Observability for hybrid 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 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.

A Sufficient and Controllability Necessary Condition for the of Linear Hybrid Systems

An algebraic approach for the controllability analy sir of a class of h) brid control syslems rallcd cootrolled awltching linear h)hrid ryaemr is proposcd. A rufficicnl and neccrrar, condition is obtained bared on the algebraic manipulalion 01 related system matriccs. This consequence is directly oriented Io numerical romputnlion of Ibe controllability. Beside that, the existing resull for LTI systems 141 and rerulls in 151. 1181, 1191, 1141 become special cases of Ihc result of this paper. Finally, numerical examples are used I o illuslralr Ihe obtained remlt.

A structural approach to detectability for a class of hybrid systems

Automatica, 2009

We address detectability of linear switching systems. We show that detectability of a linear switching system reduces to asymptotic stability of a suitable switching system with guards extracted from it. A condition for checking asymptotic stability of linear switching systems with guards is also derived.

A study of the observability of multidimensional hybrid linear systems

WSEAS Transactions on Systems and Control archive, 2008

A class of multidimensional hybrid linear systems is presented, with the time vector composed by q continuous-time real components and by r discrete-time integer ones, q, r ≥ 1. The state equation is of multidimensional partial differential-difference type. A generalized variation-of-parameters formula is provided and it is used to obtain the state and the general response of the system. The fundamental concept of observability is studied for these systems. An observability Gramian is introduced, which is a generalization of the Gramians corresponding to the classical 1D continuous-time and 1D discrete-time systems. In the case of completely observable systems this Gramian is used to obtain a formula which provides the initial state of the system for any input-output pair. A list of observability criteria is given for time-invariant systems and the duality between the concepts of observability and reachability is emphasized.

Controllability and falsification of hybrid systems

2009 European Control Conference, 2009

In this paper we consider the controllability problem for hybrid systems, namely that of determining the set of states which can be driven into a given target set. We show that given a suitable definition of controllability, we can effectively compute arbitrarily accurate under-approximations to the controllable set using Turing machines. However, due to grazing or sliding along guard sets, we see that it may be able to demonstrate that an initial state can be controlled to the target set, without knowing any trajectory which solves the problem.

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.

Observability to the identifiability of hybrid dynamical system

2011

Hybrid complex systems are heterogeneous dynamical systems whose behavior can be defined by interacting continuously and by having discrete changes in their dynamics. Therefore, this class of systems presents commutations which can be autonomous or driven by some external events. So, the identification of this class of systems is a challenging problem that involves estimation of both parameters of the sub-models, and the partitioning of states, data and input space. In this paper, an approach to modeling this kind of system is introduced and analyzed for observability and identifiability properties.