Asynchronous l-complete approximations
TL;DR: An asynchronous version of the well-known concepts of state property, memory span and l -completeness is introduced, extending the behavioral systems theory in a consistent way to ensure that the resulting approximation can be realized by a finite state machine.
About: This article is published in Systems & Control Letters.The article was published on 2014-11-01. It has received 16 citations till now. The article focuses on the topics: Completeness (order theory) & Asynchronous communication.
Citations
More filters
[...]
TL;DR: In this paper, the authors studied the effect of local derivatives on the detection of intensity edges in images, where the local difference of intensities is computed for each pixel in the image.
Abstract: Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:
1,829 citations
TL;DR: This work states that the next generation of transportation systems will include connected vehicles, connected infrastructure, and increased automation, and these advances must coexist with legacy technology into the foreseeable future.
Abstract: Today's increasingly populous cities require intelligent transportation systems that make efficient use of existing transportation infrastructure. However, inefficient traffic management is pervasive [1], [2], costing US$160 billion in the United States in 2015, including 6.9 billion h of additional travel time and 3.1 billion gal of wasted fuel [3]. To mitigate these costs, the next generation of transportation systems will include connected vehicles, connected infrastructure, and increased automation. In addition, these advances must coexist with legacy technology into the foreseeable future. This complexity makes the goal of improved mobility and safety even more daunting.
42 citations
Posted Content•
07 Feb 2020TL;DR: The proposed algorithm for constructing sound finite-state abstractions is inspired by the simultaneous reachability and bisimulation minimization algorithm of Lee and Yannakakis and generalizes feedback-refinement relations from ABCD with state-feedback.
Abstract: We consider abstraction-based design of output-feedback controllers for dynamical systems with a finite set of inputs and outputs against specifications in linear-time temporal logic. The usual procedure for abstraction-based controller design (ABCD) first constructs a finite-state abstraction of the underlying dynamical system, and second, uses reactive synthesis techniques to compute an abstract state-feedback controller on the abstraction. In this context, our contribution is two-fold: (I) we define a suitable relation between the original system and its abstraction which characterizes the soundness and completeness conditions for an abstract state-feedback controller to be refined to a concrete output-feedback controller for the original system, and (II) we provide an algorithm to compute a sound finite-state abstraction fulfilling this relation.
Our relation generalizes feedback-refinement relations from ABCD with state-feedback. Our algorithm for constructing sound finite-state abstractions is inspired by the simultaneous reachability and bisimulation minimization algorithm of Lee and Yannakakis. We lift their idea to the computation of an observation-equivalent system and show how sound abstractions can be obtained by stopping this algorithm at any point. Additionally, our new algorithm produces a realization of the topological closure of the input/output behavior of the original system if it is finite-state realizable.
18 citations
Cites background from "Asynchronous l-complete approximati..."
...[17, 20, 23, 29]....
[...]
...The construction of finite-state abstractions of input/output traces for the purpose of output-feedback control is further enabled by so called l-complete abstractions [17, 20, 23, 29]....
[...]
01 Dec 2015
TL;DR: This paper compares quotient based abstractions (QBA) with different realizations of strongest (asynchronous) l-complete approximations (SAlCA) and shows that they are generally incomparable both in terms of behavioral inclusion and similarity relations.
Abstract: This paper is concerned with a detailed comparison of two different abstraction techniques for the construction of finite state symbolic models for controller synthesis of hybrid systems. Namely, we compare quotient based abstractions (QBA) with different realizations of strongest (asynchronous) l-complete approximations (SAlCA). Even though the idea behind their construction is very similar, we show that they are generally incomparable both in terms of behavioral inclusion and similarity relations. We therefore derive necessary and sufficient conditions for QBA to coincide with particular realizations of SAlCA. Depending on the original system, either QBA or SAlCA can be a tighter abstraction.
14 citations
22 Apr 2020
TL;DR: In this paper, an abstraction-based design of output-feedback controllers for dynamical systems with a finite set of inputs and outputs against specifications in linear-time temporal logic is considered.
Abstract: We consider abstraction-based design of output-feedback controllers for dynamical systems with a finite set of inputs and outputs against specifications in linear-time temporal logic. The usual procedure for abstraction-based controller design (ABCD) first constructs a finite-state abstraction of the underlying dynamical system, and second, uses reactive synthesis techniques to compute an abstract state-feedback controller on the abstraction. In this context, our contribution is two-fold: (I) we define a suitable relation between the original system and its abstraction which characterizes the soundness and completeness conditions for an abstract state-feedback controller to be refined to a concrete output-feedback controller for the original system, and (II) we provide an algorithm to compute a sound finite-state abstraction fulfilling this relation. Our relation generalizes feedback-refinement relations from ABCD with state-feedback. Our algorithm for constructing sound finite-state abstractions is inspired by the simultaneous reachability and bisimulation minimization algorithm of Lee and Yannakakis. We lift their idea to the computation of an observation-equivalent system and show how sound abstractions can be obtained by stopping this algorithm at any point. Additionally, our new algorithm produces a realization of the topological closure of the input/output behavior of the original system if it is finite-state realizable.
11 citations
References
More filters
Book•
01 Jan 1979
TL;DR: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
Abstract: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity. The authors present the theory in a concise and straightforward manner, with an eye out for the practical applications. Exercises at the end of each chapter, including some that have been solved, help readers confirm and enhance their understanding of the material. This book is appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
13,779 citations
TL;DR: In this paper, the control of a class of discrete event processes, i.e., processes that are discrete, asynchronous and possibly non-deterministic, is studied. And the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language, where the control process is described as the generator of a formal language, while the supervisor is constructed from the grammar of a specified target language that incorporates the desired closed-loop system behavior.
Abstract: This paper studies the control of a class of discrete event processes, i.e. processes that are discrete, asynchronous and possibly nondeter-ministic. The controlled process is described as the generator of a formal language, while the controller, or supervisor, is constructed from the grammar of a specified target language that incorporates the desired closed-loop system behavior. The existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language. Two examples are provided.
3,432 citations
"Asynchronous l-complete approximati..." refers background or methods in this paper
...With this specification type supervisory control theory (SCT) [1, 2] can be used to synthesize a correct by design control system if the abstracted plant model can be represented by a regular language as well....
[...]
...Even though SCT cannot be directly applied to ω-languages, it was shown in [3], and recently generalized in [12], that for ω-languages realizable by finite state machines (FSM), a variant of SCT can be used to synthesize a minimally restrictive controller for specifications representable by the closure of a regular language (for details, see [12] and the references therein)....
[...]
...Observe that after the first piece we are only allowed to pick from the set B|[1,3]....
[...]
01 Jan 1989
TL;DR: The focus is on the qualitative aspects of control, but computation and the related issue of computational complexity are also considered.
Abstract: A discrete event system (DES) is a dynamic system that evolves in accordance with the abrupt occurrence, at possibly unknown irregular intervals, of physical events. Such systems arise in a variety of contexts ranging from computer operating systems to the control of complex multimode processes. A control theory for the logical aspects of such DESs is surveyed. The focus is on the qualitative aspects of control, but computation and the related issue of computational complexity are also considered. Automata and formal language models for DESs are surveyed. >
2,829 citations
"Asynchronous l-complete approximati..." refers methods in this paper
...With this specification type supervisory control theory (SCT) [1, 2] can be used to synthesize a correct by design control system if the abstracted plant model can be represented by a regular language as well....
[...]
...Even though SCT cannot be directly applied to ω-languages, it was shown in [3], and recently generalized in [12], that for ω-languages realizable by finite state machines (FSM), a variant of SCT can be used to synthesize a minimally restrictive controller for specifications representable by the closure of a regular language (for details, see [12] and the references therein)....
[...]
[...]
TL;DR: In this paper, the authors studied the effect of local derivatives on the detection of intensity edges in images, where the local difference of intensities is computed for each pixel in the image.
Abstract: Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:
1,829 citations
Book•
01 Mar 1988TL;DR: Great Aunt Eugenia and other automata Sundry machines Implementing finite automata Implementation and realization Behavioural equivalence, SP partitions and reduced machines
Abstract: Great Aunt Eugenia and other automata Sundry machines Implementing finite automata Implementation and realization Behavioural equivalence, SP partitions and reduced machines Parallel and serial composition of automata The parallel decomposition theorem The serial decomposition theorem The lattice of SP partitions Analysis of machines Concurrent systems: net theory Concurrent systems: the calculus of communicating systems. Appendix: Sets, relations and functions.
1,582 citations