Comparison of Combined Embodiment Design and Control Optimization Strategies Using Optimality Conditions

Abstract

Optimal embodiment design and control systems can be solved using several different strategies. This paper considers whether those strategies will find the true system optimum. Optimality conditions determine whether a point is an optimum of a system. This paper presents a development and comparison of the optimality conditions for several methods of optimizing fully coupled embodiment design and control systems. The results demonstrate that the methods do not possess the same optimality conditions and therefore will not converge to the same optimal solutions, often leading to sub-optimal solutions. Since these strategies have been used successfully to solve various examples, criteria are developed to determine when the various methods will find the true system optimum.

Sub-Structuring Modeling of Large Space Truss Structures for Structure/Control Optimization in Presence of Parametric Uncertainties

“…where w S and w C are weighting coefficients. The resolution of this non-trivial optimization problem has been performed numerically by means of a nested optimization routine, as proposed by [31,32]. For this optimization method, the solution for the overall optimization problem is found with respect to Θ, while the optimal K PMA is computed as a function of Θ by solving an inner control optimization problem [31].…”

“…Monolithic architectures solve the MDO problem using a unique optimization process. They are proven to be more efficient [31,32] than classical optimization techniques [33,34], especially when bidirectional coupling is present between the structural and control sub-problem. This is the case when one problem depends on some variables or parameters of the other sub-problem [35].…”

Concurrent optimization on the powertrain of robot manipulators for optimal motor selection and control in a point-to-point trajectory planning

“…11 In contrast, a concurrent optimization method deals with multi-objective optimization problems, obtaining solutions for the combined system. [12][13][14] Then, dynamical parameters are considered for motor-gearbox selection, control, and planning method in a concurrent multi-objective optimization problem, in contrast to classical methods where only motor selection is considered and torque and motion profiles are a priori known to the selection purposes. The constrained multi-objective optimization problem with a concurrent approach is solved by a Non-dominated Sorting Genetic Algorithm-II (NSGA-II algorithm 15 ), since it is an evolutionary algorithm widely used to deal with multi-objective optimization problems, 16 and has been successfully used for path planning 4,10,[17][18][19] and concurrent design.…”

Integrated structure-passive control design of linear structures under seismic excitations

“…In general, an energy dissipation system is optimally designed to improve the seismic performance after the structure has been initially designed under constraints on weigh, strength and displacements [3,4]. However, because of the coupling between the structure and control system, a simultaneous integrated design of both leads to a better performance (optimal solution) than a sequential design [5][6][7]. Reyer [6] formally classified the various optimization strategies into sequential, iterative, bi-level (nested), and simultaneous.…”

“…However, because of the coupling between the structure and control system, a simultaneous integrated design of both leads to a better performance (optimal solution) than a sequential design [5][6][7]. Reyer [6] formally classified the various optimization strategies into sequential, iterative, bi-level (nested), and simultaneous. A comparison between those strategies was also conducted by the author.…”