Measures and Linear Matrix Inequalities for Verification and Validation of a Flexible Aircraft with Adaptive Control

Occupations measures and linear matrix inequality (LMI) relaxations (called the moment sums-of-squares or Lasserre hierarchy) can be used for verification and validation (VV) of adaptive control with piecewise polynomial dynamics and uncertain parameters. Specifically, we investigate the susceptibility to closed-loop instability for model reference adaptive control in the presence of large parameter uncertainties and/or unmodeled dynamics. In this document, we use our VV framework to validate a linear/polynomial F-16 model with MRAC and flexible dynamics with uncertain coupling. This is accomplished by addressing the uncertainties explicitly in the space of occupation measures and through exploiting sparsity for ordinary differential equations (ODEs). We show numerically that the closed-loop with simple model reference adaptive control (MRAC) can tolerate these phenomena at certain limits. This is achieved without the expense of conservative Lyapunov estimates and/or complex control law modifications. These numerical certificates guarantee finite-time convergence and the boundedness of all trajectories constrained in compact semi-algebraic sets. For comparison, worst-case behavior of the closed-loop is also obtained using Monte-Carlo simulations