Discrete Supervisory Control of Switched Linear Systems

This contribution deals with the synthesis of discrete supervisory control for switched linear systems. Via two successive approximation steps, this hybrid control problem is transformed into a purely discrete problem. The latter can then be solved using a slightly modified version of P. J. Ramadge’s and W. M. Wonham’s “supervisory control theory”. By embedding both approximation steps within J. C. Willems’ “behavioural systems theory”, we can guarantee that any solution of the resulting discrete synthesis problem will also solve the underlying hybrid problem. All algorithms employed within the approximation and the synthesis procedure terminate after a finite number of steps. The approach is illustrated by means of a simple three-plate thermal system.