Exact State Sensitivity Calculation and its Role in Moving Horizon Estimation for Nonlinear Networked Control Systems

This paper deals with the exact state sensitivity calculation required in the moving horizon estimator (MHE) for nonlinear networked control systems (NCS) presented in [4]. This NCS-MHE is capable of dealing with the network induced imperfections by formulating the estimation problem as a suitable optimization problem within a moving horizon framework. The resulting nonlinear program (NLP) can be efficiently solved by an adapted sequential quadratic programming (SQP) approach which exploits the structure in the associated derivatives by utilizing state sensitivities. However, their exact calculation via direct derivation of the state is infeasible as no general closed form solution of the state equation can be given. Therefore, a new method based on first-order sensitivity differential equations is proposed which provides several advantages compared to a finite difference method, like e. g. exactness, reduced numerical complexity and a higher degree of parallelization.