Nonlinear systems analysis (2nd ed.)
Nonlinear systems analysis (2nd ed.)
Robust constrained model predictive control using linear matrix inequalities
Automatica (Journal of IFAC)
Piecewise Linear Control Systems
Piecewise Linear Control Systems
Survey paper: Set invariance in control
Automatica (Journal of IFAC)
Brief Analysis of discrete-time piecewise affine and hybrid systems
Automatica (Journal of IFAC)
Survey Constrained model predictive control: Stability and optimality
Automatica (Journal of IFAC)
Control of systems integrating logic, dynamics, and constraints
Automatica (Journal of IFAC)
Brief Equivalence of hybrid dynamical models
Automatica (Journal of IFAC)
The explicit linear quadratic regulator for constrained systems
Automatica (Journal of IFAC)
Technical Communique: Evaluation of piecewise affine control via binary search tree
Automatica (Journal of IFAC)
Convexity recognition of the union of polyhedra
Computational Geometry: Theory and Applications
Transformation of Fuzzy Takagi-Sugeno Models into Piecewise Affine Models
RSEISP '07 Proceedings of the international conference on Rough Sets and Intelligent Systems Paradigms
Synthesis of Trajectory-Dependent Control Lyapunov Functions by a Single Linear Program
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Robust filtering for discrete time piecewise impulsive systems
Signal Processing
Linear control of time-domain constrained systems
Automatica (Journal of IFAC)
Hi-index | 22.15 |
Piecewise affine (PWA) systems are powerful models for describing both non-linear and hybrid systems. One of the key problems in controlling these systems is the inherent computational complexity of controller synthesis and analysis, especially if constraints on states and inputs are present. In addition, few results are available which address the issue of computing stabilizing controllers for PWA systems without placing constraints on the location of the origin. This paper first introduces a method to obtain stability guarantees for receding horizon control of discrete-time PWA systems. Based on this result, two algorithms which provide low complexity state feedback controllers are introduced. Specifically, we demonstrate how multi-parametric programming can be used to obtain minimum-time controllers, i.e., controllers which drive the state into a pre-specified target set in minimum time. In a second segment, we show how controllers of even lower complexity can be obtained by separately dealing with constraint satisfaction and stability properties. To this end, we introduce a method to compute PWA Lyapunov functions for discrete-time PWA systems via linear programming. Finally, we report results of an extensive case study which justify our claims of complexity reduction.