A system model is developed where the criterion to partition the world into a system and a rest is based on the functional relation between its states. This approach implies that the gestalt of systems becomes very dynamic. Especially interactions between systems may create temporary super systems "on the fly". The reference to the function notion establishes the link to computation. Based on the distinction between the intended determinism versus nondeterminism of the interaction, two classes of system interactions are distinguished: composition and cooperation. Composition means that by interaction super systems are created and the interacting systems become subsystems. Cooperation means that systems sensibly interact loosely without creating any identifiable super system function and therefore without super system creation from the perspective of the interacting systems. Cooperative system interactions are described with the help of the protocol notion based on shared states, interpreted as the stateful exchange of characters via Shannon channels between roles - the projection of systems onto the interaction channels. It is shown that roles can be internally coordinated by a set of rules, leading to a very flexible process notion which unfolds its full potential only in a new type of execution environment capable of executing spontaneous transitions. The system model has immediate implications for componentization which can be viewed as an attempt to either hide functional recursion and provide only functionality whose composition behavior is easy to understand, or to provide loosely coupled interactions via protocols. To be complete, component models should therefore at least support three general classes of components: one for loose coupling, one for hierarchical composition, and one for pipes.
In @cite_43 David Harel and Amir Pnueli distinguish between ''transformational'' and ''reactive'' systems. They define: "A transformational system accepts input, performs transformation on them and produces outputs'' - which is consistent with the definition of a system. They further define ''Reactive systems ... are repeatedly prompted by the outside world and their role is to continuously respond to external inputs ... A reactive system, in general, does not compute or perform a function, but is supposed to maintain a certain ongoing relationship, so to speak, with its environment.''
@cite_43
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We deal with nonlinear dynamical systems, consisting of a linear nominal part perturbed by model uncertainties, nonlinearities and both additive and multiplicative random noise, modeled as a Wiener process. In particular, we study the problem of finding suitable measurement feedback control laws such that the resulting closed-loop system is stable in some probabilistic sense. To this aim, we introduce a new notion of stabilization in probability, which is the natural counterpart of the classical concept of regional stabilization for deterministic nonlinear dynamical systems and stands as an intermediate notion between local and global stabilization in probability. This notion requires that, given a target set, a trajectory, starting from some compact region of the state space containing the target, remains forever inside some larger compact set, eventually enters any given neighborhood of the target in finite time and remains thereinafter, all these events being guaranteed with some probability. We give a Lyapunov-based sufficient condition for achieving stability in probability and a separation result which splits the control design into a state feedback problem and a filtering problem. Finally, we point out constructive procedures for solving the state feedback and filtering problem with arbitrarily large region of attraction and arbitrarily small target for a wide class of nonlinear systems, which at least include feedback linearizable systems. The generality of the result is promising for applications to other classes of stochastic nonlinear systems. In the deterministic case, our results recover classical stabilization results for nonlinear systems. Some observations are made concerning the process of developing complex systems. A broad class of systems, termed reactive, is singled out as being particularly problematic when it comes to finding satisfactory methods for behavioral description. In this paper we recommend the recently proposed statechart method for this purpose. Moreover, it is observed that most reactive systems cannot be developed in a linear stepwise fashion, but, rather, give rise to a two-dimensional development process, featuring behavioral aspects in the one dimension and implementational ones in the other. Concurrency may occur in both dimensions, as orthogonality of states in the one and as parallelism of subsystems in the other. A preliminary approach to working one’s way through this “magic square” of system development is then presented. The ideas described herein seem to be relevant to a wide variety of application areas. Abstract This article describes computer simulation of the dynamics of a distributed model of the olfactory system that is aimed at understanding the role of chaos in biological pattern recognition. The model is governed by coupled nonlinear differential equations with many variables and parameters, which allow multiple high-dimensional chaotic states. An appropriate set of the parameters is identified by computer experiments with the guidance of biological measurements, through which this model of the olfactory system maintains a low dimensional global chaotic attractor with multiple “wings.” The central part of the attractor is its basal chaotic activity, which simulates the electroencephalographic (EEG) activity of the olfactory system under zero signal input (exhalation). It provides the system with a ready state so that it is unnecessary for the system to “wake up” from or return to a “dormant” equilibrium state every time that an input is given (by inhalation). Each of the wings may be either a near-limit cycle (a narrow band chaos) or a broad band chaos. The reproducible spatial pattern of each near-limit cycle is determined by a template made in the system. A novel input with no template activates the system to either a nonreproducible near-limit cycle wing or a broad band chaotic wing. Pattern recognition in the system may be considered as the transition from one wing to another, as demonstrated by the computer simulation. The time series of the manifestations of the attractor are EEG-like waveforms with fractal dimensions that reflect which wing the system is placed in by input or lack of input. The computer simulation also shows that the adaptive behavior of the system is scaling invariant, and it is independent of the initial conditions at the transition from one wing to another. These properties enable the system to classify an uninterrupted sequence of stimuli. A higher order recurrent neural network architecture learns to recognize and generate languages after being “trained” on categorized exemplars. Studying these networks from the perspective of dynamical systems yields two interesting discoveries: First, a longitudinal examination of the learning process illustrates a new form of mechanical inference: Induction by phase transition. A small weight adjustment causes a “bifurcation” in the limit behavior of the network. This phase transition corresponds to the onset of the network's capacity for generalizing to arbitrary-length strings. Second, a study of the automata resulting from the acquisition of previously published training sets indicates that while the architecture is not guaranteed to find a minimal finite automaton consistent with the given exemplars, which is an NP-Hard problem, the architecture does appear capable of generating non-regular languages by exploiting fractal and chaotic dynamics. I end the paper with a hypothesis relating linguistic generative capacity to the behavioral regimes of non-linear dynamical systems. In previous work, we proposed a logic-based framework in which computation is the execution of actions in an attempt to make reactive rules of the form if antecedent then consequent true in a canonical model of a logic program determined by an initial state, sequence of events, and the resulting sequence of subsequent states. In this model-theoretic semantics, reactive rules are the driving force, and logic programs play only a supporting role. In the canonical model, states, actions, and other events are represented with timestamps. But in the operational semantics (OS), for the sake of efficiency, timestamps are omitted and only the current state is maintained. State transitions are performed reactively by executing actions to make the consequents of rules true whenever the antecedents become true. This OS is sound, but incomplete. It cannot make reactive rules true by preventing their antecedents from becoming true, or by proactively making their consequents true before their antecedents become true. In this paper, we characterize the notion of reactive model, and prove that the OS can generate all and only such models. In order to focus on the main issues, we omit the logic programming component of the framework. We present a method to design controllers for safety specifications in hybrid systems. The hybrid system combines discrete event dynamics with nonlinear continuous dynamics: the discrete event dynamics model linguistic and qualitative information and naturally accommodate mode switching logic, and the continuous dynamics model the physical processes themselves, such as the continuous response of an aircraft to the forces of aileron and throttle. Input variables model both continuous and discrete control and disturbance parameters. We translate safety specifications into restrictions on the system's reachable sets of states. Then, using analysis based on optimal control and game theory for automata and continuous dynamical systems, we derive Hamilton-Jacobi equations whose solutions describe the boundaries of reachable sets. These equations are the heart of our general controller synthesis technique for hybrid systems, in which we calculate feedback control laws for the continuous and discrete variables, which guarantee that the hybrid system remains in the "safe subset" of the reachable set. We discuss issues related to computing solutions to Hamilton-Jacobi equations. Throughout, we demonstrate out techniques on examples of hybrid automata modeling aircraft conflict resolution, autopilot flight mode switching, and vehicle collision avoidance. Our researches on adaptive systems are inspired by their ability of building by themselves a representation of their surrounding world. Using cooperation as a local criterion of self-organization, we study in a network of neuro-agents the evolution of the system and in the same way, the emergence of a functioning coherent with the environmental feed-back. In this paper we expose the abilities of the neuro-agents that give them the autonomy required to build an ab nihilo topology. And finally we want to emphasize the dynamic of the network organization that is basically its best property of adaptation to a changing environment. The work presented here concerns our approach to self-organization in a dynamic neural network. We present some experiments of emergent learning based on our knowledge of complex systems through multi-agent systems technology and cellular biology. In fact we are most interested in the mechanisms involved in the construction of a network able to stabilize its structure in a given environment, than in the efficiency of the learning supported by this structure. Obviously those two ontogenetic processes are strongly coupled and appear simultaneously as mutual consequences. Under those conditions, we conceive artificial systems presenting an inherent complexity close to biological systems as they are open and as their structure evolves from nothing (at least an empty shell) up to an organized, stable and functional network of neuro-agents. Our working hypothesis tells minimal entities of such a system can be built and given with sufficient behavioral potentialities in order to organize themselves to satisfy the whole system activity. In this study, we want to show that a coherent and useful system can emerge without any global model for its functioning, solely from activity and organizational rules of its sub-parts; only agents are designed, not the topology of the network they will belong to. Our thought process supposes four distinct steps that description will be formerly extended. Firstly the neuro-agent unit has to be designed, their properties, their abilities (calculus, communication) and their knowledge. Secondly, initial system is constituted of a minimal number of unlinked neuro-agents. Those pre-built neuro-agents are only receptors (inputs) and actuators (outputs) of the network. Thirdly the global system has to be plunged in a dynamic and open environment in which it will have to adapt to; regarding neuromimetic systems, this phase suppose Reliable systems have always been built out of unreliable components [1]. Early on, the reliable components were small such as mirrored disks or ECC (Error Correcting Codes) in core memory. These systems were designed such that failures of these small components were transparent to the application. Later, the size of the unreliable components grew larger and semantic challenges crept into the application when failures occurred. Fault tolerant algorithms comprise a set of idempotent subalgorithms. Between these idempotent sub-algorithms, state is sent across the failure boundaries of the unreliable components. The failure of an unreliable component can then be tolerated as a takeover by a backup, which uses the last known state and drives forward with a retry of the idempotent sub-algorithm. Classically, this has been done in a linear fashion (i.e. one step at a time). As the granularity of the unreliable component grows (from a mirrored disk to a system to a data center), the latency to communicate with a backup becomes unpalatable. This leads to a more relaxed model for fault tolerance. The primary system will acknowledge the work request and its actions without waiting to ensure that the backup is notified of the work. This improves the responsiveness of the system because the user is not delayed behind a slow interaction with the backup. There are two implications of asynchronous state capture: 1) Everything promised by the primary is probabilistic. There is always a chance that an untimely failure shortly after the promise results in a backup proceeding without knowledge of the commitment. Hence, nothing is guaranteed! 2) Applications must ensure eventual consistency [20]. Since work may be stuck in the primary after a failure and reappear later, the processing order for work cannot be guaranteed. Platform designers are struggling to make this easier for their applications. Emerging patterns of eventual consistency and probabilistic execution may soon yield a way for applications to express requirements for a “looser” form of consistency while providing availability in the face of ever larger failures. As we will also point out in this paper, the patterns of probabilistic execution and eventual consistency are applicable to intermittently connected application patterns. This paper recounts portions of the evolution of these trends, attempts to show the patterns that span these changes, and talks about future directions as we continue to “build on quicksand”. Safety critical systems involve the tight coupling between potentially conflicting control objectives and safety constraints. As a means of creating a formal framework for controlling systems of this form, and with a view toward automotive applications, this paper develops a methodology that allows safety conditions—expressed as control barrier functions —to be unified with performance objectives—expressed as control Lyapunov functions—in the context of real-time optimization-based controllers. Safety conditions are specified in terms of forward invariance of a set, and are verified via two novel generalizations of barrier functions; in each case, the existence of a barrier function satisfying Lyapunov-like conditions implies forward invariance of the set, and the relationship between these two classes of barrier functions is characterized. In addition, each of these formulations yields a notion of control barrier function (CBF), providing inequality constraints in the control input that, when satisfied, again imply forward invariance of the set. Through these constructions, CBFs can naturally be unified with control Lyapunov functions (CLFs) in the context of a quadratic program (QP); this allows for the achievement of control objectives (represented by CLFs) subject to conditions on the admissible states of the system (represented by CBFs). The mediation of safety and performance through a QP is demonstrated on adaptive cruise control and lane keeping, two automotive control problems that present both safety and performance considerations coupled with actuator bounds. Nonlinear dynamical systems have been used in many disciplines to model complex behaviors, including biological motor control, robotics, perception, economics, traffic prediction, and neuroscience. While often the unexpected emergent behavior of nonlinear systems is the focus of investigations, it is of equal importance to create goal-directed behavior e.g., stable locomotion from a system of coupled oscillators under perceptual guidance. Modeling goal-directed behavior with nonlinear systems is, however, rather difficult due to the parameter sensitivity of these systems, their complex phase transitions in response to subtle parameter changes, and the difficulty of analyzing and predicting their long-term behavior; intuition and time-consuming parameter tuning play a major role. This letter presents and reviews dynamical movement primitives, a line of research for modeling attractor behaviors of autonomous nonlinear dynamical systems with the help of statistical learning techniques. The essence of our approach is to start with a simple dynamical system, such as a set of linear differential equations, and transform those into a weakly nonlinear system with prescribed attractor dynamics by means of a learnable autonomous forcing term. Both point attractors and limit cycle attractors of almost arbitrary complexity can be generated. We explain the design principle of our approach and evaluate its properties in several example applications in motor control and robotics. Maintenance tends to degrade the structure of software, ultimately making maintenance more costly. At times, then, it is worthwhile to manipulate the structure of a system to make changes easier. However, it is shown that manual restructuring is an error-prone and expensive activity. By separating structural manipulations from other maintenance activities, the semantics of a system can be held constant by a tool, assuring that no errors are introduced by restructuring. To allow the maintenance team to focus on the aspects of restructuring and maintenance requiring human judgment, a transformation-based tool can be provided--based on a model that exploits preserving data flow-dependence and control flow-dependence--to automate the repetitive, error-prone, and computationally demanding aspects of restructuring. A set of automatable transformations is introduced; their impact on structure is described, and their usefulness is demonstrated in examples. A model to aid building meaning-preserving restructuring transformations is described, and its realization in a functioning prototype tool for restructuring Scheme programs is discussed. This book is downloadable from http: www.irisa.fr sisthem kniga . Many monitoring problems can be stated as the problem of detecting a change in the parameters of a static or dynamic stochastic system. The main goal of this book is to describe a unified framework for the design and the performance analysis of the algorithms for solving these change detection problems. Also the book contains the key mathematical background necessary for this purpose. Finally links with the analytical redundancy approach to fault detection in linear systems are established. We call abrupt change any change in the parameters of the system that occurs either instantaneously or at least very fast with respect to the sampling period of the measurements. Abrupt changes by no means refer to changes with large magnitude; on the contrary, in most applications the main problem is to detect small changes. Moreover, in some applications, the early warning of small - and not necessarily fast - changes is of crucial interest in order to avoid the economic or even catastrophic consequences that can result from an accumulation of such small changes. For example, small faults arising in the sensors of a navigation system can result, through the underlying integration, in serious errors in the estimated position of the plane. Another example is the early warning of small deviations from the normal operating conditions of an industrial process. The early detection of slight changes in the state of the process allows to plan in a more adequate manner the periods during which the process should be inspected and possibly repaired, and thus to reduce the exploitation costs. Massachusetts Institute of Technology and the University of Washington Reactive point processes (RPPs) are a new statistical model designed for predicting discrete events in time, based on past history. RPPs were developed to handle an important problem within the domain of electrical grid reliability: short term prediction of electrical grid failures (“manhole events”), including outages, fires, explosions, and smoking manholes, which can cause threats to public safety and reliability of electrical service in cities. RPPs incorporate self-exciting, self-regulating, and saturating components. The self-excitement occurs as a result of a past event, which causes a temporary rise in vulnerability to future events. The self-regulation occurs as a result of an external inspection which temporarily lowers vulnerability to future events. RPPs can saturate when too many events or inspections occur close together, which ensures that the probability of an event stays within a realistic range. Two of the operational challenges for power companies are i) making continuous-time failure predictions, and ii) cost benefit analysis for decision making and proactive maintenance. RPPs are naturally suited for handling both of these challenges. We use the model to predict power-grid failures in Manhattan over a short term horizon, and use to provide a cost benefit analysis of different proactive maintenance programs. A source submits status updates to a service facility for delivery to a monitor. Each update requires energy and the source is powered by a stochastic energy harvesting system. With knowledge of the service facility state, the source avoids queue-induced delays by submitting a fresh update only after the service completion of a prior update. For a source with a large battery, we evaluate updating policies using a status age timeliness metric. We show that an optimal policy is lazy; following a service completion, the service facility is frequently left idle even though the server may have sufficient energy to submit an update. We give logical characterizations of bisimulation relations for the probabilistic automata of Segala in terms of three Hennessy-Milner style logics. The three logics characterize strong, strong probabilistic and weak probabilistic bisimulation, and differ only in the kind of diamond operator used. Compared to the Larsen and Skou logic for reactive systems, these logics introduce a new operator that measures the probability of the set of states that satisfy a formula. Moreover, the satisfaction relation is defined on measures rather than single states. We rederive previous results of by defining sublogics for Reactive and Alternating Models viewed as restrictions of probabilistic automata. Finally, we identify restrictions on probabilistic automata, weaker than those imposed by the Alternating Models, that preserve the logical characterization of These restrictions require that each state either enables several ordinary transitions or enables a single probabilistic transition. People speak at different levels of specificity in different situations. Depending on their knowledge, interlocutors, mood, etc. A conversational agent should have this ability and know when to be specific and when to be general. We propose an approach that gives a neural network--based conversational agent this ability. Our approach involves alternating between and model training : removing training examples that are closest to the responses most commonly produced by the model trained from the last round and then retrain the model on the remaining dataset. Dialogue generation models trained with different degrees of data distillation manifest different levels of specificity. We then train a reinforcement learning system for selecting among this pool of generation models, to choose the best level of specificity for a given input. Compared to the original generative model trained without distillation, the proposed system is capable of generating more interesting and higher-quality responses, in addition to appropriately adjusting specificity depending on the context. Our research constitutes a specific case of a broader approach involving training multiple subsystems from a single dataset distinguished by differences in a specific property one wishes to model. We show that from such a set of subsystems, one can use reinforcement learning to build a system that tailors its output to different input contexts at test time. Functional Reactive Programming , or FRP , is a general framework for programming hybrid systems in a high-level, declarative manner. The key ideas in FRP are its notions of behaviors and events . Behaviors are time-varying, reactive values, while events are time-ordered sequences of discrete-time event occurrences. FRP is the essence of Fran , a domain-specific language embedded in Haskell for programming reactive animations, but FRP is now also being used in vision, robotics and other control systems applications. In this paper we explore the formal semantics of FRP and how itrelates to an implementation based on streams that represent (and therefore only approximate) continuous behaviors. We show that, in the limit as the sampling interval goes to zero, the implementation is faithful to the formal, continuous semantics, but only when certain constraints on behaviors are observed. We explore the nature of these constraints, which vary amongst the FRP primitives. Our results show both the power and limitations of this approach to language design and implementation. As an example of a limitation, we show that streams are incapable of representing instantaneous predicate events over behaviors. In this thesis we present a technique for the composition of robot control laws in dynamical environments. We propose a challenging robotic task, called Dynamical Pick and Place, in which a robot equipped with merely a soft paddle must capture and contain a ball, safely negotiate it past obstacles, and bring it to rest at a desired location. We develop a composition technique for local controllers that provides a formal guarantee of the stability of the switching behavior required in this task, and provide descriptive statistics of a working implementation. Our robotic system displays unusually dexterous behavior in the face of significant system noise, and recovers gracefully from large unexpected perturbations caused by the experimenters. Our approach to controller composition makes use of the funnel as a metaphor for asymptotic stability, is motivated by the pre-image backchaining techniques developed by Lozano-Perez, Mason and Taylor, and extends their ideas from quasi-static environments to systems with full dynamics. We introduce the concepts of "dynamical obstacle avoidance" and "dynamical safety" for systems with only intermittent control of their environment, and show that it is important not only that the system avoid obstacles directly, but also that the system will never reach an obstacle before getting another chance to effect control. The Dynamical Pick and Place problem addressed by this thesis is a difficult control problem, but an easy planning problem. The system we develop provides a way to engage more powerful AI planning tools without sacrificing access to the stability arguments of dynamical systems theory. We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important in modeling and understanding many applications, including embedded systems and cyber-physical systems. In discrete dynamical systems, the state evolves in discrete steps, one step at a time, as described by a difference equation or discrete state transition relation. In continuous dynamical systems, the state evolves continuously along a function, typically described by a differential equation. Hybrid dynamical systems or hybrid systems combine both discrete and continuous dynamics. This is a brief survey of differential dynamic logic for specifying and verifying properties of hybrid systems. We explain hybrid system models, differential dynamic logic, its semantics, and its axiomatization for proving logical formulas about hybrid systems. We study differential invariants, i.e., induction principles for differential equations. We briefly survey theoretical results, including soundness and completeness and deductive power. Differential dynamic logic has been implemented in automatic and interactive theorem provers and has been used successfully to verify safety-critical applications in automotive, aviation, railway, robotics, and analogue electrical circuits. To sustain perpetual operation, systems that harvest environmental energy must carefully regulate their usage to satisfy their demand. Regulating energy usage is challenging if a system's demands are not elastic and its hardware components are not energy-proportional, since it cannot precisely scale its usage to match its supply. Instead, the system must choose when to satisfy its energy demands based on its current energy reserves and predictions of its future energy supply. In this paper, we explore the use of weather forecasts to improve a system's ability to satisfy demand by improving its predictions. We analyze weather forecast, observational, and energy harvesting data to formulate a model that translates a weather forecast to a wind or solar energy harvesting prediction, and quantify its accuracy. We evaluate our model for both energy sources in the context of two different energy harvesting sensor systems with inelastic demands: a sensor testbed that leases sensors to external users and a lexicographically fair sensor network that maintains steady node sensing rates. We show that using weather forecasts in both wind- and solar-powered sensor systems increases each system's ability to satisfy its demands compared with existing prediction strategies.