Efficient Adjoint-based Design Optimization with Optimal Control

Abstract

Multidisciplinary engineering system design typically employs a sequential process, progressing from system dynamics to design variables and control. However, this process is inefficient and may lead to a suboptimal design. We propose formulating the optimal control and multidisciplinary design optimization (MDO) problems as a single problem with linear quadratic regulator (LQR) control. We use the coupled adjoint method to compute the design variable derivatives, which are critical for gradient-based design optimization. The computational cost of the derivative computation using the adjoint method is independent of the number of design variables, making it suitable for large-scale problems. We show that the coupled adjoint can be solved indirectly and more efficiently by solving three smaller adjoint equations that leverage the feedforward structure of the problem. We demonstrate this new approach on two test problems: design optimization of a classic cart-pole problem and the aerodynamic shape of a quadrotor blade. For the quadrotor blade design problem, we reduce the control cost by 10% by optimizing the blade for a specific control task with a slight penalty in steady hovering power consumption.

Figures (9)

• Figure 1: XDSM for CCD analysis and optimization.
• Figure 2: The control input $u$ in the cart-pole problem causes the cart to slide with no friction.
• Figure 3: Cost contour of $M$ and $m$ with $l = 1$, where the infeasible region is shaded.
• Figure 4: Comparison of optimized and baseline results.
• Figure 5: Schematic of the quadrotor's longitudinal dynamics.