A study of the observability of multidimensional hybrid linear systems (original) (raw)

Observability of Linear Hybrid Systems

Lecture Notes in Computer Science, 2003

We analyze the observability of the continuous and discrete states of continuous-time linear hybrid systems. For the class of jumplinear systems, we derive necessary and sufficient conditions that the structural parameters of the model must satisfy in order for filtering and smoothing algorithms to operate correctly. Our conditions are simple rank tests that exploit the geometry of the observability subspaces. For linear hybrid systems, we derive weaker rank conditions that are sufficient to guarantee the uniqueness of the reconstruction of the state trajectory, even when the individual linear systems are unobservable.

The Observability Concept in a Class of Hybrid Control systems

ArXiv, 2017

In the discrete modeling approach for hybrid control systems, the continuous plant is reduced to a discrete event approximation, called the DES-plant, that is governed by a discrete event system, representing the controller. The observability of the DES-plant model is crucial for the synthesis of the controller and for the proper closed loop evolution of the hybrid control system. Based on a version of the framework for hybrid control systems proposed by Antsaklis, the paper analysis the relation between the properties of the cellular space of the continuous plant and a mechanism of plant-symbols generation, on one side, and the observability of the DES-plant automaton on the other side. Finally an observable discrete event abstraction of the continuous double integrator is presented.

Observability and Geometric Approach of 2D Hybrid Systems

International Journal of Computers, 2021

A connection is emphasized between two branches of the Systems Theory, namely the Geometric Approach and 2D Systems, with a special regard to the concept of observability. An algorithm is provided which determines the maximal subspace which is invariant with respect to two commutative matrices and which is included in a given subspace. Observability criteria are obtained for a class of 2D systems by using a suitable 2D observability Gramian and some such criteria are derived for LTI 2D systems, as well as the geometric characterization of the subspace of unobservable states. The presented algorithm is applied to determine this subspace.

State observer and observability conditions for a class of hybrid continuous-discrete dynamic system

2007 46th IEEE Conference on Decision and Control, 2007

This paper deals with observability conditions and state observer design for a class of hybrid systems combining continuous and discrete dynamics. The main contribution of the work lies in the performed observability conditions for this class of systems and a design of hybrid observer to reconstruct both continuous and discrete states starting only from the knowledge of a continuous output. An illustrative example is presented showing the efficiency of the proposed observer. * M. Djemaï and J.P. Barbot (IEEE Member, and Member of Projet Alien INRIA-Futurs) are with ECS, ENSEA,

Observability for hybrid systems

2003

Abstract The notion of generic final-state asymptotically determinable hybrid system is introduced. Then, sufficient conditions for a linear hybrid system to be generic final-state asymptotically determinable are given. These conditions show that generic final-state asymptotic determinability can be verified even if each of the continuous subsystems of the hybrid system is not observable.

Observability and identifiability of jump linear systems

Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2002

We analyze the observability of the continuous and discrete states of a class of linear hybrid systems. We derive rank conditions that the structural parameters of the model must satisfy in order for filtering and smoothing algorithms to operate correctly. We also study the identifiability of the model parameters by characterizing the set of models that produce the same output measurements. Finally, when the data are generated by a model in the class, we give conditions under which the true model can be identified.

Observability of the discrete state for dynamical piecewise hybrid systems

Nonlinear Analysis: Theory, Methods & Applications, 2005

In this paper, we deal with the observability of piecewise-affine hybrid systems. Our aim is to give sufficient conditions to observe the discrete and continuous states, in terms of algebraic and geometrical conditions. Firstly, we will give the algebraic conditions to observe the discrete state based on the switch function reconstruction for linear hybrid systems. Secondly, we will give a geometrical condition based on the transversality concept for nonlinear hybrid systems. Throughout this paper, we illustrate our propositions with examples and simulations.

Discrete state observability of hybrid systems

International Journal of Robust and Nonlinear Control, 2009

We propose a novel definition of observability, motivated by safety critical applications, given with respect to a subset of critical discrete states that model unsafe or unallowed behaviors. For the class of discrete event systems, we address the problem in the setting of formal (regular) languages and propose a novel observability verification algorithm. For the class of switching systems, we characterize the minimal set of extra output information to be provided by the continuous signals in order to satisfy observability conditions, and propose a milder observability notion that allows a bounded delay in state observation. For the class of hidden Markov models, we analyze decidability and complexity of the verification problem.