A method to modify a developable surface locally based on the designers' demand is proposed. A developable surface, which can be flattened without stretching or expanding e.g. a cone or cylinder, widely used in many products, such as shipbuilding, clothing, and so on. Since these products are manufactured by bending, they are required not only their three-dimensional shape but also its developed shape. Nevertheless, its design process is not done by the CAD system but mainly by the experience or intuition of designers because the developable condition of a surface is complicated. Therefore, modifying a developable surface according to the designers' demand is much more difficult than doing a free-form surface, such as Bezier surface. In this study, we aim to improve efficiency of the design process and propose a method to modify a developable surface when a point of its boundary curve changes. First, we model the developable surface based on the differential geometry. Then we formulate its modification process and obtain the differential equation regarding the direction of modifying and its amount. From the features of this equation, we propose a simple algorithm, not spending much calculation time. Finally, we verify the validity of the proposed method through some examples of numeric calculation. This method can modify not only its three-dimensional shape of the surface, but also its developed shape.

This paper proposes a method of model predictive control (MPC) based on Gaussian process regression for stochastic linear systems with uncertainty such as unknown dynamics and disturbances. The unknown dynamics refer to an unknown function of the input and output signals. In the proposed method, the mean and variance of the unknown function values estimate the function using Gaussian process regression. Updating the system model with the estimated function enhances the performance of MPC. Moreover, the stochastic reachable set of the system reduces the chance constraints into second-order cone constraints, which means the MPC problem becomes a convex problem. Finally, numerical examples illustrate the effectiveness of the proposed MPC.

In this paper, we propose a time-based event-driven control protocol for finite-time consensus. Compared with the state-based triggering function, each agent only needs to monitor its own state continuously to determine when to trigger the event and broadcast its state to the neighbors. The agent updates its controller when it broadcasts its state or receives information from neighbors. The estimated settling time depends on the initial condition, triggering function and topology. Furthermore, the system does not exhibit Zeno behavior if and only if the triggering threshold is lower bounded. Simulation results show that although time-based method has greater estimation error in convergence time, it saves computation and communication resource compared with state-based method.