This paper is concerned with the stability analysis of the stochastic infectious model with time delay. In the vector-borne diseases such as malaria and Japanese encephalitis, there exists time delay caused by an incubation period in the virus development in the vectors on the transmission of disease. Moreover, environmental change and individual difference cause some kinds of random fluctuations in the infection, recovery rates, etc. Hence, we propose the stochastic infectious model with time delay. The equilibrium solution with zero infected individuals is called the disease-free steady state. Since the stability of the disease-free steady state is related to whether or not the infectious disease spreads, we analyze stability of the disease-free steady state using the stochastic Lyapunov function. Moreover, we study the influence of the random noise on the stability based on the calculation of the Lyapunov exponent, and show results of numerical simulations.
This paper provides an efficient decision making framework for pricing of demand resources to manage voltage in a distribution network. Assuming that consumers in the distribution network have controllable loads which are helpful to manage voltage fluctuated by uncontrollable photovoltaic generations, we address an optimization problem of rewards for responses of consumers. This problem is a Stackelberg game in which a leader is a distribution network operator and followers are the consumers. It can be formulated as a bi-level programming problem, which is well-known as a NP-hard problem to solve due to its non-convexity. In order to obtain an exact optimal solution within a practical computational time, we employ a method to transform the problem with bilinear terms into the mixed-integer linear programming problem by a commercial optimization solver. Since the Pareto frontier is visualized for the distribution network operator, the most preferred solution can be chosen according to preference of he/she. In examples of computational experiments, the proposed approach successfully works to make a decision for the efficient distribution network management.
In this paper, we consider a target tracking problem of a multicopter. The target is assumed to move along a path that is unknown for the multicopter. We formulate this problem as a nonlinear receding-horizon differential game problem and solve the problem with a real-time algorithm for nonlinear model predictive control. Some simulation results show a satisfactory tracking performance of the proposed method.
This paper presents sufficient conditions for persistence of the interconnected positive systems for MIMO subsystems. The obtained conditions are on the structure of the transfer function matrix, the steady state gain for every subsystem and the structure of the interconnection matrix. As a result, the output of the subsystem converges to a vector on a convex cone which is included in the positive cone. The resulting conditions include the existing conditions for the persistence in the case where every subsystem is SISO. Numerical examples illustrate the persistence analysis results.
When multi-agent systems explore in actual environments, it is difficult to manage agents centralizedly from outside due to communicable range. This paper proposes a maze exploration algorithm for distributed control system considering communicable range of agents. In proposed algorithm, agents share information each other within communicable range and then each agent detects deadlocks generating a wait-for graph from the shared information. Sharing cycle of wait-for graphs enables agents to take over the explorations each other and resolve deadlocks. This paper verifies the effectiveness of the proposed deadlock resolution algorithm via numerical experiments about some of communicable ranges and numbers of agents of exploration system. The simulation results show the influence of the proposed deadlock resolution algorithm on the efficiency of exploration and the path length of agents. The simulation results also show the relationship between the communicable range, the number of agents of exploration system and the failure probability of exploration.