This paper deals with path-following control. In existing path-following methods, velocity of e.g. vehicles has been often given as reference inputs. However, velocity is tied in with other tracking characteristics and there exist trade-offs between velocity, tracking errors, control costs and so on. To deal with the trade-offs explicitly, we first formulate a cost function based on difference between a reference path and trajectories of vehicle motion. The difference is modeled in terms of dynamics of curvature. This formulation enables us to deal with trade-offs among tracking error, reaching time and control costs. The control input can be given by solving a two point boundary problem numerically. The effectiveness of the proposed method is examined by numerical examples.
In this paper, a robust stability analysis problem is considered. μ-Analysis is a useful tool in order to guarantee stability robustness, but obtained results by conventional procedures are sometimes conservative. On the other hand, to guarantee stability robustness of active control systems in space is extremely important. A new robust stability analysis procedure by using virtual parametric variations is proposed in order to carry out tight evaluation of the stability robustness for active control systems. Performance of the proposed procedure is verified by an example of a mechanical vibration control system.
Descriptor equations have much more flexibility in describing nonlinear systems than state equations. In this paper, based on the Lyapunov's direct method, stability conditions are developed for nonlinear descriptor systems. An existence condition of solutions of descriptor equations is also derived. The results remove the differentiability assumptions on nonlinearities in descriptor equations, which are required in the existing works. As an application of the conditions, stability analysis of a Lur'e-type feedback system whose linear part has a direct path is considered by using a descriptor expression.
An image-based inverted pendulum control system with a large time delay of camera has some analogies with human stick balancing control. Cabrera and his group pointed out that time delays and state-dependent fluctuations play an essential role in neural control mechanism. In this paper, we investigate some properties of the time delays and the fluctuations using our new model which is consistent with the actual inverted pendulum control system. For noise free case, a sufficient condition for the stability of our time-delayed control system is derived.
Humans can keep a stick on the fingertip upright position for a certain time after a brief exercise, although we have a large time delay due to the signal transfer in the optic nerve and due to information processing in the brain. Correspondingly in an experiment on the stabilization of the mechanical inverted pendulum, we use a normal frame rate camera as an angle sensor of the pendulum, and its large time delay makes the stabilization difficult. How can humans compensate the large time delay? In order to answer this question, we apply Just-In-Time method to the inverted pendulum control system. This memory-based scheme corresponds to the mechanism of human learning and memory. This method can stabilize the inverted pendulum for a certain amount of time just like humans. An analysis of the behavior of the pendulum may give an interpretation for the motor control mechanism of human.