This is in contrast to gradient-based optimization meth- ods that require the existence of continuous first derivatives of the objective function, e. Parsopoulos and M. Table 3. Another benefit of this manner of dealing with constraints is that the swarm population can be initialized over a reasonably large search space, relying on the non-stationary penalty function method to ensure that constraint violation is minimized. Indeed, under such circumstances, full-state oDwnload must be achieved based on estimates obtained from a non-linear estimator such as the unscented Kalman filter.
In particular, the state-control parameterization method is discussed in the context of a global collocation method known as the Gauss pseudospectral method GPM that was adopted for some of the problems solved in this work. Figure 6.
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This and the two sub- sequent operations of matrix multiplication and addition are relatively lightweight and almost-instantaneous even on legacy hardware running unoptimized software. Clearly, the actual control history is known only after the Activatlon has been solved.
It may also be noted that the number of interpolation points used in reference  is also relatively large; points for a three-state problem and for a five-state one.
The Ackley function is multi-modal, with a large number of local minima and is considered a benchmark for evolutionary search algorithms .
View full EZ Schematics 5. The initial velocity and radial position are known. Naidu, J.
Luo, and Z. Consequently, a considerable fraction of the initial swarm population could ini- tially hover around non-optimal regions of the search space, without influencing swarm movement towards a better landscape.
Note that tilde signifies numerical approximations of the corresponding quantities, a convention introduced in Section 4.
In particular, the state-control parameterization method is discussed in the context of a global collocation method known as the Gauss pseudospectral method GPM that was adopted for some of the problems solved in this work. Vrabie, and V. Finally, the complementary nature of the two newly-developed methodologies was demonstrated through the computation of an approximate-optimal feedback guidance law for a challenging aeroassisted orbital transfer problem.