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This paper presents a bounded confidence gossip algorithm for describing the process of opinion formation over a communication network. Each agent in the network keeps a time-varying opinion vector (or state), which represents its opinion about a set of matters. A common confidence threshold is set for all of the agents. The states of agents in the network will be updated time by time according to an iterative procedure: At each time, 1) one agent is chosen randomly, then it chooses one of its neighbors on the communication graph to contact with; 2) they exchange their states; and 3) if they have different states and the distance between their states is strictly smaller than the confidence threshold, they update their states as the average of the two. This algorithm converges almost surely to some equilibrium point such that any two adjacent agents either have the same state or have distinct states whose distance is no less than the confidence threshold. This is called the constant confidence threshold algorithm. An increasing confidence threshold algorithm, which repeats the constant confidence threshold algorithm several times with increasing confidence threshold, is also proposed. The algorithm is also convergent almost surely to some equilibrium point. Applicability of the method to clustering problems is shown through numerical examples.

This paper presents a characterization of the algebraic connectivity of a multi-agent system (MAS) with hierarchical network structure having heterogeneous subsystems. The MAS is represented as an interconnected system of several kinds of multi-agent subsystems via a certain structure, where several vertices of each subsystem are connected to the structure, that is, to other subsystems. The algebraic connectivity of this MAS can be computed by using a corresponding MAS having homogeneous subsystems under a certain condition, which is investigated in this paper.

A distributed optimization for a multi-agent system connected by a directed unbalanced random network is considered. It is shown that a sequense of candidate solutions of the standard algorithm for distributed optimization converges to a Pareto optimal solution of a multi-objective optimization which is to minimize objective functions of agents in a mean square sense. This is illustrated through a numerical example.

An asynchronous gossip algorithm with a restart strategy is proposed to an approximated distributed minimax optimization in this paper. The restart strategy controls a step length of a subgradient method and resets a local clock under a certain criteria in the algorithm. The convergence property is analyzed for the algorithm with the restart strategy. Numerical examples illustrate that the proposed algorithm works well in various instances and high approximation ratios.

This study is concerned with the consensus problems of multi-agent systems with cooperative and antagonistic noisy interactions described by two-layered network. That is, each agent is simultaneously influenced by the force of attraction and repulsion between each neighboring agents in cooperative and antagonistic layers. A distributed algorithm for achieving the consensus in a probabilistic sense is proposed and its sufficient conditions are clarified. The conditions tell us rigorous stopping rules which enable us to know the number of iterations that achieves consensus within a prespecified accuracy and probability. Some applications of consensus problems with cooperative and antagonistic interactions are shown through numerical examples.

In the last 10 years, with the increase of renewable energies, great attention is devoted to operation and maintenance of wind turbines and wind farms, which are the fundamental objectives to be guaranteed by the design of control systems. This study proposes a trade-off approach between fatigue reduction and power extraction for wind farm scenarios. The focus of this approach is to reduce maintenance costs for fatigue loads. This issue is solved by an optimisation problem, in which the maximum fatigue load among the turbines in the wind farm is minimised, then pitch angle and tip-speed ratio are given as reference points for each turbine in the wind farm. Furthermore, the super-twisting sliding mode algorithm is used for the rotor speed control and it shows that the turbines work at the optimised operating points. Moreover, the sliding mode controller produces continuous torques and improves the wind turbine performance by enhancing energy capture and reducing dynamic loads. The effectiveness of the method is illustrated through simulations of two wind farm scenarios. The results obtained with the proposed approach are compared with the case when each turbine in the wind farm tracks the maximum power operating point.

This paper proposes a Boolean satisfiability (SAT)-based approach to the analysis of cascading failures in systems of interdependent networks. Typical examples of such systems are power systems, where a power transmission network and a SCADA (Supervisory Control And Data Acquisition) network are dependent on each other. The proposed approach reduces the problem of analyzing cascading failures to the SAT problem by constructing Boolean formulas that symbolically represent all possible failure scenarios under given conditions. This allows us to examine a numerous number of scenarios by means of fast modern SAT solvers. The results of experiments show that the proposed approach can deal with practical size systems, such as the IEEE 39 bus system, which ordinary approaches fail to handle.

A time averaging algorithm is proposed for load balancing in distributed power dispatch, where a multi-agent system technique is employed. Each agent is connected to each generator to be controlled, and the agents are linked by the information lines modeled by a directed graph. The objective of this distributed algorithm is to achieve an average load balancing of generators over time. The convergence analysis of the algorithm is provided, which reveals an explicit relation between the number of iterations and the closeness of the ideal balancing in terms of the characteristic values of the graph Laplacian. This result also gives a rigorous stopping rule for the time averaging algorithm. Numerical examples demonstrate preferable behaviors of the proposed algorithm.

This paper proposes a distributed multi-agent optimization protocol to minimize the average of objective functions of the agents in the network with satisfying equality and inequality constraints o...

Operation optimization of a wind farm with robust fatigue load minimization is considered. Since wind turbines are installed as a firm in a restricted area, their interferences cause their mechanical fatigue loads. Thus their maintenance cost can be managed via fatigue load reduction. In this paper, this issue is solved by an optimization problem which minimizes the maximum fatigue load among turbines and gives reference points of pitch angle and tip speed ratio for each turbine. Furthermore, a super-twisting sliding mode controller for each wind turbine is proposed, which is robust to uncertainties of turbine and generator, as well as to electric grid disturbances. The sliding mode controller designs a continuous torque and improves the wind turbine performance by enhancing energy capture and reducing dynamic loads. Then the controller realizes operation on the reference points of each wind turbine. The effectiveness of the method is illustrated through a numerical example.

An uncertain cooperative game with transferable utilities is considered, where payoffs of coalitions are random variables. An iterative algorithm based on stochastic approximation is proposed for finding an element of the core of this game. An explicit relationship between the number of iterations and accuracy of a candidate of the element is also established. The result is demonstrated through numerical examples.

In this paper, model order reduction is considered for externally positive systems. Since to verify external positivity of a given transfer function is NP-hard, an externally finitely positive system is introduced as an extension of an externally positive system. It is shown that the externally finitely positive system is useful for model order reduction of externally positive systems, where the q-Markov COVER theory is employed.

In this paper, efficient inventory management is addressed. The considered system has multiple suppliers with lead-time, and the order rate to each supplier is time-varying. Also, the demand is unknown and time-varying. Then the optimal regulator theory is employed. The derived rule of order quantity reduces the deviation from the target stock level and the order cost.

Stabilizable dilated linear matrix inequality (LMI) conditions are derived for discrete-time structured feedback controller design. Since the number of decision variables in the dilated LMIs is larger than that in the standard LMIs, the LMI problem via stabilizable dilation could be feasible even if the standard LMI conditions is infeasible. This result is demonstrated thorough a numerical example.

This paper presents a method for finding the algebraic connectivity of multi-agent systems with homogeneous substructure. The systems consist of several homogeneous substructure where only one vertex is connected with main structure. Their algebraic connectivity can be calculated from properties of graphs corresponding to substructure and main structure. Also, it is shown that the algebraic connectivity of an entire system is less than or equals to that of substructure and that of main structure.

This paper presents a data-driven algorithm for tracking control of a linear discrete-time plant. No traditional mathematical model of the plant such as transfer function or state equation is employed. Instead, the plant dynamics is represented by an array whose elements are plant input-output data. Sensitivity of the array to input and output noise is introduced. Then, it is shown that, for an arbitrary reference signal, the tracking control input which minimizes the sensitivity can readily be computed by solving a linear matrix inequality which is composed of the array.

The objectives of secondary cooling zone control in continuous casting are (i) to achieve a suitable profile of strand temperature for a given casting speed and (ii) to suppress its deviation when casting speed changes due to a temporal operation. This paper presents a simulator based design of the cooling zone control which employs both static and dynamic compensators. A simulator of continuous casting process is developed, which enables us to quantify transient and steady state behaviors of the strand temperature. With the help of this simulator, a static nonlinear compensator for (i) is determined via a nonlinear optimization technique. Then, a dynamic simulation with the compensator is performed for a casting speed change, which gives a linear parameter varying (LPV) model that describes the transient behavior. Based on the model, a dynamic LPV compensator for (ii) is derived via an exact model matching technique. Simulation results show that a desirable strand temperature profile is obtained by the static nonlinear and the dynamic LPV compensators even when casting speed changes.

A simple adaptive servosystem with a tuning parameter is considered for a linear continuous-time plant. A reference model is introduced for specifying a desirable transient response, while an integ...

A model based networked control system is investigated in this paper, which is useful for realizing plant-level networked control of iron and steel processes. Sampled data of the state of a plant are transfered to a controller over a network with a communication delay. Then, a model based state feedback is introduced, which uses the model state instead of the plant state. An update rule is presented for resetting the model state appropriately based on the sampled data of the plant state. A necessary and sufficient condition of stability of the system is also derived as an eigenvalue test of a matrix.

A guaranteed cost regulator design is presented for uncertain linear discrete-time systems, where its objective is to find a state feedback such that a quadratic performance index is less than a given value for any uncertainty. The design is recast as a feasibility problem described by a parametrized linear matrix inequality (LMI). A notion of probabilistic solution that satisfies the LMI for almost all uncertainties is introduced and an efficient randomized algorithm based on the gradient method with random samples of the uncertainty is developed. The proposed algorithm always stops in a finite number of iterations. Then, it can either find a probabilistic solution with a given probabilistic confidence or detect the infeasibility of the problem in the sense that the feasibility set is too small to contain a ball with a given radius.

A probabilistic approach is considered for robust optimization, where a convex objective function is minimized subject to a parameter dependent convex constraint. A novel sequential randomized algorithm is proposed for solving this optimization employing the stochastic ellipsoid method. It is shown that the upper bounds of the numbers of random samples and updates of the algorithm are much less than those of the stochastic bisection method utilizing the stochastic ellipsoid method at each iteration. This feature actually leads to a computational advantage, which is demonstrated through a numerical example.

A stochastic ellipsoid method with multiple cuts is proposed for a class of robust feasibility problems which is to find a solution satisfying a set of parameter-dependent convex constraints for all possible parameter values. In particular, a new update rule is presented for constructing a smaller ellipsoid which contains the intersection of a previous ellipsoid and strips determined by given multiple gradients. A quantitative analysis of the volume of the updated ellipsoid is also provided, which leads to a further modification of the algorithm achieving fast convergence.