Subclass Of Hybrid Systems Research Articles

Interval Estimation for Linear Switched System

In this paper, the problem of state estimation is investigated for linear switched system, a subclass of hybrid systems. It will be shown that the interval observer is very often exists under moderate conditions at least in discrete time instants from continuous-time measurements. The novelty consists in proposing new conditions of cooperativity for switched systems in discrete time instants, which guarantee errors nonnegativity of interval observation. The efficiency of the interval observers is shown through simulation examples.

On the existence of periodic behaviour of switched linear systems

A generalised implicit function theorem is used to show the existence of periodic solutions of switched linear systems with inhomogeneous terms (a subclass of hybrid systems) around an operating (compare: equilibrium) point. If the period concerned is small, the solutions ‘move around’ such an operating point. These points cannot generally be achieved by the individual linear systems. A central question to be answered is: which operating points are possible? Another question answered is what the asymptotic behaviour of the solutions near such an operating point look like (as a function of the period). For some specific cases, for instance when the systems only differ in the inhomogeneous terms, special results are obtained. The implicit function theorem used makes use of expansions in formal power series.

Max-plus-linear model-based predictive control for constrained hybrid systems: linear programming solution

In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the (max, +) algebra, a typical subclass of hybrid systems called max-plus-linear (MPL) systems is obtained. And then, model predictive control (MPC) framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem (ELCP) were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling (MMPS) functions (using the operations maximization, minimization, addition and scalar multiplication) with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.

STABILIZABILITY BASED STATE SPACE REDUCTIONS FOR HYBRID SYSTEMS

In this paper, we focus on a particular subclass of hybrid systems, the class of linear switching systems. We propose hybrid state space decompositions, based on hybrid invariant subspaces, which reduce the computational effort required for checking the structural property of asymptotic stabilizability.