Some issues of structure and control for linear time-invariant systems

The objective of this paper is to emphasise the role played by particular structures in the solution of some control problems. The so-called “structural approach” relies on various indicators of dynamical systems such as, for instance, finite and infinite zeros, kernel indices, …. The fundamental invariance properties of these structures under the action of some transformations groups (e.g. feedback) are at the origin of their key role. Structural solutions to “classical” control problems, such as disturbance rejection, model matching and non-interaction are now rather well known: zeros at infinity play a role in the existence of “proper” solutions, while finite (invariant) zeros allow for the characterisation of “fixed poles”, whose location in the complex plane gives answer to pole placement limitations (including stability). Among the recent contributions to this structural approach, a particular attention is here devoted to:

- “Partial” versions of some of these control problems: The control objective only concerns a finite number of (and not necessarily all) the first Markov parameters of the transfer function matrix of the controlled system (e.g. to be zero for disturbance rejection or model matching, to be diagonal for non-interaction). Some interesting new issues in the dual context of failure detection are also sketched.

- Generalised solutions: Based on proportional and derivative feedback laws, with new issues in the context of systems with variable internal structures, and also for systems with delays.

Geometric concepts, such as invariant and almost invariant subspaces, and algebraic counterparts, such as factorisations on some special rings, are intermediary tools which support the characterisations of those particular structures and which allow for a structural treatment of the considered control and/or observation problems.

The results are here presented without proof: references are given to previous published results (in most cases in books and journals which are easily available), and some simple examples are used to illustrate non-standard notions (among which systems with variable internal structure, and time domain left invertibility).

Most of the results here presented rely on long and intensive collaborations between the author and various colleagues.     

A “mixed” small gain and passivity theorem in the frequency domain

We show that the negative feedback interconnection of two causal, stable, linear time-invariant systems, with a “mixed” small gain and passivity property, is guaranteed to be finite-gain stable. This “mixed” small gain and passivity property refers to the characteristic that, at a particular frequency, systems in the feedback interconnection are either both “input and output strictly passive”; or both have “gain less than one”; or are both “input and output strictly passive” and simultaneously both have “gain less than one”. The “mixed” small gain and passivity property is described mathematically using the notion of dissipativity of systems, and finite-gain stability of the interconnection is proven via a stability result for dissipative interconnected systems.     

Personalization of internet telephony services for presence with SIP and extended CPL

This paper discusses issues of personalization of presence services in the context of Internet Telephony. Such services take into consideration the willingness and ability of a user to communicate in a network, as well as possibly other factors such as time, address, etc. Via a three-layer service architecture for communications in the session initiation protocol (SIP) standard, presence system basic services and personalized services (personal policies) are clearly separated and discussed. To enrich presence related services, presence information is illustratively extended from the well known “online” and “offline” indicators to a much broader meaning that includes “location”, “lineStatus”, “role”, “availability”, etc. Based on this, the call processing language (CPL) is extended in order to describe presence related personalized services for both call processing systems and presence systems using information such as a person’s presence status, time, address, language, or any of their combinations. A web-based system is designed and implemented to simulate these advanced services. In the implementation, personal policies are programmed by end users via a graphic user interface (GUI) and are automatically translated into extended CPL. The simulation system clearly displays when, where and what CPL policies should be used for the provision of personalized presence services and call processing services. Policy conflicts are also addressed by setting policy priorities in the system.     

Constrained multibody system dynamics an automated approach

The governing equations for constrained multibody systems are formulated in a manner suitable for their automated, numerical development and solution. Specifically, the “closed loop” problem of multibody chain systems is addressed.

The governing equations are developed by modifying dynamical equations obtained from Lagrange's form of d'Alembert's principle. This modification, which is based upon a solution of the constraint equations obtained through a “zero eigenvalues theorem,” is, in effect, a contraction of the dynamical equations.

It is observed that, for a system with n generalized coordinates and m constraint equations, the coefficients in the constraint equations may be viewed as “constraint vectors” in n-dimensional space. Then, in this setting the system itself is free to move in the n−m directions which are “orthogonal” to the constraint vectors.     

Stability analysis of switched systems using variational principles: An introduction

Many natural and artificial systems and processes encompass several modes of operation with a different dynamical behavior in each mode. Switched systems provide a suitable mathematical model for such processes, and their stability analysis is important for both theoretical and practical reasons. We review a specific approach for stability analysis based on using variational principles to characterize the “most unstable” solution of the switched system. We also discuss a link between the variational approach and the stability analysis of switched systems using Lie-algebraic considerations. Both approaches require the use of sophisticated tools from many different fields of applied mathematics. The purpose of this paper is to provide an accessible and self-contained review of these topics, emphasizing the intuitive and geometric underlying ideas.     

Robust analysis and control for a class of uncertain nonlinear discrete-time systems

This paper deals with the problem of robust analysis and control of a class of nonlinear discrete-time systems with (constant) uncertain parameters. For the analysis problem we use a polynomial Lyapunov function and we generalize, for nonlinear systems, the “extended stability” notion proposed by Oliveira et al. (1999) in the context of linear discrete-time uncertain systems. As a result, we propose an LMI optimization problem to maximize an estimate of the domain of attraction, and also extend this approach to the synthesis problem by considering parameter-dependent Lyapunov functions and nonlinear multipliers. Numerical examples illustrate the approach and show its potential for solving analysis and control problems of nonlinear discrete-time systems.     

Towards a theory of delegation for agent-based systems

In this paper a theory of delegation is presented. There are at least three reasons for developing such a theory. First, one of the most relevant notions of “agent” is based on the notion of “task” and of “on behalf of”. In order to found this notion a theory of delegation among agents is needed. Second, the notion of autonomy should be based on different kinds and levels of delegation. Third, the entire theory of cooperation and collaboration requires the definition of the two complementary attitudes of goal delegation and adoption linking collaborating agents.

After motivating the necessity for a principled theory of delegation (and adoption) the paper presents a plan-based approach to this theory. We analyze several dimensions of the delegation/adoption (on the basis of the interaction between the agents, of the specification of the task, of the possibility to subdelegate, of the delegation of the control, of the help levels). The agent's autonomy and levels of agency are then deduced. We describe the modelling of the client from the contractor's point of view and vice versa, with their differences, and the notion of trust that directly derives from this modelling.

Finally, a series of possible conflicts between client and contractor are considered: in particular collaborative conflicts, which stem from the contractor's intention to help the client beyond its request or delegation and to exploit its own knowledge and intelligence (reasoning, problem solving, planning, and decision skills) for the client itself.     

Overload effects and their prevention

The so-called “thrashing effect”, well known from virtual storage, but also reported from data-base systems and packet switching networks, has turned out to be a common phenomenon of large systems with concurrent processing. It simply means that beyond a saturation point an increase of the load (e.g. number of jobs) leads to a (sometimes sudden) decrease in performance (e.g. throughput). With growing size and complexity of computer systems and the general trend towards distribution, overload phenomena of different origin can interfere and superimpose mutually, resulting in a composite overload effect that can hardly be broken down into its constituents. Because the complexity of such systems defies detailed modeling, it is more appropriate to look at those systems in a more macroscopic, behavioral way, considering only the two externally measurable variables “load” and “throughput”. The resulting abstraction from internal details can smooth the way to a more general treatment and application. The article deals with such overload phenomena and their prevention in a general way using a control-theoretic approach. Special emphasis is placed on dynamic behavior, where load characteristics are changing with time, making feedback mechanisms necessary. The problem is approached as a dynamic optimum search problem for which different algorithms are presented and compared by simulation.     

On the almost-sure sample stability of systems with randomly time-varying delays

In a large class of multi-loop control systems, many feedback loops are “closed” through a time-shared digital computer, by means of algorithms which require information from sources which are sampled at a rate which is not synchronized with the sampling of the individual “plants”. This mis-synchronization, coupled with variations in the computer's task load caused by “interrupts”, results in a randomly time-varying delay in the closing of the various feedback loops. Consequently, the dynamics of each controlled “plant” in such a system may be modeled by means of a stochastic delay-differential equation. This paper presents some new research results concerning the sample stability, as opposed to statistical, or ensemble stability, of linear stochastic delay-differential equations.     

G-networks with resets

Gelenbe networks (G-networks) are product form queuing networks which, in addition to ordinary customers, contain unusual entities such as “negative customers” which eliminate normal customers and “triggers” which move other customers from some queue to another. These models have generated much interest in the literature since the early 1990s. The present paper discusses a novel model for a reliable system composed of N unreliable systems, which can hinder or enhance each other’s reliability. Each of the N systems also tests other systems at random; it is able to reset another system if it is itself in working condition and discovers that the other system has failed, so that the global reliability of the system is enhanced. This paper shows how an extension of G-networks that includes novel “reset” customers can be used to model this behavior. We then show that a general G-network model with resets has product form, and prove existence and uniqueness of its solution.     

Expert systems in the context of multi-brain systems

In this article, we postulate the possibility of building a four-brain like expert system. For this purpose we have taken ideas from Minsky’s “Society of Mind” some concepts from Brooks and Stein’s “Brains for Bodies” project, and some mechanisms from neurophysiology. In our search for conceptualization of a minimum multi-brain like system oriented to expert systems, we found that: (a) expert systems with blackboard architecture can be seen as primitive topological approaches to multi-brain systems, (b)in our multi-brain like expert systems conception, as in many other expert systems, we feel that we have to impose our external language as their internal language and our external symbols as their internal symbols. These are the kind of entities discussed by philosophers as “What is it like to be a Bat?”. In this context our conception is still a “Batman”. True-cognitive expert systems might be produced in the future if the matters are self constructed internal languages, and its post-hoc knowledge, and (c) in the scope of multi-brain systems, expert systems are not an engineering subject of artificial intelligence (AI) but a substantive subject that goes from philosophical to neurophysiological aspects.     

Importance in knowledge systems

In knowledge systems, pieces of information (evidence, hypotheses, attributes, terms, documents, rules) are usually assumed to carry equal importance and to be independent of each other, although it might not actually be the case. Issues for a logic of weighted queries, with possibility of also weighting documents and logical connectors (in terms of intelligent retrieval, for example) are presented here, using “min” or t-norms, and soft operators involving p-norms. This logic cannot be a conventional one for, when introducing relative importance between concepts, definitions are different for ANDed and ORed weighted queries. A concept of “nought”, a limit case of no-importance queries, and its behaviour with fuzzy sets operations is developed, in particular the notion of an extended membership is introduced. Finally it is shown, with a biomedical example, how to combine importance with soft matching in rule-based systems.     

A structure for expert systems maintenance

An approach to the design of maintainable expert systems is presented. Central to this approach is a conceptual model in which the data and knowledge are both modelled as formal “items” in a uniform way. “Objects” are introduced as “item building” operators. The notion of the “decomposition” of items and objects provides the foundation for a single rule of normalization. This single rule applies to all items and objects, including knowledge items, and is a non-trivial generalization of the traditional normal forms for database. Coupling relationships represent the necessary maintenance paths in the conceptual model. A complete characterization of coupling relationships is given, and the value of normalization to the reduction of maintenance costs is discussed.     

New Branches, Old Roots: A Study of Methods and Techniques in Web/Hypermedia Systems Design

Despite claims in the literature that “traditional” methods and techniques are inadequate and poorly matched to the demands of the Web design context, the findings from a field survey of Web/hypermedia systems designers in Ireland indicate quite the contrary. in general, the notion of “method” in the traditional sense seems to have been largely displaced by hybrid aggregations of techniques and other method fragments - selected on the basis of usefulness and purposefully blended within an overarching framework of an in-house development process.     

Limits of economic and strategic rationality for agents and MA systems

AI adoption of the game-theoretic paradigm although motivated and productive, suffers from basic limits for modelling autonomous agents and MA systems. First, we briefly restate game-theory's role for DAI and MAS: the introduction of formal prototypical social situations (“games”); the use of formal and sound notions, a self-interested view of autonomous agents, etc. Then, a number of criticisms, that have an impact on modelling intelligent social/individual action, are examined: the economicist interpretation of rationality; its instrumentalist conception, which leaves implicit the ends of agents' choices; the consequent multiple equilibria allowed by the theory; the context-unboundedness of rationality. Some contributions for a more heterarchic, context-bounded, architecture of rational agent are given, and a goal-based strategy, as distinct from a strictly utilitarian principle of decision-making, is proposed. Troubles of game-theory with multi-agent systems and in particular with modelling “cooperation” are outlined. Finally, some limits inherent in the notion of “incentive engineering” are pointed out.     

A small gain theorem for linear stochastic systems

A well-known result in linear control theory is the so-called “small gain” theorem stating that if given two plants with transfer matrix functions T₁ and T₂ in H^∞ such that T₁ < γ and T₂ < 1/γ, when coupling T₂ to T₁ such that u₂ = y₁ and u₁ = y₂ one obtains an internally stable closed system. The aim of the present paper is to describe a corresponding result for stochastic systems with state-dependent white noise.     

Chattering suppression methods in sliding mode control systems

The implementation of sliding mode control is often irritated by high frequency oscillations known as “chattering” in system outputs issued by dynamics from actuators and sensors ignored in system modeling. This paper provides analysis of chattering in such systems with unmodeled based on the Lyapunov theory and the describing function method. It also describes various approaches to reduce chattering including methods based on relay control gain adaptation. And for those systems to which the methods are not applicable, chattering frequency control using hysteresis loop will be provided.     

A distributed approach for fault detection and diagnosis based on Time Petri Nets

This paper proposes an algorithm for the model based design of a distributed protocol for fault detection and diagnosis for very large systems. The overall process is modeled as different Time Petri Net (TPN) models (each one modeling a local process) that interact with each other via guarded transitions that becomes enabled only when certain conditions (expressed as predicates over the marking of some places) are satisfied (the guard is true). In order to use this broad class of time DES models for fault detection and diagnosis we derive in this paper the timing analysis of the TPN models with guarded transitions. In this paper we also extend the modeling capability of the faults calling some transitions faulty when operations they represent take more or less time than a prescribed time interval corresponding to their normal execution. We consider here that different local agents receive local observation as well as messages from neighboring agents. Each agent estimates the state of the part of the overall process for which it has model and from which it observes events by reconciling observations with model based predictions. We design algorithms that use limited information exchange between agents and that can quickly decide “questions” about “whether and where a fault occurred?” and “whether or not some components of the local processes have operated correctly?”. The algorithms we derive allow each local agent to generate a preliminary diagnosis prior to any communication and we show that after communicating the agents we design recover the global diagnosis that a centralized agent would have derived. The algorithms are component oriented leading to efficiency in computation.     

Positive N-periodic descriptor control systems

A small-gain theorem is presented for almost global stability of monotone control systems which are open-loop almost globally stable, when constant inputs are applied. The theorem assumes “negative feedback” interconnections. This typically destroys the monotonicity of the original flow and potentially destabilizes the resulting closed-loop system.