Results 1  10
of
67
Equivalence of hybrid dynamical models
 AUTOMATICA
, 2001
"... This paper establishes equivalences among five classes of hybrid systems: mixed logical dynamical (MLD) systems, linear complementarity (LC) systems, extended linear complementarity (ELC) systems, piecewise affine (PWA) systems, and maxminplusscaling (MMPS) systems. Some of the equivalences are es ..."
Abstract

Cited by 70 (24 self)
 Add to MetaCart
This paper establishes equivalences among five classes of hybrid systems: mixed logical dynamical (MLD) systems, linear complementarity (LC) systems, extended linear complementarity (ELC) systems, piecewise affine (PWA) systems, and maxminplusscaling (MMPS) systems. Some of the equivalences are established under (rather mild) additional assumptions. These results are of paramount importance for transferring theoretical properties and tools from one class to another, with the consequence that for the study of a particular hybrid system that belongs to any of these classes, one can choose the most convenient hybrid modeling framework.
A Clustering Technique for the Identification of Piecewise Affine Systems
, 2001
"... We propose a new technique for the identification of discretetime hybrid systems in the PieceWise Affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multidimensional domain. In order to achieve our goal, we provide an algorithm that ..."
Abstract

Cited by 53 (7 self)
 Add to MetaCart
We propose a new technique for the identification of discretetime hybrid systems in the PieceWise Affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multidimensional domain. In order to achieve our goal, we provide an algorithm that exploits the combined use of clustering, linear identification, and pattern recognition techniques. This allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid avoiding gridding procedures. Moreover, the clustering step (used for classifying the datapoints) is performed in a suitably defined feature space which allows also to reconstruct different submodels that share the same coefficients but are defined on different regions. Measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering and the final linear regression procedure.
An Algebraic Geometric Approach to the Identification of a Class of Linear Hybrid Systems
 In Proc. of IEEE Conference on Decision and Control
, 2003
"... We propose an algebraic geometric solution to the identification of a class of linear hybrid systems. We show that the identification of the model parameters can be decoupled from the inference of the hybrid state and the switching mechanism generating the transitions, hence we do not constraint the ..."
Abstract

Cited by 40 (11 self)
 Add to MetaCart
We propose an algebraic geometric solution to the identification of a class of linear hybrid systems. We show that the identification of the model parameters can be decoupled from the inference of the hybrid state and the switching mechanism generating the transitions, hence we do not constraint the switches to be separated by a minimum dwell time. The decoupling is obtained from the socalled hybrid decoupling constraint, which establishes a connection between linear hybrid system identification, polynomial factorization and hyperplane clustering. In essence, we represent the number of discrete states n as the degree of a homogeneous polynomial p and the model parameters as factors of p. We then show that one can estimate n from a rank constraint on the data, the coe#cients of p from a linear system, and the model parameters from the derivatives of p. The solution is closed form if and only if n 4. Once the model parameters have been identified, the estimation of the hybrid state becomes a simpler problem. Although our algorithm is designed for noiseless data, we also present simulation results with noisy data. 1
Observability and Identifiability of Jump Linear Systems
 In Proc. of IEEE Conference on Decision and Control
, 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 mo ..."
Abstract

Cited by 38 (8 self)
 Add to MetaCart
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.
OptimizationBased Verification and Stability Characterization of Piecewise Affine and Hybrid Systems
 In Hybrid Systems: Computation and Control
, 2000
"... In this paper, we formulate the problem of characterizing the stability of a piecewise affin (PWA) system as a verification problem. The basic idea is to take the whole R^n as the set of initial conditions, and check that all the trajectories go to the origin. More precisely, we test for semiglobal ..."
Abstract

Cited by 29 (8 self)
 Add to MetaCart
In this paper, we formulate the problem of characterizing the stability of a piecewise affin (PWA) system as a verification problem. The basic idea is to take the whole R^n as the set of initial conditions, and check that all the trajectories go to the origin. More precisely, we test for semiglobal stability by restricting the set of initial conditions to an (arbitrarily large) bounded set X(0), and label as "asymptotically stable in T steps" the trajectories that enter an in variant set around the origin within a finite time T ,or as "unstable in T steps" the trajectories which enter a (very large) set X_inst . Subsets of X (0) leadin ton2W of the two previous cases are labeled as "nv classifiable in T steps". The domain of asymptotical stability in T steps is a subset of the domain of attraction ofan equilibrium poin t, an has the practicalmeanca of collectin inPv)v convW2xvP from which the settlin time of the system is smaller than T . In addition it can be computed algorithmically i...
Observability of Linear Hybrid Systems
 In Hybrid Systems: Computation and Control, LNCS
, 2003
"... We analyze the observability of the continuous and discrete states of continuoustime linear hybrid systems. For the class of jumplinear systems, we derive necessary and su#cient conditions that the structural parameters of the model must satisfy in order for filtering and smoothing algorithms t ..."
Abstract

Cited by 28 (5 self)
 Add to MetaCart
We analyze the observability of the continuous and discrete states of continuoustime linear hybrid systems. For the class of jumplinear systems, we derive necessary and su#cient 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 su#cient to guarantee the uniqueness of the reconstruction of the state trajectory, even when the individual linear systems are unobservable.
Identification of piecewise affine systems via mixedinteger programming
 Automatica
, 2004
"... This paper addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes (HHARX) and Wiener piecewise affine (WPWARX) autoregressive exogenous models. In particular, we provide algorithms based on mixedinteger linear or quadratic programming ..."
Abstract

Cited by 27 (3 self)
 Add to MetaCart
This paper addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes (HHARX) and Wiener piecewise affine (WPWARX) autoregressive exogenous models. In particular, we provide algorithms based on mixedinteger linear or quadratic programming which are guaranteed to converge to a global optimum. For the special case where switches occur only seldom in the estimation data, we also suggest a way of trading off between optimality and complexity by using a change detection approach. 1
Optimal controllers for hybrid systems: Stability and piecewise linear explicit form
 in Proceedings of the 39th IEEE Conference on Decision and Control
, 2000
"... In this paper we propose a procedure for synthesizing piecewise linear optimal controllers for hybrid systems and investigate conditions for closedloop stability. Hybrid systems are modeled in discretetime within the mixed logical dynamical (MLD) framework[8], or, equivalently [7], as piecewise af ..."
Abstract

Cited by 25 (7 self)
 Add to MetaCart
In this paper we propose a procedure for synthesizing piecewise linear optimal controllers for hybrid systems and investigate conditions for closedloop stability. Hybrid systems are modeled in discretetime within the mixed logical dynamical (MLD) framework[8], or, equivalently [7], as piecewise affine (PWA) systems. A stabilizing controller is obtained by designing a model predictive controller (MPC), which is based on the minimization of a weighted 1/∞norm of the tracking error and the input trajectories over a finite horizon. The control law is obtained by solving a mixedinteger linear program (MILP) which depends on the current state. Although efficient branch and bound algorithms exist to solve MILPs, these are known to be NPhard problems, which may prevent their online solution if the samplingtime is too small for the available computation power. Rather than solving the MILP on line, in this paper we propose a different approach where all the computation is moved off line, by solving a multiparametric MILP (mpMILP). As the resulting control law is piecewise affine, online computation is drastically reduced to a simple linear function evaluation. An example of piecewise linear optimal control of the heat exchange system [16] shows the potential of the method.
Nonlinear normobservability notions and stability of switched systems
 IEEE Trans. Automat. Contr
, 2005
"... Abstract—This paper proposes several definitions of “normobservability” for nonlinear systems and explores relationships among them. These observability properties involve the existence of a bound on the norm of the state in terms of the norms of the output and the input on some time interval. A Ly ..."
Abstract

Cited by 19 (2 self)
 Add to MetaCart
Abstract—This paper proposes several definitions of “normobservability” for nonlinear systems and explores relationships among them. These observability properties involve the existence of a bound on the norm of the state in terms of the norms of the output and the input on some time interval. A Lyapunovlike sufficient condition for normobservability is also obtained. As an application, we prove several variants of LaSalle’s stability theorem for switched nonlinear systems. These results are demonstrated to be useful for control design in the presence of switching as well as for developing stability results of Popov type for switched feedback systems. Index Terms—LaSalle’s stability theorem, nonlinear system, observability, switched system. I.
Schuppen. Observability of piecewiseaffine hybrid systems
 In Hybrid Systems: Computation and Control, LNCS
, 2004
"... Abstract. We consider observability for a class of piecewiseaffine hybrid systems without inputs. The aim is to give verifiable conditions for observability in terms of linear equations and inequalities. We first discuss a number of important concepts, such as discreteevent detectability and traje ..."
Abstract

Cited by 17 (1 self)
 Add to MetaCart
Abstract. We consider observability for a class of piecewiseaffine hybrid systems without inputs. The aim is to give verifiable conditions for observability in terms of linear equations and inequalities. We first discuss a number of important concepts, such as discreteevent detectability and trajectory observability. We give sufficient conditions for observability, observability in infinitesimal time, and observability after a single discrete event. The former conditions are used to construct an observer for the system, the latter are applied to deduce observability for an example system. 1