A generalized truncated least squares adaptive algorithm is presented in this paper. The algorithm is a generalization of the algorithms by the truncated least squares method (TLSM) and the least squares method (LSM). The TLSM utilizes truncated data and is effective for systems with drastic parameter variations. This method is sensitive for small parameter variations and also for any disturbance. To accomodate the variations of the estimated parameters, a performance index of TLSM is generalized to include a new term of parameter variations in the form of a linear combination. The combination parameter introduced acts as an ability of adaptivity. Adaptive control experimentations of the liquid level controlled system is presented which show the effectiveness of the proposed algorithm.
Recently, new global optimization procedure called Random Tunneling Algorithm has been proposed for the problems which have differential objective functions. In this paper, we generalize it and propose a method which can also solve the problems which have non-differentiable objective functions. We apply the proposed method to system identification and control problems using neural networks in order to show its effectiveness. There exist two phases in the tunneling algorithm for global minimization problems, 1) minimization phase and 2) tunneling phase. The local minimum is searched in the minimization phase and the point in the lower valley is searched in the tunneling phase. In the proposed algorithm, we use the random search which generates the increments according to Cauchy distribution in the minimization phase. Likewise, in the tunneling phase, we generate the increments from the local minimum at some temperature according to Cauchy distribution and search the points in the lower valley. The wide range of search becomes possible owing to the property of Cauchy distribution and temperature cooling. In addition to numerical test problems, system identification and adaptive control problems using neural networks are solved. The proposed method works very well for these application problems and is very promising for many types of global optimization problems.
Considering information associated with the power spectrum characteristics of a system (2nd-order information) as well as information associated with its transfer characteristics (1st-order information), a better outcome is obtained in the field of the system approximation and reduction. In this paper, we discuss the problem of finding discrete-time systems such that its transfer function and the causal part of its power spectrum function have the desired Taylor expansion coefficients, respectively, about the given complex frequency points. Such systems are called system interpolating 1st-and 2nd-order information. We present a parametrization of all such systems, which turns out to be a generalization of some known results. Our result provides a method for the system approximation and reduction which can meet various specifications of frequency characteristics.
In this paper, propriety of the linearized servo system model for an industrial articulated robot arm was discussed. Industrially, the contour control of the robot arm has been implemented in such a way that an objective trajectory of the robot arm is divided into small segments and actuators of the servo motors have been controlled to pursue the divided segments, sequentially. In the conventional controller, the model of the robot arm control system has been regarded as the linear dynamic model in working coordinates. We consider this problem and analyzed the error of the linearized model. Based on the error analysis, we derive the permissible working region where the linearization error is negligibly small. In the permissible region, the robot arm dynamics can be expressed by a linear dynamic model in working coordinates.