OPTIMAL-CONTROL OF SYSTEMS DESCRIBED BY INDEX 2 DIFFERENTIAL-ALGEBRAIC EQUATIONS

The optimal control problems considered here seek to determine a time- varying control action and a set of time-invariant parameters that opt imize the performance of a dynamic system whose behaviour is described by index two differential-algebraic equations (DAEs). The problem for mulation accommodates equality and inequality end and interior point c onstraints as well as constraints on control variables and parameters. The control parameterization approach, whereby the original problem i s transformed into a nonlinear. programming problem, is adopted. Due t o the features of index two DAEs, the control representation employed may yield a discontinuous system trajectory and for this reason it is necessary to define functions yielding consistent initial conditions f ollowing control variable discontinuities. Variational analysis is car ried out to derive expressions for the objective and constraint functi on gradients with respect to the optimization decision variables. A ke y characteristic of this analysis is that, in addition to the original equations, it is necessary to adjoin equations resulting from manipul ation of the original algebraic equations and their time derivatives.