Reachability computations for constrained discrete-time systems with state- and input-dependent disturbances
Rakovic S. V. and Kerrigan E. C. and Mayne D. Q.
August 2003
Technical Report: EEE/C&P/SVR/8-a/2003
Abstract
This paper presents new results that allow one to compute the set of states which can be robustly steered in a finite number of steps, via state feedback control, to a given target set. The assumptions that are made in this paper are that the system is discrete-time, nonlinear and time-invariant and subject to mixed constraints on the state and input. A persistent disturbance, dependent on the current state and input, acts on the system. Existing results are not able to address state- and input-dependent disturbances and the results in this paper are therefore a generalization of previously-published results. The application of the results to the computation of the maximal robustly controlled invariant set is also briefly discussed. Specific results, which allow one to perform the set computations using polyhedral algebra, linear programming and computational geometry software, are presented for linear and piecewise affine systems with additive state disturbances. Some simple examples are given which show that, even if all the relevant sets are convex and the system is linear, convexity of the robustly controllable sets cannot be guaranteed.
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BibTex Entry
- @TechReport{rakovic:kerrigan:mayne:2003b,
- author = {Rakovic S. V. and Kerrigan E. C. and Mayne D. Q.},
- institution = {Department of Electrical and Electronic Engineering, Imperial College London},
- title = {Reachability computations for constrained discrete-time systems with state- and input-dependent disturbances},
- year = {2003},
- address = {London, UK},
- bibkey = {rakovic:kerrigan:mayne:2003b},
- month = {August},
- note = {EEE/C&P/SVR/8-a/2003}
- }
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