This paper is concerned with analysis of positive invariance and regional almost convergence of nonlinear systems by using density functions. It is shown that if there exists a density function that is positive inside a set and zero on its boundary then the set is positively invariant and almost all of the trajectories starting from the set are convergent. This result is applicable to controller synthesis for nonlinear systems by using convex optimization with satisfying state and input constraints. Furthermore, converse theorems are provided to ensure the existence of such density functions under mild assumptions.
This paper proposes the model used Petri Net in which the population of Sika deer in Hyogo can be estimated. In the proposed model, Hyogo is divided into 16 small areas and the number, birth, death, and movemont of Sika deer in each area can be expressed. However the number of Sika deer cannot be measured directly, a new conversion coefficient of density index into the number of Sika deer is defined. Unknown parameters, i.e., death rate, traveling rate between two areas and the conversion coefficient, are identified by a genetic algorithm from using the measured data.The availability of this proposed method is proven through some simulation results.
When the frequency domain ICA is applied to noise reduction in a real environment, it is essential to solve the scaling and permutation problems peculiar inherent in frequency domain ICA. The present paper gives a solution to the problems in a real environment. The proposed method is simple, the amount of calculation is small. And the method has high correction performance without depending on the frequency bands and distances from source signals to microphones. Furthermore, it can be applied under the real environment. From several experiments in a virtual room and a real room, it clarifies that the proposed method has been verified.
This paper addresses a trajectory tracking problem of mechanical systems with obstacle avoidance. Our strategy to improve obstacle avoidance is based on the field potential method using an existing navigation function. However, direct application of this function to trajectory tracking can hinder obstacle avoidance. We newly introduce a parameterized function representing a reference trajectory and propose a feedback law to control the parameter, thereby ensuring effective obstacle avoidance. Successful trajectory tracking is achieved by the convergence of the coordinates of the systems to the parameterized function. Because our method adopts a bounded navigation function, the proposed controller produces a bounded input signal even when the coordinates approach obstacles. Finally, a simulation of a two-link manipulator illustrates the effectiveness of the proposed method.
This paper considers vibration suppression of a two-mass transfer system, where the work is connected with the hand flexibly. We adopt the idea of jerk reduction of the hand. For this purpose, we derive a state equation including the jerk and acceleration of the hand. Since it contains the differential of input, it is not possible to apply standard control theory. For this reason, we modify the state equation to exclude the differential of input by introducing a new state variable. Then, we design optimal state feedback for a suitable cost function, and show that jerk reduction of the hand is effective for vibration suppression of the work. Since the state feedback containing the jerk and acceleration is not practical, we propose a computation method for an optimal feedback control law using only displacements and velocities.