# Adaptive Control in Problems

with Dynamic Disturbance

of Unknown Level

## Valery S. Patsko, Sergey A. Ganebny, Sergey S. Kumkov

Institute of Mathematics and Mechanics RAS,

Ekaterinburg, Russia

### International Symposium on Guidance and Differential Games

Dedicated to the 75th birthday of Prof. Josef Shinar

November 8, 2007, Haifa, Israel

The file patsko.pdf contains the presentation to the talk "Adaptive Control in Problems with Dynamic Disturbance of Unknown Level" with short comments to each slide.

In the file missiles_relative.avi, there is a movie of simulation of system motion in the relative coordinates of the objects' geometric positions in projection to the plane *YZ* (upper left). The dynamics of the system and initial data for the simulation are given in the final part of the presentation. The blue circle denotes the terminal set. The pursuer uses the suggested adaptive control, a random piecewise-constant function is applied as the disturbance (the evader's control). The upper right part of the frame shows the hodographs of the useful control *u*(*t*) and the disturbance *v*(*t*). In the bottom part, there are the graphs of levels of the realizations of the useful control with respect to the constriant *P* and of the disturbance with respect to the auxiliary constraint *Q*_{max}. In all figures, a moving point denotes the position, which corresponds to the current time instant.

In the file missiles_equivalent.avi, there is a similar movie, but the system trajectory is shown in the equivalent coordinates *x*_{1}, *x*_{2}. They are the coordinates of the space, where the numerical constructions of the stable bridges are made. Here, the dark blue line shows the time section of the main bridge *W*_{main}. At the terminal instant, its section coincides with the terminal set. The light blue line denotes the time section of a bridge, which is used for the extremal aiming during generation of the adaptive control at the current instant. The red segment shows the direction of the current useful control. One can see as the position of the system moves with respect to the sections of the main bridge with the flow of time.

In the file missiles_equivalent_scaled.avi, one can see the same as in the file missiles_equivalent.avi. The difference is that the previous movie keeps the original scale of the figure, so, the final stage of the process can be hardly seen. Now, the scale is changed automatically in such a way that the sections of the bridges and the current state of the system are seen well.