Schedulability analysis of window-constrained execution time tasks for real-time control

Feasibility tests for hard real-time systems provide information about the schedulability of a set of tasks. However, this information is a yes or no answer whether the task set achieves the test or not [13]. From the system design point of view, it would be useful to have more information, for example, how much can vary some task parameters, such as computation time, without jeopardize the system feasibility The aim of this work is to provide a method to determine how much a task can increase its computation time, maintaining the system feasibility under a dynamic priority scheduling. This extra time can be determined not only in all the task activations, but in n of a window of m task invocations. This is what we call a window-constrained execution time system. This can be very useful in several fields: complex control algorithms, fault tolerance management, imprecise computation, etc. In control applications, this information can be used to execute supervision activities, such as model updating which is not required to be executed all the periods, or to determine new controller parameters for the current operating conditions. In fault tolerance, this information allows to recover n faults in m activations.