The size of the membership set is analyzed probabilistically in the presence of not only bounded disturbance but also l2bounded parameter uncertainty. In particular, the diameter of the membership set is estimated with a probabilistic confidence for a finite number of samples, where the regressor is assumed to be persistently exciting and the disturbance and the parameter uncertainty are assumed to be random variables and to take their extreme values with a probability. It is also shown that the estimated diameter converges to zero as the number of samples tends to infinity.
This paper proposes new stabilizing control laws for a variable length pendulum. By introducing a Lyapunov-type nonnegative function representing the magnitude of the angular oscillation of the pendulum, a stabilizing condition for the pendulum is derived that is more general than the one proposed by Yoshida et al. Two stabilizing control laws are developed on the basis of this condition. One is a control law that changes the velocity of the weight along the pendulum sinusoidally, which can reduce the load on the actuator and has good robustness properties to the nonlinearities and noise of the system. The other is a control law that performs a bang-bang control of the acceleration of the weight to approximate the optimal control law that maximizes the damping ratio of the angular oscillation of the pendulum. Furthermore, a formula is derived to evaluate the ratio between adjacent amplitudes of the oscillation for a given velocity profile of the weight, and then the ratios for the proposed control laws are evaluated. Numerical and experimental results are given to show the validity of the proposed methods.
The purpose of this paper is to analyze the stability of Passive Dynamic Walking using Poincaré map of the impact point which is the state of walking robot at the collision between a swing leg and ground. Especially, in this paper, we focus on the feedback structure which exist in equations which are used to get the Poincaré map, and consider the relationship between stability of Passive Dynamic Walking and the feedback structure focusing on the relationship to LQR or output zeroing control.
In this paper, we consider a vibration isolation control problem in case that narrow-band fre-quency disturbances are applied to a system. The frequency shaping method byH∞control is suitable for the problem. But we can't locate closed-loop poles in preferable region even if we use the robust stability-degree assignment method, because poles of weighting functions of the generalized system become undetectable modes. In order to overcome this problem, we use extendedH∞control combined with the robust stability-degree assignment method. By the method, we can design a controller that provides desirable frequency shaping and preferable closed-loop poles location at the same time. The performance of the designed controller is conformed by experiments.