Upper bound estimation of the spectral abscissa for switched linear systems via coordinate transformations

summary:In this paper, we develop computational procedures to approximate the spectral abscissa of the switched linear system via square coordinate transformations. First, we design iterative algorithms to obtain a sequence of the least $\mu_1$ measure. Second, it is shown that this sequence is convergent and its limit can be used to estimate the spectral abscissa. Moreover, the stopping condition of Algorithm 1 is also presented. Finally, an example is carried out to illustrate the effectiveness of the proposed method

The low-level guidance of an experimental autonomous vehicle

This thesis describes the data processing and the control that constitutes a method of guidance for an autonomous guided vehicle (AGV) operating in a predefined and structured environment such as a warehouse or factory. A simple battery driven vehicle has been constructed which houses an MC68000 based microcomputer and a number of electronic interface cards. In order to provide a user interface, and in order to integrate the various aspects of the proposed guidance method, a modular software package has been developed. This, along with the research vehicle, has been used to support an experimental approach to the research. The vehicle's guidance method requires a series of concatenated curved and straight imaginary Unes to be passed to the vehicle as a representation of a planned path within its environment. Global position specifications for each line and the associated AGV direction and demand speed for each fine constitute commands which are queued and executed in sequence. In order to execute commands, the AGV is equipped with low level sensors (ultrasonic transducers and optical shaft encoders) which allow it to estimate and correct its global position continually. In addition to a queue of commands, the AGV also has a pre-programmed knowledge of the position of a number of correction boards within its environment. These are simply wooden boards approximately 25cm high and between 2 and 5 metres long with small protrusions ("notches") 4cm deep and 10cm long at regular (Im) intervals along its length. When the AGV passes such a correction board, it can measure its perpendicular distance and orientation relative to that board using two sets of its ultrasonic sensors, one set at the rear of the vehicle near to the drive wheels and one set at the front of the vehicle. Data collected as the vehicle moves parallel to a correction board is digitally filtered and subsequently a least squares line fitting procedure is adopted. As well as improving the reliability and accuracy of orientation and distance measurements relative to the board, this provides the basis for an algorithm with which to detect and measure the position of the protrusions on the correction board. Since measurements in three planar, local coordinates can be made (these are: x, the distance travelled parallel to a correction board; and y,the perpendicular distance relative to a correction board; and Ɵ, the clockwise planar orientation relative to the correction board), global position estimation can be corrected. When position corrections are made, it can be seen that they appear as step disturbances to the control system. This control system has been designed to allow the vehicle to move back onto its imaginary line after a position correction in a critically damped fashion and, in the steady state, to track both linear and curved command segments with minimum error