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

  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},

Figures from this paper

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

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

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

  • M. HelwaM. Broucke
  • Mathematics
    IEEE 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

  • Min WuG. YanZhiyun Lin
  • Mathematics
    Proceedings 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

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

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

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

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

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.



Control of Piecewise-Linear Hybrid Systems on Simplices and Rectangles

A necessary and sufficient condition for the reachability of a piecewise-linear hybrid system is formulated in terms of reachability of a finite-state discrete-event system and of a finite family of

A controllability result for piecewise-linear hybrid systems

An approach to controllability is described for which the problem decomposes into a reachability problem for a finite-state automaton and one for a family of affine systems on polytopes.

On invariant polyhedra of continuous-time linear systems

  • E. CastelanJ. Hennet
  • Mathematics
    [1991] Proceedings of the 30th IEEE Conference on Decision and Control
  • 1991
This note presents some conditions of existence of positively invariant polyhedra for linear continuous-time systems, first described algebraically, then interpreted on the basis of the system eigenstructure.

Admissible sets and feedback control for discrete-time linear dynamical systems with bounded controls and states

A variable structure linear state feedback controller, given in terms of the controls at the vertices of the polyhedral state constraint set, is presented.

Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems

In this paper we describe an experimental system called d/dt for approximating reachable states for hybrid systems whose continuous dynamics is defined by linear differential equations. We use an

Nonlinear regulation: The piecewise linear approach

This paper approaches nonlinear control problems through the use of (discrete-time) piecewise linear systems. These are systems whose next-state and output maps are both described by PL maps, i.e.,

Observability and controllability of piecewise affine and hybrid systems

It is proved through counterexamples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems, and practical numerical tests based on mixed-integer linear programming are proposed.

Control of switching systems under state and input constraints

Necessary and sufficient conditions are given for the existence of a solution and a constructive procedure is illustrated, based on the structure of the FSM, for the hybrid control problem addressed.

Convergence of an algorithm to find maximal state constraint sets for discrete-time linear dynamical systems with bounded controls and states

In [1] an algorithm was presented to find an approximant to the maximal state constraint set for a linear discrete time dynamical system with polyhedral state and input bounds. Here it is shown that

Remarks on piecewise-linear algebra

This note studies some of the basic properties of the category whose objects are finite unions of (open and closed) polyhedra and whose morphisms are (not necessarily continu- ous) piecewise-linear