In this paper, we deal with two problems of input-affine polynomial dynamical systems. One aims to obtain a state feedback controller such that a prescribed algebraic set is invariant for the resulting closed-loop system. The other aims to obtain a state feedback controller such that the resulting closed-loop system has a prescribed vector field on a given algebraic set. It is shown that the two problems can be represented by a particular inclusion of polynomials, and the inclusion can be solved. As a result, all the state feedback controllers required in the problems can be exactly represented by using free polynomial parameters.
In this paper, we deal with group multiattribute utility analysis incorporating preferences of multiple interested individuals.Since it is difficult to repeatedly ask them questions for determining parameters of a multiattribute utility function, we gather preference information of them by asking not difficult questions to answer, and develop a method for selecting an alternative consistent with the preference information. For a given set of single-attribute utility functions, assuming multiattribute utility functions to be in the multiplicative form, we evaluate trade-off between attributes by utilizing neural networks. Using the preference information actually gathered in an application study, we verify the effectiveness of the proposed method.
In this paper, we investigate estimation performance of a vision-based observer, presented in one of the authors’ previous work, when a target object takes stochastic motion in three dimensional space. The configuration space of the full 3-D rigid object motion is known to be given by the product space SE(3)=R3 ×SO(3). Consequently, the stochastic motion must be described by a stochastic differential equation (SDE) on SE(3). We thus first formulate the SDE on SE(3) describing the evolution of the estimation error between the actual motion and its estimate produced by the visual observer. Then, we analyze the estimation accuracy in the framework of the noise-to-state stability (NSS). However, since NSS guarantees qualitative properties, we also take the notion of ultimately exponential boundedness in mean sense to clarify the quantitative estimation accuracy. Finally, we demonstrate validity of the latter result through simulation.
This paper is concerned with stability of a regional power and heat supply system. The system has two combined heat and power plants (or co-generation units) supplying both power and heat. A mathematical model is derived to represent dynamics occurring in the system due to the coupling between power network and heat network. Numerical simulations of the model are performed for investigating its static and dynamic characteristics in order to estimate the stability of the system. It is shown that the heat transfer management between the two co-generation units affects the stability of the system and possibly destabilizes the synchronized operation of the two generators.