Hogg and Huberman have proposed a strategy for stabilizing chaotic multi-agent systems. This paper applies their strategy to a resource allocation problem in a manufacturing system consisting of two machines and two types of parts. These part-types conflict each other over resource allocation. We introduce a discrete-time model of the system by using game theory, and examine stability and bifurcation phenomena of its fixed point. We show by computer simulation that chaotic behaviors are observed after successive occurrence of period-doubling bifurcations. It is also shown that the optimal state of the system is stabilized by a reward mechanism.

This paper considers a motion planning method for humanoid robots. First, we review a modular state net which is a state net representing behavior of a part of the humanoid robots. Each whole body motion of the humanoid robots is represented by a combination of modular state nets for those parts. In order to obtain a feasible path of the whole body, a timed Petri net is used as an abstracted model of a set of all modular state nets. Next, we show an algorithm for constructing nonlinear dynamics which describes a periodic motion. Finally, we extend the state net in order to represent primitive periodic motions and their transition relation so that we can generate a sequence of primitive periodic motions satisfying a specified task.

In this paper, we propose a formal method for detection of three automation surprises in human-machine interaction; a mode confusion, a refusal state, and a blocking state. The mode confusion arises when a machine is in a different mode from that anticipated by the user, and is the most famous automation surprise. The refusal state is a situation that the machine does not respond to a command the user executes. The blocking state is a situation where an internal event occurs, leading to change of an interface the user does not know. In order to detect these phenomena, we propose a composite model in which a machine and a user model evolve concurrently. We show that the detection of these phenomena in human-machine interaction can be reduced to a reachability problem in the composite model.

In a population which consists of a large number of players interacting with each other, the payoff of each player often conflicts with the total payoff of the population which he/she belongs to. In such a situation, a "government" which has the comprehensive perspective is needed to govern the population. Recently, to discuss the population with the government, the authors have proposed replicator dynamics with reallocation of payoffs to analyze an effect of the government. In this model, the government is willing to lead the population to a desirable target state by collecting a part of players' payoffs and reallocating them depending on the target state. The government's action is the rate of collecting payoffs from players and the rate is assumed to be constant and independent of the population state. Thus, in this paper, we suppose that the government change their intervention strategy depending on the current population state. We consider the government as a game player and define the government's payoff as a sum of a benefit and a cost of intervention. We propose a model which describes the evolution of the government's reallocation strategy and investigate stability of its equilibrium points.

A consensus problem has been studied in many fundamental and application fields to analyze coordinated behavior in multi-agent systems. In a consensus problem, it is usually assumed that a state of each agent is scalar and all agents have an identical linear consensus protocol. We present a consensus problem of multi-agent systems where each agent has multiple state variables and a performance value evaluated by a nonlinear performance function according to its current state. We derive sufficient conditions for agents to achieve consensus on the performance value using an algebraic graph theory and the mean value theorem. We also consider an application of a performance consensus problem to resource allocation in soft real-time systems so as to achieve a fair QoS (Quality of Service) level.

This paper analyzes automation surprises in human-machine systems with time information. Automation surprises are phenomena such that the underlying machine's behavior diverges from user's intention and may lead to critical situations. Thus, designing human-machine systems without automation surprises is one of fundamental issues to achieve reliable user interaction with the machines. In this paper, we focus on timed human-machine interaction and address their formal aspects. The presented framework is essentially an extension of untimed human-machine interaction and will cover the previously proposed methodologies. We employ timed automata as a model of human-machine systems with time information. Modeling the human-machine systems as timed automata enables one to deal with not only discrete behavior but also time constraints. Then, by introducing the concept of timed simulation of the machine model and the user model, conditions which guarantee the nonexistence of automation surprises are derived. Finally, we construct a composite model in which a machine model and a user model evolve concurrently and show that automation surprises can be detected by solving a reachability problem in the composite model.

This paper studies stabilization of timed discrete event systems with forcible events. We present an algorithm for computing the region of weak attraction for legal states.

A composite system consists of many subsystems, which have interconnections with other subsystems. For such a system, in general, we utilize decentralized control, where each subsystem is controlled by a local controller. On the other hand, event-triggered control is one of useful approaches to reduce the amount of communications between a controller and a plant. In the event-triggered control, an event triggering mechanism (ETM) monitors the information of the plant, and determines the time to transmit the data. In this paper, we propose a design of ETMs for the decentralized event-triggered control of nonlinear composite systems using an M-matrix. We consider the composite system where there is an ETM for each subsystem, and ETMs monitor local states of the corresponding subsystems. Each ETM is designed so that the composite system is stabilized. Moreover, we deal with the case of linear systems. Finally, we perform simulation to show that the proposed triggering rules are useful for decentralized control.

The Smith method has been used to control physical plants with dead time components, where plant states after the dead time is elapsed are predicted and a control input is determined based on the predicted states. We extend the method to the symbolic control and design a symbolic Smith controller to deal with a nondeterministic embedded system. Due to the nondeterministic transitions, the proposed controller computes all reachable plant states after the dead time is elapsed and determines a control input that is suitable for all of them in terms of a given control specification. The essence of the Smith method is that the effects of the dead time are suppressed by the prediction, however, which is not always guaranteed for nondeterministic systems because there may exist no control input that is suitable for all predicted states. Thus, in this paper, we discuss the existence of a deadlock-free symbolic Smith controller. If it exists, it is guaranteed that the effects of the dead time can be suppressed and that the controller can always issue the control input for any reachable state of the plant. If it does not exist, it is proved that the deviation from the control specification is essentially inevitable.

This paper studies the supervisory control of partially observed quantitative discrete event systems (DESs) under the fixed-initial-credit energy objective. A quantitative DES is modeled by a weighted automaton whose event set is partitioned into a controllable event set and an uncontrollable event set. Partial observation is modeled by a mapping from each event and state of the DES to the corresponding masked event and masked state that are observed by a supervisor. The supervisor controls the DES by disabling or enabling any controllable event for the current state of the DES, based on the observed sequences of masked states and masked events. We model the control process as a two-player game played between the supervisor and the DES. The DES aims to execute the events so that its energy level drops below zero, while the supervisor aims to maintain the energy level above zero. We show that the proposed problem is reducible to finding a winning strategy in a turn-based reachability game.

In this paper, we present new stability conditions for a class of large-scale hybrid dynamical systems composed of a number of interconnected hybrid subsystems. The stability conditions are given in terms of discontinuous Lyapunov functions of the stable hybrid subsystems. Furthermore, the stability conditions are represented by LMIs (Linear Matrix Inequalities) which are computationally tractable.

The OGY method is one of control methods for a chaotic system. In the method, we have to calculate a target periodic orbit embedded in its chaotic attractor. Thus, we cannot use this method in the case where a precise mathematical model of the chaotic system cannot be identified. In this case, the delayed feedback control proposed by Pyragas is useful. However, even in the delayed feedback control, we need the mathematical model to determine a feedback gain that stabilizes the periodic orbit. Thus, we propose a reinforcement learning algorithm to the design of a controller for the chaotic system. Recently, reinforcement learning algorithms with deep neural networks have been paid much attention to. Those algorithms make it possible to control complex systems. We propose a controller design method consisting of two steps, where we determine a region including a target periodic point first, and make the controller learn an optimal control policy for its stabilization. The controller efficiently explores its control policy only in the region.

In this paper, we study decentralized supervisory control of discrete event systems where local disabling actions are fused by the OR rule. We generalize an on-line procedure for synthesizing decentralized supervisors proposed by Prosser. By using the generalized procedure, we can achieve a sublanguage of a specification which is not achieved by a class of decentralized supervisors synthesized by the Prosser's procedure.

Many controllers are implemented on digital platforms as periodic control tasks. But, in embedded systems, an amount of resources are limited and the reduction of resource utilization of the control task is an important issue. Recently, much attention has been paid to a self-triggered controller, which updates control inputs aperiodically. A control task by which the self-triggered controller is implemented skips the release of jobs if the degradation of control performances by the skipping can be allowed. Each job computes not only the updated control inputs but also the next update instant and the control task is in the sleep state until the instant. Thus the resource utilization is reduced. In this paper, we consider self-triggered predictive control (stPC) of mixed logical dynamical (MLD) systems. We introduce a binary variable which determines whether the control inputs are updated or not. Then, we formulate an stPC problem of mixed logical dynamical systems, where activation costs are time-dependent to represent the preference of activations of the control task. Both the control inputs and the next update instant are computed by solving a mixed integer programming problem. The proposed stPC can reduce the number of updates with guaranteeing stability of the controlled system.

In evolutionary game theory, to the best of our knowledge, individuals' perceptions have not been taken into consideration explicitly. When an individual interacts with the other individual under coexistence of heterogeneous sub-populations, the individual may be willing to change his/her strategy depending on the sub-population the other individual belongs to. Moreover, in such a situation, each individual may make an error about the sub-population the other individual belongs to. In this paper, we propose a multi-population model with such erroneous perceptions. We define an evolutionarily stable strategy (ESS) and formulate replicator dynamics in this model, and prove several properties of the proposed model. Moreover, we focus on a two-population chicken game with erroneous perceptions and discuss characteristics of equilibrium points of its replicator dynamics.

In this paper, we study supervisory control of a class of discrete event systems with simultaneous event occurrences, which we call concurrent discrete event systems. The behavior of the system is described by a language over the simultaneous event set. We introduce a notion of concurrent well-posedness of languages. We then prove that Lm(G)-closure, controllability, and concurrent well-posedness of a specification language are necessary and sufficient conditions for the existence of a nonblocking supervisor. We address the computational complexity for verifying the existence conditions.

We study state feedback control of discrete event systems described by the Golaszewski-Ramadge model. We derive a necessary and sufficient condition for the existence of a balanced state feedback controller under partial observations.

In this paper, we study nonblocking supervisory control of discrete event systems under partial observation. We introduce a weak normality condition defined in terms of a modified natural projection map. The weak normality condition is weaker than the original one and stronger than the observability condition. Moreover, it is preserved under union. Given a marked language specification, we present a procedure for computing the supremal sublanguage which satisfies Lm(G)-closure, controllability, and weak normality. There exists a nonblocking supervisor for this supremal sublanguage. Such a supervisor is more permissive than the one which achieves the supremal Lm(G)-closed, controllable, and normal sublanguage.