modal interval analysis approach
Institut d'Informàtica i Aplicacions, Universitat de
Girona, Campus Montilivi, 17071 Girona, Spain. email@example.com; firstname.lastname@example.org; email@example.com; firstname.lastname@example.org
Revised: 11 June 2007
A general framework for computing robust controllable sets of constrained nonlinear uncertain discrete-time systems as well as controlling such complex systems based on the computed robust controllable sets is introduced in this paper. The addressed one-step control approach turns out to be a robust model predictive control scheme with feasible unit control horizon and contractive constraint. The solver of 1-dimensional quantified set inversion in modal interval analysis is extended to 2-dimensional cases for computing robust controllable sets off-line with a clear semantic interpretation, where both universal and existential quantifiers are concerned simultaneously. An interval-based solver of constrained minimax optimization is also proposed to compute one-step control inputs online in a reliable way, which guarantee to drive the system state contractively along the computed robust controllable sets to a selected terminal robust control invariant set.
Mathematics Subject Classification: 65G40 / 93B05 / 93B51
Key words: Nonlinearity / uncertainty / constraints / robust controllable set / quantified set inversion / minimax optimization / interval analysis / modal intervals
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