Hybrid system modeling and autonomous control systems

Antsaklis, Panos J.; Stiver, James A.; Lemmon, Michael

doi:10.1007/3-540-57318-6_37

Cited by 195 publications

(100 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…A fair amount of research has been done on the modeling of hybrid systems [1,3,10,12,31,32,39,43,49,51], but most of this work concentrated on deterministic systems.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Hybrid Systems: Application to Communication Networks

Hespanha

2004

Lecture Notes in Computer Science

134

122

View full text Add to dashboard Cite

Abstract. We propose a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuous-time Markov chains. However, the rate at which transitions occur is allowed to depend both on the continuous and the discrete states of the SHS. Based on results available for Piecewise-Deterministic Markov Process (PDPs), we provide a formula for the extended generator of the SHS, which can be used to compute expectations and the overall distribution of the state. As an application, we construct a stochastic model for on-off TCP flows that considers both the congestion-avoidance and slow-start modes and takes directly into account the distribution of the number of bytes transmitted. Using the tools derived for SHSs, we model the dynamics of the moments of the sending rate by an infinite system of ODEs, which can be truncated to obtain an approximate finite-dimensional model. This model shows that, for transfer-size distributions reported in the literature, the standard deviation of the sending rate is much larger than its average. Moreover, the later seems to vary little with the probability of packet drop. This has significant implications for the design of congestion control mechanisms.

show abstract

“…A fair amount of research has been done on the modeling of hybrid systems [1,3,10,12,31,32,39,43,49,51], but most of this work concentrated on deterministic systems.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Hybrid Systems: Application to Communication Networks

Hespanha

2004

Lecture Notes in Computer Science

134

122

View full text Add to dashboard Cite

show abstract

“…Finally, we would like to emphasize that the idea of using symbolic models for the control of continuous systems is not new and motivated much research in the area of hybrid systems [4], [12], [14], [24], [29], [32], [34], [40], [42], [47], [54]. Even though the use of symbolic models was advocated by these and many other researchers, the applicability of the proposed methods has always remained an open problem due to the lack of results ensuring existence of symbolic models for control systems.…”

Section: Related Workmentioning

confidence: 99%

Symbolic Control of Linear Systems Based on Symbolic Subsystems

Tabuada

2006

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

Abstract-This paper describes an approach to the control of continuous systems through the use of symbolic models describing the system behavior only at a finite number of points in the state space. These symbolic models can be seen as abstract representations of the continuous dynamics enabling the use of algorithmic controller design methods. We identify a class of linear control systems for which the loss of information incurred by working with symbolic subsystems can be compensated by feedback. We also show how to transform symbolic controllers designed for a symbolic subsystem into controllers for the original system. The resulting controllers combine symbolic controller dynamics with continuous feedback control laws and can thus be seen as hybrid systems. Furthermore, if the symbolic controller already accounts for software/hardware requirements, the hybrid controller is guaranteed to enforce the desired specifications by construction thereby reducing the need for formal verification.

show abstract

“…ii From Lemma 3.5, it turns out that, by the coordinate transformation given in (11), any linear system with the smooth continuation property is transformed into a system whose -matrix is given by (9). In addition, the equivalence between ii) and iii) suggests that all the coordinates transformations given by elements in preserve the smooth continuation property of the linear system.…”

Section: B Characterization Of Smooth Continuation Propertymentioning

confidence: 99%

“…In the control community, from the dynamical systems and control point of view, models of hybrid systems have been proposed (see e.g. [9], [10]), and several properties such as stability and controllability have been discussed; see [11] and [12] for controllability of switched systems and integrator hybrid systems, respectively, [13] and [14] for stability of general hybrid systems, and [15]- [17] for stability of piecewise-linear systems. One of the main concerns in these researches is how to define and analyze various kinds of properties of hybrid systems with discontinuous changes of vector fields and jumps of solutions (i.e., autonomous switchings and autonomous jumps in the terminology of [10]).…”

Section: Introductionmentioning

confidence: 99%

Characterization of well-posedness of piecewise-linear systems

Imura

Schaft

2000

IEEE Trans. Automat. Contr.

187

127

View full text Add to dashboard Cite

Abstract-One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. The paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Carathéodory. The concepts of jump solutions or of sliding modes are not considered here. In this sense, the problem to be discussed is one of the most basic problems in the study of well-posedness for discontinuous dynamical systems. First, we derive necessary and sufficient conditions for bimodal systems to be well-posed, in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions. Next, its extensions to the multi-modal case are discussed. As an application to switching control, in the case that two state feedback gains are switched according to a criterion depending on the state, we give a characterization of all admissible state feedback gains for which the closed loop system remains wellposed.

show abstract

Hybrid system modeling and autonomous control systems

Cited by 195 publications

References 31 publications

Stochastic Hybrid Systems: Application to Communication Networks

Stochastic Hybrid Systems: Application to Communication Networks

Symbolic Control of Linear Systems Based on Symbolic Subsystems

Characterization of well-posedness of piecewise-linear systems

Contact Info

Product

Resources

About