Nonlinear Robust Performance Analysis using Gradient-Based Optimisation - An Aeroelastic Case-Study

This paper considers the problem of computing lower bounds on the worst-case performance of nonlinear systems using gradient-based optimisation. Four different gradient-based local optimisation methods are applied to a robust performance analysis problem for a nonlinear aeroelastic system. The first method formulates the optimisation problem in the classical Euler-Lagrange setting and computes the gradient by backward integration of the resulting adjoint system. The second method also uses the Euler-Lagrange formulation, but uses complex perturbations to calculate the gradient. The third method employs Sequential Quadratic Programming, while the fourth method considered is Simultaneous Perturbation Stochastic Approximation (SPSA), which uses a stochastic approach to decide the search direction. The performance of all four methods is evaluated in terms of computational complexity, numerical accuracy, and ease of implementation, and compared with a standard industrial approach based on a gridding of the uncertain parameter space.