# A control problem for affine dynamical systems on a full-dimensional polytope

@article{Habets2004ACP, title={A control problem for affine dynamical systems on a full-dimensional polytope}, author={Luc C. G. J. M. Habets and Jan H. van Schuppen}, journal={Autom.}, year={2004}, volume={40}, pages={21-35} }

## 205 Citations

### Control to facet problems for affine systems on simplices and polytopes – With applications to control of hybrid systems

- MathematicsProceedings of the 44th IEEE Conference on Decision and Control
- 2005

In this paper, a general control-to-facet problem for affine systems on polytopes is studied: find an affine feedback law such that all trajectories of the closed-loop system leave the state polytope…

### Reachability and control of affine hypersurface systems on polytopes

- Mathematics2007 46th IEEE Conference on Decision and Control
- 2007

First, a conceptual framework for the constrained reachability problem is provided, then necessary and sufficient conditions for the problem for affine hypersurface systems are obtained and a geometric characterization of the maximal set of initial states from which the objective can be met is provided.

### Monotonic reach control on polytopes

- MathematicsIEEE Conference on Decision and Control and European Control Conference
- 2011

It is shown that, generically,solvability via arbitrary triangulations is equivalent to monotonic solvability, and this provides an avenue for reach control on polytopes that does not depend on the choice of triangulation of the polytope.

### Necessary and sufficient conditions for reachability of discrete time affine systems on simplices

- MathematicsProceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference
- 2009

This paper studies reachability problems in discrete time affine systems on simplices by studying the case where the union of the simplex and the target polytope is convex and generalizes the results by dropping the convex assumption.

### Reduction of affine systems on polytopes

- Mathematics
- 2002

Consider an affine system with a polytope as state set. State trajectories are terminated when they reach a facet of the polytope and attempt to exit. The realization problem is considered based on…

### Monotonic Reach Control on Polytopes

- MathematicsIEEE Transactions on Automatic Control
- 2013

The focus is on solvability by continuous piecewise affine feedback, and a variant of the problem in which trajectories exit in a monotonic sense is formulated, which allows to obtain necessary and sufficient conditions for solvable in certain geometric situations.

### In-block controllability of affine systems on polytopes

- Mathematics53rd IEEE Conference on Decision and Control
- 2014

This paper provides easily checkable necessary conditions for in-block controllability (IBC) of affine systems on polytopes and shows that these conditions are also sufficient for an important class ofpolytopes, simplicial poly topes.

### Control to Facet by Piecewise-Affine Output Feedback

- MathematicsIEEE Transactions on Automatic Control
- 2012

The control-to-facet problem plays an important role in the design of feedback controllers for piecewise-affine hybrid systems on polytopes and a triangulation of the output polytope is made which satisfies additional conditions to guarantee compatibility with the induced subdivision of the statepolytope.

### Relaxed in-block controllability of affine systems on polytopes

- Mathematics53rd IEEE Conference on Decision and Control
- 2014

The notion of relaxed in-block controllability (RIBC) is introduced and whether all the states in the interior of a given polytope are mutually accessible through the interiorof a given biggerpolytope by applying uniformly bounded control inputs is studied.

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