We study global control problems for time-independent nonlinear state equations from a view point of an intersection theory on “configuration spaces of control systems”. Singularities of a feedback controlled system appear as the intersection of the null set of a state equation and an input manifold that is a geometrization of a feedback control law. We decompose the null set of the state equation into the null manifold, the degenerated null manifold and the set of critical points in relation to a feature of singularities of feedback controlled systems. We also discuss generic properties of control laws in the case that the controlled system has only simple or hyperbolic singularities.
This paper is concerned with global control problems for time-independent nonlinear state equations from a view point of an intersection theory on “configuration spaces of control systems”. In this paper, we show a relationship between parity of Morse indices of hyperbolic points on a controlled system and local intersection numbers of an input manifold and a null manifold. We also discuss this result for cases that the closure of a null manifold has self-intersections or intersections to the closure of other unit components. Moreover, we define the projective dimension of the null manifold to disscuss the assignability of hyperbolic points on controlled systems.
In this paper, we propose a new method of estimating the physical parameters for a non-linear system with known structure by using a genetic algorithm (GA). Since a simple GA is empirically known in many cases to cause initial convergence or fall into a local minimum, we introduce a new algorithm named Pool GA and verify its effectiveness for the identification.
In this paper, we consider position and vibration control of a one-link flexible arm with a non-symmetric rigid tip body, of which the mass center does not lie on the centroidal axis of the arm. In this case, the bending vibration and the torsional vibration of the arm are coupled. Firstly, we derive the distributed parameter model using Hamilton's principle. Secondly, on the basis of this model we construct PDS control law using Lyapunov method and examine the asymptotic stability of the closed-loop system. The PDS controller consists of PD feedback of the motor angle and a bending strain (S) feedback of the flexible arm. Finally, some experiments are performed to demonstrate the effectiveness of the proposed controller.
A design procedure for data compression and equalization for digital communication systems is developed based on the multirate sampled-data H∞ control theory. The procedure provides transmitting/receiving filters so as to minimize the error between the original signal and the received signal with a time delay, and to reduce the noise added to the channel. While the system is multirate and infinite-dimensional due to up-and downsampling and a delay, the design problem can be reduced to a finite-dimensional discrete-time problem using the lifting and the FSFH (fast-sample and fast-hold) approximation. Numerical examples are presented to illustrate the effectiveness of the proposed method.
This paper proposes an optimal inverse system for a max-plus linear system with a linear parameter-varying structure. For the design of inverse systems of max-linear systems, the prediction equation using max-plus linear systems and the greatest subsolution for the linear algebraic equation are required. Hence, this paper newly gives a prediction equation and the greatest sub-solution for the linear parameter-varying system. In addition to those, this paper shows an optimization method for the system parameters in the inverse systems, and this optimization problem can be reduced to the linear programming. Finally, the proposed method is applied to a two-inputs, two-outputs production system with four machines, and the efficiency of the proposed method is demonstrated by using numerical simulations.
In calculating steady-state flows of water distribution networks, one of the conventional assumptions is that the consumption outflows are constant. In actual networks, however, outflows depend on the pressures. In order to achieve more precise analysis of actual networks, we present in this paper a new method of steady-state flow calculation under the condition that outflows are given as functions of pressures. The newly proposed method for dealing with pressure-dependency of outflows is based on the mesh-flow analysis and is much more efficient compared with the previous method proposed by the authors based on the traditional node-head analysis. It is especially effective for the analysis of fire prevention water networks installed in temples, shrines and villages with many cultural buildings.