Derivative-free Kalman Filtering for sensorless control of MIMO nonlinear dynamical systems

Abstract

The paper proposes derivative-free nonlinear Kalman Filtering and state estimation-based control for MIMO nonlinear dynamical systems. The considered nonlinear filtering scheme which is based on differential flatness theory extends the class of systems to which Kalman Filtering can be applied without the need for calculation of Jacobian matrices. Nonlinear systems satisfying the differential flatness property can be written in the Brunovsky (canonical) form via a transformation of their state variables and control inputs. After transforming the nonlinear system to the canonical form it is straightforward to apply the standard Kalman Filter recursion. The performance of the proposed derivative-free nonlinear filtering scheme is tested through simulation experiments on benchmark nonlinear multi-input multi-output dynamical systems, such as robotic manipulators.