In control theory, control barrier functions have been actively studied to improve the safety of control systems. Moreover, visualization techniques to reduce the risk of accidents have also been studied. However, there is no discussion on visualization using human assist control. In this study, we propose a visualization technique of risks using virtual inputs that are not performed directly on the system. The effectiveness of risk visualization is discussed through experiments using a personal mobility.

A necessary and sufficient condition for linear time-varying (LTV) systems to be exponentially stable has been given based on differential Lyapunov inequalities (DLIs). The exponential stability of an LTV system is guaranteed if the DLI for the system has a solution, however, few systematic methods have been reported for finding a solution of DLIs. We have proposed a method to search solutions of DLIs using linear matrix inequalities (LMIs) for recent several years, especially when the system matrices of LTV systems are periodic. In this paper, we propose a method to design periodic time-varying state feedback controllers that stabilize periodic LTV systems by utilizing our DLI solutions search method. Moreover, we add new variables to the LMIs that use the addition theorems of trigonometric functions to reduce the conservatism in stability analysis and controller design. An example shows the process of stabilizing a periodic LTV system using our proposed design method.

In this paper, using a high-speed vision system, we propose high-speed autofocus methods to acquire clear images of vibrating objects in the focal direction, in order to realize in-line precision visual inspection. These methods include a single-process method with a single camera, and a multi-process method with a laser displacement meter, to estimate focal lengths. We evaluated the high-speed autofocus performance for vibrating objects in the focal direction using a vibration tester. In addition, since the vibration is not only in the focal direction but generally in three dimensions, we established a method to track this three-dimensional high-speed vibrating object and acquire clear images at high speed. Compared to the ideal autofocus performance defined in this study, high-quality results of 110% for simple harmonic motion and 146% for rotational motion were obtained, proving that the system is highly practical.

If the true parameter of a system is unknown, a parameter estimation method is used to obtain the true parameter. One of the estimation methods is the minimization of the evaluation function of the parameter-dependent model and the observed data, which is implemented by an optimization method. Using Newton's method for this optimization, we can expect the quadratic convergence to the true parameter. However, if the true parameter is sensitivity unidentifiable (non-sensitivity identifiable (SI)), quadratic convergence is not guaranteed. Thus, detecting the true parameter being non-SI a priori is important. Considering the target system has a network structure, we can expect to use the network structure for this detection if we have a network condition that implies that the true parameter is non-SI. Therefore, in this paper, we consider linear systems with graph Laplacians as a network system class and address a problem to find the network condition that implies that the true parameter is non-SI. Then, we obtain a sufficient condition which implies that the true parameter is non-SI. The condition is explained by the graph's symmetric structure and proven by the decomposition of the graph's incidence matrix.