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

Authors:
L. C. G. J. M. Habets;J. H. Van Schuppen
Affiliations:
CWI-Centrum voor Wiskunde en Informatica, P.O. Box 94079, NL-1090 GB Amsterdam, Netherlands and Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, NL ...;CWI-Centrum voor Wiskunde en Informatica, P.O. Box 94079, NL-1090 GB Amsterdam, Netherlands
Venue:
Automatica (Journal of IFAC)
Year:
2004

Citing 12
Cited 23

Constrained regulation of linear continuous-time dynamical systems

Systems & Control Letters
Interconnected automata and linear systems: a theoretical framework in discrete-time

Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Handbook of discrete and computational geometry

Handbook of discrete and computational geometry
Subdivisions and triangulations of polytopes

Handbook of discrete and computational geometry
Voronoi diagrams and Delaunay triangulations

Handbook of discrete and computational geometry
Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control

HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control

HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
A Sufficient Condition for Controllability of a Class of Hybrid Systems

HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems

HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Control of Piecewise-Linear Hybrid Systems on Simplices and Rectangles

HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Survey paper: Set invariance in control

Automatica (Journal of IFAC)
Control of systems integrating logic, dynamics, and constraints

Automatica (Journal of IFAC)

Brief paper: A mathematical framework for the control of piecewise-affine models of gene networks

Automatica (Journal of IFAC)
Dealing with Nondeterminism in Symbolic Control

HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Qualitative Stability Patterns for Lotka-Volterra Systems on Rectangles

HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Brief paper: Tracking and synchronisation for a class of PWA systems

Automatica (Journal of IFAC)
Temporal logic motion planning for dynamic robots

Automatica (Journal of IFAC)
Simple and Efficient Algorithms for Computing Smooth, Collision-free Feedback Laws Over Given Cell Decompositions

International Journal of Robotics Research
Reach control on simplices by continuous state feedback

ACC'09 Proceedings of the 2009 conference on American Control Conference
Synthesis of output feedback control for motion planning based on LTL specifications

IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
MARCO: a reachability algorithm for multi-affine systems with applications to biological systems

HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Algorithms for the analysis and synthesis of a bio-inspired swarm robotic system

SAB'06 Proceedings of the 2nd international conference on Swarm robotics
Automatic deployment of distributed teams of robots from temporal logic motion specifications

IEEE Transactions on Robotics
Decentralized feedback controllers for multiagent teams in environments with obstacles

IEEE Transactions on Robotics
Reach Control on Simplices by Continuous State Feedback

SIAM Journal on Control and Optimization
Brief paper: On a reachability problem for affine hypersurface systems on polytopes

Automatica (Journal of IFAC)
Exact control of genetic networks in a qualitative framework: The bistable switch example

Automatica (Journal of IFAC)
Necessary and sufficient conditions for reachability on a simplex

Automatica (Journal of IFAC)
On fluidization of discrete event models: observation and control of continuous Petri nets

Discrete Event Dynamic Systems
Brief paper: Reachability and stabilization of discrete-time affine systems with disturbances

Automatica (Journal of IFAC)
Optimal path planning for surveillance with temporal-logic constraints*

International Journal of Robotics Research
A fully automated framework for control of linear systems from LTL specifications

HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Reachability analysis of multi-affine systems

HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
On reachability and controllability of switched Boolean control networks

Automatica (Journal of IFAC)
On approximative reachability analysis of biochemical dynamical systems

Transactions on Computational Systems Biology XIV

Quantified Score

Hi-index	22.16

Visualization

Abstract

Given an affine system on a full-dimensional polytope, the problem of reaching a particular facet of the polytope, using continuous piecewise-affine state feedback is studied. Necessary conditions and sufficient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the vertices of the polytope. Special attention is paid to affine systems on full-dimensional simplices. In this case, the necessary and sufficient conditions are equivalent and a constructive procedure yields an affine feedback control law, that solves the reachability problem under consideration.