This study extends the particle swarm optimization (PSO)-based bifurcation points derivation method to the autonomous systems. PSO avoids the need to carefully set the initial parameters of the dynamical system or to differentiate the objective function. In addition, it can derive the bifurcation points quickly and accurately, and its efficacy has previously been demonstrated for discrete dynamical systems and non-autonomous systems but not for autonomous systems. This paper proposes an extended PSO-based method for autonomous systems by incorporating the computation of a Poincaré map and a bisection method in the algorithm. To validate the effectiveness of the proposed method, it was applied to deriving the local bifurcation points of a three-dimensional autonomous system to confirm and demonstrate its effectiveness.
In this study, our proposed parameter estimation method is furtherly tested on a nonlinear random dynamical system. Our method assumes that a probability density function (PDF) data is measured from a random dynamical system whose model structure is known as a stochastic differential equation but having unknown parameter values. The Fokker–Planck equation (FPE) is derived from the random dynamical system with the help of Itô calculus. The measured PDF data and candidate parameter values are substituted into the FPE to calculate an FPE residual. The residual is minimized by our method to estimate the parameter values. The results of application to a random Duffing–van der Pol system show that our method is capable of estimating unknown parameters even when the system is nonlinear.
Chaotic neural networks (ChNNs) provide an effective method to solve combinatorial optimization problems, because their chaotic behavior is considered to encourage smooth escape from local optima. However, whether ChNN models exhibit chaotic behavior when searching for solutions remains unknown, which means there may be other reasons for their good performance. From this perspective, we analyzed the deterministic features of a chaotic time series from the transition of the objective function value. The results obtained by the E1, IDNP, and R series indicate that the transitions of the objective function value for solving the Steiner tree problem in graphs exhibited weak determinism, similar to that of the transition of a chaotic neuron’s internal state in a plain ChNN.
In recent years, shortages of worker caused by declining birthrate and aging population have been seen as serious problem in various industries. So using of robots has been considered for labor saving and shortening of working hours. Especially in the construction industry, the illuminance measurement work is a heavy load for the worker because this work requires measurement, recording, data organization, etc. at night when influence of light from outside is small. Therefore it is hoped to develop a robot that can replace the illuminance measurement work at indoor construction sites. We have developed the illuminance measurement robot and have shown its effectiveness.
For autonomous movement, we use evolutionary SLAM which can estimate the position with high accuracy even in an unknown environment. But it has problem of position loss, which causes failure of illuminance measurement work. In this paper, we proposed the method using a robot kinematic model which can localization with high success rate, the method using CAD map which can fix position loss, and the method which combines these. Then, we discussed its effectiveness from the viewpoint of improving efficiency of the illuminance measurement work.