A new approach for estimating controllable and recoverable regions for systems with state and control constraints

Abstract

SUMMARYIn this paper the problem of estimating controllable and recoverable regions for classes of nonlinear systems in the presence of uncertainties, state and control constraints is considered. A new computational technique is proposed based upon a ray-gridding idea in contrast to the usual gridding techniques. The new technique is also based on the positive invariance principle and the use of piecewise linear (PL) Lyapunov functions to generate polytopic approximations to the controllable/recoverable region with arbitrary accuracy. Various types of stabilizing controllers achieving certain trade-o!s between robustness, performance and safety, while respecting state and control constraints, can be easily generated. The technique allows the approximation of nonlinear systems via piecewise linear uncertain models which reduces the conservatism associated with linear uncertain models.

Stability Criteria for Switched and Hybrid Systems

“…This problem is partially avoided in the ray-gridding method developed by Yfoulis and his co-authors in [184,186,187]. The approach is based on uniform partitions of the state-space in terms of ray directions which allow refinable families of polytopes of adjustable complexity.…”

Robust constrained stabilization of boost DC–DC converters through bifurcation analysis

“…To this end, flexible piecewise linear (PL) Lyapunov functions proposed recently in [17] are utilized, which rely on ray-gridding as a systematic technique for dealing with low dimensional PL systems via the construction of UDOAs using PL Lyapunov functions. The technique has been applied successfully to several different linear switched system analysis and design problems in the past [21,22,23].…”

“…The two curves do not intersect, since there are always two different solutions k 21,22 . All these suggest, that for a-priori known bounds for the varying parameters V in , R we are able to specify precisely the bifurcation boundary between one and three real equilibria.…”

A Numerical Technique for Stability Analysis of Linear Switched Systems

“…with admissible controls and applies them to the problem of robust controller synthesis under state and control constraints for linear uncertain systems. Yfoulis [50] developed another algorithm, the ray-gridding technique for the same problem for linear and PL uncertain systems. Both techniques can be applied to three-dimensional systems.…”

“…A ray-gridding technique has been developed for the problem of calculating controllable and recoverable regions in [50] and is a useful framework for systematic generation of refinable families of polytopes with adjustable complexity, having their vertices on certain ray directions.…”