Adaptive boundary sine cosine optimizer with population reduction for robustness analysis of finite time horizon systems

Abstract

This paper proposes an adaptive boundary sine cosine optimizer with population reduction. It is designed specifically to calculate an upper bound on the worst-case gain of a known finite horizon Linear Time Varying (LTV) system and a perturbation. The input/output behavior of the perturbation is described by a time domain Integral Quadratic Constraint (IQC). The analysis condition is formulated as a parametric Riccati differential equation which depends on the IQC representation. A nonlinear optimization problem is posed that minimizes the upper bound on the worst-case gain over the IQC parameterization. For industrial size applications like a space launcher, the number of decision variables can grow arbitrarily large depending on the number of considered perturbations as well as the type and representation of the IQC. This is aggravated by nonlinear constraints on the decision variables imposed by the Riccati differential equation making it challenging to solve. Several established Meta-Heuristics (MHs) along with the proposed algorithm are applied to an industry size worst case analysis of a space launcher during its atmospheric ascend. Their respective performances are evaluated to emphasize the advantages of the developed optimizer. This work builds the foundation of applying MHs to IQC based robustness analysis of finite horizon LTV systems.