Optimal Integrated Control and On-line Scheduling of Resource-Constrained Systems

In this chapter, we present an algorithm based on the model predictive control approach. Such an algorithm allows assigning on-line the optimal values of the control inputs and the scheduling inputs of resource-constrained systems. By focusing on its practical implementation aspects, such as its computational requirements, we propose a more efficient heuristic, called OPP. Next, by using a pre-computed off-line schedule, OPP is able to assign on-line the values of the control inputs and the scheduling inputs based on the plant available state information. The computational requirements of this heuristic are considerably reduced compared to those of the “standard” model predictive control approach. Furthermore, we prove that if some mild conditions are satisfied, then OPP guarantees the stability of the system as well as some performance improvements compared to its basic off-line schedule. We also show that the use of the periodic optimal control in the design of the control gains that will be used by OPP leads to a significant simplification of its implementations, which boils down to the comparison of T quadratic cost functions, T being the period of the basic off-line schedule. The OPP scheduling algorithm was finally applied to two distributed control systems: the active suspension controller of car and the quadrotor attitude control.