Observability and identifiability of jump 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.

On the Observability and Detectability of Continuous-Time Markov Jump Linear Systems

Siam Journal on Control and Optimization, 2002

This paper presents a new detectability concept for discretetime Markov jump linear systems with finite Markov state, which generalizes the MS-detectability concept found in the literature. The new sense of detectability can similarly assure that the solution of the coupled algebraic Riccati equation associated to the quadratic control problem is a stabilizing solution. In addition, the paper introduces a related observability concept which also generalizes previous concepts. Tests for detectability or observability are derived from the corresponding definitions, that can be perfomed in a finite number of steps. An illustrative example is included to show that a system may be detectable in the new sense but not in the MS sense.

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.

Observability and detectability of linear switching systems: A structural approach

2008

We define observability and detectability for linear switching systems as the possibility of reconstructing and respectively of asymptotically reconstructing the hybrid state of the system from the knowledge of the output for a suitable choice of the control input. We derive a necessary and sufficient condition for observability that can be verified computationally. A characterization of control inputs ensuring observability of switching systems is given. Moreover, we prove that checking detectability of a linear switching system is equivalent to checking asymptotic stability of a suitable switching system with guards extracted from it, thus providing interesting links to Kalman decomposition and the theory of stability of hybrid systems.

On Observability and Detectability of Continuous-time Linear Switching Systems

2003

The notion of observability and detectability for a particular class of hybrid systems, linear continuous-time switching systems, is investigated. We compare some of the definitions of observability previously offered and we analyze their drawbacks. A novel definition of observability is proposed corresponding to the possibility of reconstructing the state of the system from the knowledge of the discrete and continuous outputs and inputs. The notion of detectability is also introduced. Sufficient and necessary conditions for these properties to hold for switching systems are presented.

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.

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.

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.

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.