Weak reachability and controllability of discrete-time nonlinear systems: generic approach and singular points

ABSTRACT

The paper finds the singular points from which (to which) the generically accessible system is not weakly reachable (controllable) in k steps. These points are found with the help of the space of vector fields, being the discrete-time analogue of the strong accessibility distribution. Unlike in the continuous-time case, a separate object is needed to find the singular points related to weak reachability.     

Using directed hypergraphs to verify rule-based expert systems

Rule-based representation techniques have become popular for storage and manipulation of domain knowledge in expert systems. It is important that systems using such a representation are verified for accuracy before implementation. In recent years, graphical techniques have been found to provide a good framework for the detection of errors that may appear in a rule base. The authors present a graphical representation scheme that: 1) captures complex dependencies across clauses in a rule base in a compact yet intuitively clear manner and 2) is easily automated to detect structural errors in a rigorous fashion. Their technique uses a directed hypergraph to accurately detect the different types of structural errors that appear in a rule base. The technique allows rules to be represented in a manner that clearly identifies complex dependencies across compound clauses. Subsequently, the verification procedure can detect errors in an accurate fashion by using simple operations on the adjacency matrix of the directed hypergraph. The technique is shown to have a computational complexity that is comparable to that of other graphical techniques. The graphical representation coupled with the associated matrix operations illustrate how directed hypergraphs are a very appropriate representation technique for the verification task     

Complete controllability and controllability for linear autonomous systems of neutral type

We solve the complete controllability problem for linear autonomous systems of neutral type with many commensurable delays in the case when a system solution is required to be an absolutely continuous functions. We propose a control method for the said objects if they do not have the complete controllability property.     

Constructing formal rules to verify message communication in distributed systems

This study presents a method to construct formal rules used to run-time verify message passing between clients in distributed systems. Rules construction is achieved in four steps: (1) Visual specification of expected behavior of the sender, receiver, and network in sending and receiving a message, (2) Extraction of properties of sender, receiver, and network from the visual specification, (3) specification of constraints that should govern message passing in distributed systems, and (4) construction of verifier rules from the properties and the constraints. The rules are used to verify actual sender, receiver, and network behavior. Expected behavior of the client (process) is one that to be and the actual one is the behavior should be verified. The rules were applied to verify the behavior of client and servers that communicated with each other in order to compute Fibonacci numbers in parallel and some violations were discovered.     

Graph-theoretic approach to controllability and localizability of decentralized control systems

The controllability and the localizability problems are considered under the decentralized information structure using some concepts from graph theory. First of all, the information structure graph is introduced for a decentralized control system based upon local output controllability, matrices between stations when a local output feedback law is applied, and some invariant properties of the graph with respect to local output feedback laws are driven. Then by using these results, necessary and sufficient conditions of controllability under decentralized information structure are obtained. Also obtained are several conditions for localizability, of decentralized control systems, which is newly introduced in the present paper as an extended concept of a class of disturbance localization and decoupling for centralized systems.     

A new approach to verify rule-based systems using petri nets

In the past several years, various graphical techniques were proposed to analyze various types of structural errors, including inconsistency (conflict rules), incompleteness (missing rules), redundancy (redundant rules), and circularity (circular depending rules), in rule-based systems in which rules can be represented in propositional logic. In this paper, we present a special reachability graph technique based on ω-nets (a special type of low-level petri nets) to detect all of the above types of structural errors. Our new technique is simple, efficient, and can be easily automated. We highlight the unique features of this new approach and demonstrate its application through two examples.     

Local controllability of nonlinear systems

The local controllability of control systems with an arbitrary number of controls is considered, first on an open set and then at a given point; necessary conditions are derived concerning the Lie algebra T′ generated by the input vector fields, and applied to gradient systems.The main results are a geometric sufficient condition for local controllability at a point, and an equivalent condition based on the computation of Lie brackets, assuming T′ to be (n − 1)-dimensional.     

Local controllability of quantum systems

We give a criterion that is sufficient for controllability of multipartite quantum systems. We generalize the graph infection criterion to the quantum systems that cannot be described with the use of a graph theory. We introduce the notation of hypergraphs and reformulate the infection property in this setting. The introduced criterion has a topological nature and therefore it is not connected to any particular experimental realization of quantum information processing.