Optimal periodic control with environmental application

Abstract

We consider the problem of designing an optimal control for linear discrete-time systems assuming that total cost for the control efforts is limited and cost function is periodic in behaviour. (seasonal, for example) This Model was developed as a result of analysis of real data of the project “Modelling River Murray Estuary” from the Environmental Modelling Research Group, the University of South Australia.

Nonlinear control systems are of a great significance in the field of control engineering since most practical dynamic systems are nonlinear. Using arbitrary control strategy as an initial we can compute coefficients in nonlinear system as a function of corresponding output variables. (previous output variables) As a result we shall transform nonlinear system into linear system with known optimal solution. (new output variables) Repeating this procedure again and again we shall generate sequence of control strategies. Optimal control strategy for given nonlinear system may be obtained as a limit of this sequence. This fact has been demonstrated by the particular example relating to the above environmental research Project.