This article introduces a nonlinear ordinary differential equation model of mood dynamics for disorders on the bipolar spectrum. Motivated by biopsychosocial findings, the model characterizes mood as a 2-D state corresponding to manic and depressive features, enabling the representation of most diagnoses of bipolar and depressive disorders. We perform a mathematical analysis of conditions for the mood to stabilize to euthymia and discuss its psychotherapeutic implications. Furthermore, a computational analysis applied to pharmacotherapy depicts a mechanism that results in a switch from depression to mania when the bipolar disorder was misdiagnosed as major depressive disorder, and an antidepressant is administered without a mood stabilizer. This work innovates by offering a concise representation of most features of mood disorders in existing mathematical models, providing a framework for studying dynamics in the bipolar spectrum.

This paper employs control-theoretic tools to provide guidelines for in-situ interventions aimed at reducing high-risk alcohol consumption at drinking events. A dynamical directed network model of a drinking event with external intervention, suitable for mathematical analysis and parameter estimation using field data is proposed, with insights from pharmacokinetics and psychology. Later, a characterization of a bound on blood alcohol content (BAC) trajectories is obtained via Lyapunov stability analysis, and structural controllability guarantees are obtained via a graph-theoretic method. We use the degree of controllability, given to be the trace of the system's controllability Gramian, as a metric to compare the viability of network nodes for intervention based on theoretic and heuristic centrality measures. Results of numerical examples of bars and parties, informed by field data, and the stability and controllability results, suggest that intervening in the environment in wet bars, while targeting influential individuals with high alcohol consumption motivations in private parties efficiently yield lower peak BAC levels in individuals at the drinking events.

High-risk drinking is considered a major concern in public health, being the third leading preventable cause of death in the United States. Several studies have been conducted to understand the etiology of high-risk drinking and to design prevention strategies to reduce unhealthy alcohol-consumption and related problems, but there are still major gaps in identifying and investigating the key components that affect the consumption patterns during the drinking event. There is a need to develop tools for the design of methodologies to not only identify such dangerous patterns but also to determine how their dynamics impact the event. In this paper, based on current empirical evidence and observations of drinking events, we model a human group that is in an alcohol-consumption scenario as a dynamical system whose behavior is driven by the interplay between the environment, the network of interactions between the individuals, and their personal motivations and characteristics. We show how this mathematical model complements empirical research in this area by allowing us to analyze, simulate, and predict the drinking group behaviors, to improve the methodologies for field data collection, and to design interventions. Through simulations and Lyapunov stability theory, we provide a computational and mathematical analysis of the impact of the model parameters on the predicted dynamics of the drinking group at the drinking event level. Also, we show how the dynamical model can be informed using data collected in situ and to generate information that can complement the analysis.

Heavy alcohol consumption is considered an important public health issue in the United States as over 88 000 people die every year from alcohol-related causes. Research is being conducted to understand the etiology of alcohol consumption and to develop strategies to decrease high-risk consumption and its consequences, but there are still important gaps in determining the main factors that influence the consumption behaviors throughout the drinking event. There is a need for methodologies that allow us not only to identify such factors but also to have a comprehensive understanding of how they are connected and how they affect the dynamical evolution of a drinking event. In this paper, we use previous empirical findings from laboratory and field studies to build a mathematical model of the blood alcohol concentration dynamics in individuals that are in drinking events. We characterize these dynamics as the result of the interaction between a decision-making system and the metabolic process for alcohol. We provide a model of the metabolic process for arbitrary alcohol intake patterns and a characterization of the mechanisms that drive the decision-making process of a drinker during the drinking event. We use computational simulations and Lyapunov stability theory to analyze the effects of the parameters of the model on the blood alcohol concentration dynamics that are characterized. Also, we propose a methodology to inform the model using data collected in situ and to make estimations that provide additional information to the analysis. We show how this model allows us to analyze and predict previously observed behaviors, to design new approaches for the collection of data that improves the construction of the model, and help with the design of interventions.

In the study of the behavior of human groups, it has been observed that there is a strong interaction between the cohesiveness of the group, its performance when the group has to solve a task, and the patterns of communication between the members of the group. Developing mathematical and computational tools for the analysis and design of task-solving groups that are not only cohesive but also perform well is of importance in social sciences, organizational management, and engineering. In this paper, we model a human group as a dynamical system whose behavior is driven by a task optimization process and the interaction between subsystems that represent the members of the group interconnected according to a given communication network. These interactions are described as attractions and repulsions among members. We show that the dynamics characterized by the proposed mathematical model are qualitatively consistent with those observed in real-human groups, where the key aspect is that the attraction patterns in the group and the commitment to solve the task are not static but change over time. Through a theoretical analysis of the system we provide conditions on the parameters that allow the group to have cohesive behaviors, and Monte Carlo simulations are used to study group dynamics for different sets of parameters, communication topologies, and tasks to solve.

This paper introduces a novel framework for the design of distributed agents that must complete externally generated tasks but also can volunteer to process tasks encountered by other agents. To reduce the computational and communication burden of coordination between agents to perfectly balance load around the network, the agents adjust their volunteering propensity asynchronously within a fictitious trading economy. This economy provides incentives for nontrivial levels of volunteering for remote tasks, and thus load is shared. Moreover, the combined effects of diminishing marginal returns and network topology lead to competitive equilibria that have task reallocations that are qualitatively similar to what is expected in a load-balancing system with explicit coordination between nodes. In the paper, topological and algorithmic conditions are given that ensure the existence and uniqueness of a competitive equilibrium. Additionally, a decentralized distributed gradient-ascent algorithm is given that is guaranteed to converge to this equilibrium while not causing any node to over-volunteer beyond its maximum task-processing rate. The framework is applied to an autonomous-air-vehicle example, and connections are drawn to classic studies of the evolution of cooperation in nature.

An analogy between an agent (e.g., an autonomous vehicle) and a biological forager is extended to a social environment by viewing a communication network as implementing interagent sociality. We first describe engineering design within an evolutionary game-theoretic framework. We then explain why sociality may emerge in some environments and for some agent objectives. Next, we derive the evolutionarily stable design strategy for an agent manufacturer: 1) choosing whether the agent it produces should cooperate with other agents in a search problem and 2) choosing the group size of a multiagent system tasked with a cooperative search problem. We show the impact of "agent relatedness," a measure of common descent between two agents based on their underlying manufacturers, on the choices in scenarios 1) and 2). Our predictions are evaluated in an autonomous vehicle simulation testbed. The results illustrate a new methodology for manufacturers to make robust, optimal choices for multiagent system design for a given set of objectives and domain of operation. Note to Practitioners-The design of autonomous multirobot systems with various applications, such as in parts production or search and destroy operations in a military environment, is of growing importance. Here, we integrate economic and technical issues into an unified engineering design framework for the manufacturers of robots. Our approach leads to manufacturer design decisions that are robust relative to the market for a manufacturer's products. Robot component aspects, such as sensors and communications as well as mission performance aspects, can be captured and coupled into the design process. We use the design of intervehicle cooperation and robot group size to illustrate this approach. The practical significance lies in the fact that we take a broad perspective on engineering design, one closer to the real world, due to the considerations of marketplace economics. Moreover, the approach provides a framework to study design choices that escape systematic analysis in other frameworks (e.g., group size)

We extend the theory of the "ideal free distribution" (IFD) from theoretical ecology by providing methods to analytically find the distribution for a relatively general class of "suitability" functions. We show that the resulting IFD is a Nash equilibrium and an evolutionarily stable strategy (ESS). Moreover, we show that for a certain cost function it is a global optimum point. We introduce the "replicator dynamics" for the IFD and show that we provide an allocation strategy that is guaranteed to achieve the IFD. Finally, we show how this allocation strategy can achieve an IFD for a multizone temperature control problem that corresponds to achieving the maximum uniform temperature on a grid under a multivariable saturation constraint.

This paper presents implementation results using recently introduced discrete-time adaptive prediction and control techniques using online function approximators. We consider a process control experiment as our test bed, and develop a discrete-time adaptive predictor for liquid volume and a discrete-time adaptive controller for reference volume tracking. We use Takagi-Sugeno (TS) fuzzy systems as our function approximators, and for both prediction and control we investigate the use of a least-squares update of the fuzzy system's parameters

In this correspondence, we consider a discrete time one-dimensional asynchronous swarm. First, we describe the mathematical model for motions of the swarm members. Then, we analyze the stability properties of that model. The stability concept that we consider, which matches exactly with stability of equilibria in control theory, characterizes stability of a particular position (relative arrangement) of the swarm members. We call that position the comfortable position (with comfortable intermember distances). Our swarm model and stability analysis are different from other asynchronous swarm models considered in the literature. In particular, in our analysis we employ results on contractive mappings from the parallel and distributed computation literature. The application of these results to the swarm coordination problem is important by itself since they might prove useful also in n-dimensional swarms.

In direct adaptive control, the adaptation mechanism attempts to adjust a parameterized nonlinear controller to approximate an ideal controller. In the indirect case, however, we approximate parts of the plant dynamics that are used by a feedback controller to cancel the system nonlinearities. In both cases, "approximators" such as linear mappings, polynomials, fuzzy systems, or neural networks can be used as either the parameterized nonlinear controller or identifier model. In this paper, we present algorithms to tune some of the parameters (e.g., the adaptation gain and the direction of descent) for a gradient-based approximator parameter update law used for a class of nonlinear discrete-time systems in both direct and indirect cases. In our proposed algorithms, the adaptation gain and the direction of descent are obtained by minimizing the instantaneous control energy. We will show that updating the adaptation gain can be viewed as a special case of updating the direction of descent. We will also compare the direct and indirect adaptive control schemes and illustrate their performance via a simple surge tank example.

In this article we specify an M-member "individual-based" continuous time swarm model with individuals that move in an n-dimensional space according to an attractant/repellent or a nutrient profile. The motion of each individual is determined by three factors: i) attraction to the other individuals on long distances; ii) repulsion from the other individuals on short distances; and iii) attraction to the more favorable regions (or repulsion from the unfavorable regions) of the attractant/repellent profile. The emergent behavior of the swarm motion is the result of a balance between inter-individual interactions and the simultaneous interactions of the swarm members with their environment. We study the stability properties of the collective behavior of the swarm for different profiles and provide conditions for collective convergence to more favorable regions of the profile.

Adaptive control for nonlinear time-varying systems is of both theoretical and practical importance. We propose an adaptive control methodology for a class of nonlinear systems with a time-varying structure. This class of systems is composed of interpolations of nonlinear subsystems which are input-output feedback linearizable. Both indirect and direct adaptive control methods are developed, where the spatially localized models (in the form of Takagi-Sugeno fuzzy systems or radial basis function neural networks) are used as online approximators to learn the unknown dynamics of the system. Without assumptions on rate of change of system dynamics, the proposed adaptive control methods guarantee that all internal signals of the system are bounded and the tracking error is asymptotically stable. The performance of the adaptive controller is demonstrated using a jet engine control problem.

For standard fuzzy systems where the input membership functions are defined on a grid on the input space, and all possible combinations of rules are used, there is an exponential growth in the number of parameters of the fuzzy system as the number of input dimensions increases. This "curse of dimensionality" effect leads to problems with design of fuzzy controllers (e.g., how to tune all these parameters), training of fuzzy estimators (e.g., complexity of a gradient algorithm for training, and problems with "over parameterization" that lead to poor convergence properties), and with computational complexity in the implementation for practical problems. We introduce a fuzzy system whose number of parameters grows linearly depending upon the number of inputs, even though it is constructed by using all possible combinations of the membership functions in defining the rules. We prove that this fuzzy system is equivalent to the standard fuzzy system as long as its parameters are specified in a certain way. Then, we show that it still holds the universal approximator property by using the Stone-Welerstrass theorem. Finally, we illustrate the performance of the fuzzy system via an application.

In this letter, stable direct and indirect adaptive controllers are presented that use Takagi-Sugeno (T-S) fuzzy systems (1985), conventional fuzzy systems, or a class of neural networks to provide asymptotic tracking of a reference signal vector for a class of continuous time multi-input multi-output (MIMO) square nonlinear plants with poorly understood dynamics. The direct adaptive scheme allows for the inclusion of a priori knowledge about the control input in terms of exact mathematical equations or linguistics, while the indirect adaptive controller permits the explicit use of equations to represent portions of the plant dynamics. We prove that with or without such knowledge the adaptive schemes can "learn" how to control the plant, provide for bounded internal signals, and achieve asymptotically stable tracking of the reference inputs. We do not impose any initialization conditions on the controllers and guarantee convergence of the tracking error to zero.

Advances in nonlinear control theory have provided the mathematical foundations necessary to establish conditions for stability of several types of adaptive fuzzy controllers. However, very few, if any, of these techniques have been compared to conventional adaptive or nonadaptive nonlinear controllers or tested beyond simulation; therefore, many of them remain as purely theoretical developments whose practical value is difficult to ascertain. In this paper we develop three case studies where we perform a comparative analysis between the adaptive fuzzy techniques in Spooner and Passino (1995,1996) and some conventional adaptive and nonadaptive nonlinear control techniques. In each case, the analysis is performed both in simulation and in implementation, in order to show practical examples of how the performance of these controllers compares to conventional controllers in real systems.

Stable direct and indirect adaptive controllers are presented, which use Takagi-Sugeno fuzzy systems, conventional fuzzy systems, or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous-time nonlinear plants with poorly understood dynamics. The indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller. We prove that with or without such knowledge both adaptive schemes can "learn" how to control the plant, provide for bounded internal signals, and achieve asymptotically stable tracking of a reference input. In addition, for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation. The performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane.

A "learning system" possesses the capability to improve its performance over time by interacting with its environment. A learning control system is designed so that its "learning controller" has the ability to improve the performance of the closed-loop system by generating command inputs to the plant and utilizing feedback information from the plant. Learning controllers are often designed to mimic the manner in which a human in the control loop would learn how to control a system while it operates. Some characteristics of this human learning process may include: (i) a natural tendency for the human to focus their learning by paying particular attention to the current operating conditions of the system since these may be most relevant to determining how to enhance performance; (ii) after learning how to control the plant for some operating condition, if the operating conditions change, then the best way to control the system may have to be re-learned; and (iii) a human with a significant amount of experience at controlling the system in one operating region should not forget this experience if the operating condition changes. To mimic these types of human learning behavior, we introduce three strategies that can be used to dynamically focus a learning controller onto the current operating region of the system. We show how the subsequent "dynamically focused learning" (DFL) can be used to enhance the performance of the "fuzzy model reference learning controller" (FMRLC) and furthermore we perform comparative analysis with a conventional adaptive control technique. A magnetic ball suspension system is used throughout the paper to perform the comparative analyses, and to illustrate the concept of dynamically focused fuzzy learning control.

In this paper, we begin by showing that the fuzzy model reference learning controller (FMRLC) can be used to reconfigure the nominal controller in an F-16 aircraft to compensate for various actuator failures without using explicit failure information. Next, we show that the performance of the FMRLC can be significantly enhanced by exploiting failure detection and identification (FDI) information to achieve a "performance adaptive" system that seeks an appropriate performance level depending on the type of failure that occurred. We develop an expert supervision strategy for the FMRLC that uses only information about the time at which a failure occurs and show that it achieves higher performance control reconfiguration than an unsupervised FMRLC. In addition we show that similar performance can be achieved if we only use estimates of the failure time and magnitude obtained from a fuzzy estimator. We close our study with a brief assessment of the advantages and disadvantages of the approaches used in this paper.>

There are two main drawbacks in fuzzy control: 1) the design of fuzzy controllers is usually performed in an ad hoc manner where it is often difficult to choose some of the controller parameters; and 2) the fuzzy controller constructed for the nominal plant may later perform inadequately if significant and unpredictable plant parameter variations occur. In this paper we illustrate these two problems on a two-link flexible robot testbed by: 1) developing, implementing, and evaluating a fuzzy controller for the robotic mechanism, and 2) illustrating that payload variations can have negative effects on the performance of a well designed fuzzy control system. Next, we show how to develop and implement a fuzzy model reference learning controller for the flexible robot and illustrate that it can automatically synthesize a rule-base for a fuzzy controller that will achieve comparable performance to the case where it was manually constructed, and automatically tune the fuzzy controller so that it can adapt to variations in the payload.>

This investigation focuses on the design and implementation of rule-based controllers for end point position control of a two-degree-of-freedom robot with very flexible links. We begin by showing how our intuitive understanding of how to control the robot, that was gained over several years of experience, can be used in the construction of a direct fuzzy controller Next, we investigate the use of a two-level hierarchical rule-based controller with a simple upper-level "expert controller" that captures our knowledge about how to supervise the application of lower-level fuzzy controllers during movements in the robot workspace. Overall, the rule-based supervisory control results have proven to be extremely effective for vibration suppression in the laboratory test bed of this study comparing favorably (in terms of performance, design complexity, and implementation issues) to a variety of conventional techniques attempted to date.>

In this paper we show that two ellipsoid algorithms can be used to train single-layer neural networks with general staircase nonlinearities. The ellipsoid algorithms have several advantages over other conventional training approaches including (1) explicit convergence results and automatic determination of linear separability, (2) an elimination of problems with picking initial values for the weights, (3) guarantees that the trained weights are in some “acceptable region,” (4) certain “robustness” characteristics, and (5) a training approach for neural networks with a wider variety of activation functions. We illustrate the training approach by training the MAJ function and then by showing how to train a controller for a reaction chamber temperature control problem.

Given a graph with arcs that have costs, the A* algorithm is designed to find the shortest path from a single node to a set of nodes. While the A* algorithm is well understood, it is somewhat limited in its application due to the fact that it is often difficult to specify the "heuristic function" so that A* exhibits desirable computational properties. In this paper a metric space approach to the specification of the heuristic function is introduced. It is shown how to specify an admissible and monotone heuristic function for a wide class of problem domains. In addition, when the cost structure for the underlying graph is specified via a metric, it is shown that admissible and monotone heuristic functions are easy to specify and further computational advantages can be obtained. Applications to an optimal parts distribution problem in flexible manufacturing systems and artificial intelligence planning problems are provided.>

In rule-based artificial intelligence (AI) planning, expert, and learning systems, it is often the case that the left-hand-sides of the rules must be repeatedly compared to the contents of some working memory. Normally, the intent is to determine which rules are relevant to the current situation (i.e., to find the conflict set). A technique using a multilayer perceptron to solve the match phase problem for rule-based AI systems is presented. A syntax for premise formulas (i.e., the left-hand-sides of the rules) is defined, and working memory is specified. From this, it is shown how to construct a multilayer perceptron that finds all of the rules which can be executed for the current situation in working memory. The complexity of the constructed multilayer perceptron is derived in terms of the maximum number of nodes and the required number of layers. A method for reducing the number of layers to at most three is presented.>