Abstract-We investigate the nonlinear exponential stability of the State-Dependent Riccati Equation (SDRE)-based control. The SDRE technique is a nonlinear control method, which has emerged since the mid 1990's and has been applied to a wide range of nonlinear control problems. Despite the systematic method of SDRE, it is difficult to prove stability because the general analytic solution to the SDRE is not known. Some notable prior work has shown local asymptotic stability of SDRE by using numerical and analytical methods. In this paper, we introduce a new strategy, based on contraction analysis, to estimate the exponential stability region for SDRE controlled systems. Examples demonstrate the superiority of the proposed method.
This paper investigates exact nonlinear dynamics and cooperative control for spacecraft formation flying with Earth oblateness (J2 perturbation) and atmospheric drag effects. The nonlinear dynamics for chief and deputy motions are derived by using Gauss' variational equation and the Euler-Lagrangian formulation, respectively. The proposed cooperative control employs adaptive time-varying Laplacian gains. The tracking and diffusive coupling gains are adapted by the synchronization/tracking errors and distance-based connectivity, thereby defining a time-varying network topology. Moreover, the proposed method relaxes the network structure requirement and permits an unbalanced graph. Nonlinear stability is proven by contraction analysis and incremental input-to-state stability. Numerical examples show the effectiveness of the proposed method.
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