Optimal Computational Resource Allocation for Control Task under Fixed Priority Scheduling

In this paper a new real-time control system co-design is presented. Given several plants controlled by Linear Quadratic Regulator algorithms running over the same real-time platform, an optimal selection method of the sampling time of each regulator is proposed. The method finds the optimal solution that minimizes an appropriate overall cost function taking into account performance of each subsystem within a constraint on the computational resource. To deal with this problem a new statespace approach for modeling systems with any value of computational delay is proposed. The structure of the optimization problem is then exploited in a way that its solution can be found by solving a minimal set of nonlinear equations. A simple example with three subsystems is presented to highlight the main features of the proposed method.