A recursive algorithm is derived for subspace system identification which is flexible and applicable to continuous/discrete-time, time-invariant/varying stochastic systems. Efficacy of the algorithm is demonstrated by simulations, comparing with another proposed algorithm.
In this paper, we propose one of the powerful iterative tuning methods for the parameters of the controller of a closed loop system. The method we provide here requires only one-shot experiment and then an iterative non-linear optimization for obtaining the optimum parameters of the controller can be performed off-line by using the fictitious reference signal computed by the first experimental data (from this reason, we refer to our method as “fictitious reference iterative tuning”, which is abbreviated to “FRIT”). The main concept and the algorithm of FRIT are provided as our main results of this paper. Moreover, we give a control experiment of the cart-system in order to show the validity of FRIT.
Iterative feedback tuning is a method to find control parameters by iteratively carring out control experiments. In this paper the IFT method is applied to adjust control parameters of multiple PID controllers and an I PD controller. Since an input signal for an integral element of an I-PD controller is different from a proportional and derivative element, parameter tuning by the IFT method has to do by the similar way for a multivariable controller. Some test signal should be added to a manipulated signal in order to apply the IFT method for a general multivariable system. It is shown that all test can be performed by setpoint response in cases of parameter tuning for an I-PD controller or multiple PID controllers. Experimental tests are carried out and show properties and results of the IFT method.
Generalization ability of the ensemble learning through linear simple perceptron is analyzed by using the stochastic mechanics method. The element of the initial connection weight is given by a Gaussian random number so that the ensemble learning is performed effectively. To analyze the effect of number of the perceptrons used in the ensemble learning, linear simple perceptrons are taken into account. Additive noise for the teacher's output or student's output is considered. Each element of teacher and student networks are considered to be initialized by Gaussian distibution of zero mean and unit valiance. From the analytical results, we found that in the limit of K is infinity, the generalization error of ensemble learning with the K linear perceptrons are a half of that of the single perceptron. For finite number of perceptrons, the generalization error converges to the value of a half of the single perceptron's one with 1/K when no noise is added. Asymptotic property of the ensemble learning is not effective for teacher's output noise, however, from analysis of dynamics of the generalization error, it is found that the ensemble learning is effective at the early stage of the learning.
In this paper, we consider the stability of periodic solution of linear systems with state jump. While this model is general enough to describe the complex dynamics of a class of hybrid systems including the (approximated) biped passive compass walking, it also retains the tractability for the analytic mathematical treatment. With an appropriate definition of the stability, we can justify the use of Poincare map in the analysis. The formula for the linearized Poincare map, which determines the local stability of the periodic solution, is given. The effect of feedback control (for the case that the nominal trajectory is known) is also discussed.