A new higher-order method for parameter optimization of time-varying and time-invariant linear dynamic systems

Dynamic systems are often designed to carry out repetitive tasks. The parameters of the dynamic system influence the optimal trajectory, thereby, affecting the cost of a typical cycle. This brings in the need to select parameters in an optimal way. The conventional method of optimal parameter design, where state equations are augmented to the cost functional using Lagrangean multipliers and the necessary conditions are solved as a 2-point boundary-value problem, is highly computation intensive and is often unreliable to give the solution. In this paper, a new formulation is proposed to solve this problem for a class of time-varying linear dynamic systems. This procedure does not use Lagrangean multipliers, hence, the optimality equations have a completely new form compared to conventional methods. Also, it is shown in the paper that these optimality equations can be solved in a very computationally efficient way to determine the parameter set for optimal design