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Abstract In this research, Net‐Zero Energy Houses (ZEHs) is investigated that harness regionally produced electricity from photovoltaic (PV) panels and fuel cells, integrating them into a local power system in pursuit of achieving carbon neutrality. This article examines the impact of electricity sharing among users who are working towards attaining ZEH status through the integration of PV panels and battery storage devices. Two potential scenarios are proposed: the first assumes that all users individually invest in storage devices, hence minimizing their costs on a local level without energy sharing; the second envisions cost minimization through the collective use of a shared storage device, managed by a central manager. These two scenarios are formulated as a stochastic convex optimization and a cooperative game, respectively. To tackle the stochastic challenges posed by multiple random variables, the Monte Carlo sample average approximation (SAA) is applied to obtain solvable deterministic convex problems. Last, to demonstrate the practical applicability of these models, the proposed scenarios are implemented in the Jono neighborhood in Kitakyushu, Japan.

In this paper, we explore the discrete time sparse feedback control for a linear invariant system, where the proposed optimal feedback controller enjoys input sparsity by using a dynamic linear compensator, that is, the components of feedback control signal having the smallest possible nonzero values. The resulting augmented dynamics ensures closed-loop stability, which infers sparse feedback controller from open-loop solution to closed-loop realization. In particular, we show that the implemented sparse feedback (closed-loop) control solution is equivalent to the original sparse (open-loop) control solution under a specified basis. We then extend the dynamic compensator to a feedforward tracking control problem. Finally, numerical examples demonstrate the effectiveness of proposed control approach.

This paper presents a distributed model reference adaptive control scheme for optimal tracking of an interconnected dynamical system in the presence of system/interconnection uncertainties. A reference model selection which achieves an optimal tracking for the nominal system is introduced by using linear quadratic regulator theory. Then an adaptive control law is developed for the uncertain interconnected dynamical system, where it employs the specified reference model. It is shown that the control law achieves the desired behaviour such that the output of the system asymptotically tracks the output of the reference model in the presence of the uncertainties. An explicit error bound regarding optimal tracking is also established.

Models of opinion dynamics have been used to depict how the opinions of agents within a social network evolve based on their interconnections and interactions. The collective behaviour of agents can also exhibit certain social phenomena such as convergence to a consensus or disagreement. In this study, we propose a gossip-based model for the opinion dynamics of interconnected groups and describe how they can reach consensus. Through analysis of the convergence properties of its expected dynamics, we show that the number of groups can affect the rate by which the network reaches consensus. We also include numerical examples to demonstrate our proposed model and its properties.

Stochastic consensus algorithms are considered for multi-agent systems over noisy unbalanced directed networks. The graph which represents a communication network of the system is assumed to contain a directed spanning tree, that is, a given digraph is weakly connected. Then two types of stochastic consensus are investigated, where one is for the agent states themselves and the other is for the time averages of the agent states. The convergence of the algorithms is investigated, which gives a stopping rule, i.e., an explicit relation between the number of iterations and the closeness of the agreement.

This paper presents algebraic connectivity invariance of a network-of-networks derived from a graph product. The network is modeled as an interconnected system of several kinds of similar subsystems via a certain structure, where several vertices of each subsystem are attached to the structure. The algebraic connectivity of this network can be characterized by using an appropriate network having homogeneous subsystems under a certain condition, which is investigated in this paper. In particular, a necessary and sufficient condition for adding links (edges) to subsystems which preserve the algebraic connectivity is clarified.

Synchronous and asynchronous algorithms are presented for distributed minimax optimization. The objective here is to realize the minimization of the maximum of component functions over the standard multi-agent network, where each node of the network knows its own function and it exchanges its decision variable with its neighbors. In fact, the proposed algorithms are standard consensus and gossip based subgradient methods, while the original minimax optimization is recast as minimization of the sum of component functions by using a p-norm approximation. A scalable step size depending on the approximation ratio p is also presented in order to avoid slow convergence. Numerical examples illustrate that the algorithms with this step size work well even in the high approximation ratios.

A chance constrained AC optimal power flow is to find the optimal economic operation plan whose probability satisfying AC power flow equations and various inequality constraints on operating limits of the power system is greater than a specified probability level. Even if a constraint condition for each uncertain power supply value is convex with respect to decision variables, the chance constrained problem is not convex in general. Thus, it is difficult to solve the problem within reasonable computational time. Employment of randomization techniques for this issue is proposed in this paper. A main advantage of the framework leads to a solution with a theoretical guarantee. Its sample complexities are of polynomial order for parameters of a given accuracy. The efficiency of this algorithm is demonstrated by applying it to the Japanese power system models.

Opinion formation is investigated over signed gossip networks, where asymptotic and transient opinion behaviors are analyzed in detail. The network is modeled by a connected signed graph, where each edge of the graph has positive or negative weight, i.e., these edges represent friendly or hostile relationship. Interactions each of which occurs between two persons chosen randomly follow an asynchronous procedure. Then it is shown that their opinions always converge in mean square and converge almost surely. A convergence time is defined as the smallest time such that it takes for the values of nodes to get within a given neighborhood of the consensus value with high probability, regardless of initial state. An upper bound and a lower bound of the convergence time of the gossip algorithm are given in terms of a structure of the given network.