Control-Oriented Design Using Surrogate-Based Optimization and Existence Conditions for Robust Performance

Abstract

M ISSION capability of a vehicle is ultimately evaluated by closed-loop performance. Such capability depends on a synergistic integration of aerodynamics, structures, propulsion, and control, which results in flight dynamics that are optimal for the mission. Unfortunately, most systems such as aircraft are traditionally designed using a sequential series of open-loop optimizations that cannot account for, or optimize, any synergistic integrations. A formulation for design that inherently considers control must therefore be developed to enable optimal closed-loop performance. The issue of cost function is actually quite critical to the inclusion of control synthesis for design optimization. Every discipline has metrics that are unique to their objectives, so a single cost that encompasses all these metrics can be challenging to formulate. One approach that considers vibration control uses norms, both for vibration level and effort, as a cost in a linear-quadratic framework [1]. A mixed-norm approach is formulated that considers both H2 andH1 in summation to represent independent metrics of the design [2]. A positive-real condition across frequency is also introduced as a cost that has time-domain interpretations for design [3]. Several formulations formulate cost functions and solution methodologies for designs that include linear matrix inequalities (LMIs) associated with H1-norm synthesis. One generates a nonconvex formulation and uses iterations to solve the associated optimization [4]. Another approximates functions associated with perturbed state-spacematrices as LMIs to be solved using an iterative approach [5]. A two-step procedure is used for an optimization coupled with an LMI solver for the controller [6] as an multidisciplinary optimization approach. Another approach considers an iterative sequential control design and a coupled redesign with each iteration involving the solution of an LMI [7]. This Note introduces a control-oriented approach for design that avoids the common difficulties of simultaneous structure-control design, which is known to be nonconvex [8–11]. The approach actually considers an existence question that notes if a controller exists for a given structure that achieves a desired level of performance. The approach does not design both the structure and control to optimize a closed-loop norm; rather, it designs a structure for which a controller exists that optimizes a closed-loop norm. Formulations using control synthesis to minimize an H1-norm metric and anH2-norm are derived using their appropriate existence conditions. As important, a solution methodology is used based on surrogate modeling to avoid the iterations and expensive computations associated with techniques doing design with LMI expressions. The surrogate-based optimization is shown to be efficient and effective and exploring a design space to optimize the closed-loop metric.