Random matrices are widely used to estimate the extent of an elliptically contoured object. Usually, it is assumed that the measurements follow a normal distribution, with its standard deviation being proportional to the object’s extent. However, the random matrix approach can filter the center of gravity and the covariance matrix of measurements independently of the measurement model. This work considers the whole chain from data acquisition to the linear Kalman Filter with extension estimation as a reference plant. The input is the (unknown) ground truth (position and extent). The output is the filtered center of gravity and the filtered covariance matrix of the measurement distribution. A virtual measurement model emulates the behavior of the reference plant. The input of the virtual measurement model is adapted using the proposed algorithm until the output parameters of the virtual measurement model match the result of the reference plant. After the adaptation, the input to the virtual measurement model is considered an estimation for position and extent. The main contribution of this paper is the reference model concept and an adaptation algorithm to optimize the input of the virtual measurement model.

A constructive nonlinear observer design for self-sensing of digital (ON/OFF) single coil electromagnetic actuators is studied. Self-sensing in this context means that solely the available energizing signals, i.e., coil current and driving voltage are used to estimate the position and velocity trajectories of the moving plunger. A nonlinear sliding mode observer is considered, where the stability of the reduced error dynamics is analyzed by the equivalent control method. No simplifications are made regarding magnetic saturation and eddy currents in the underlying dynamical model. The observer gains are constructed by taking into account some generic properties of the systems nonlinearities. Two possible choices of the observer gains are discussed. Furthermore, an observer-based tracking control scheme to achieve sensorless soft landing is considered and its closed-loop stability is studied. Experimental results for observer-based soft landing of a fast-switching solenoid valve under dry conditions are presented to demonstrate the usefulness of the approach.

Model predictive path integral (MPPI) control has recently received a lot of attention, especially in the robotics and reinforcement learning communities. This letter aims to make the MPPI control framework more accessible to the optimal control community. We present three classes of optimal control problems and their solutions by MPPI. Further, we investigate the suboptimality of MPPI to general deterministic nonlinear discrete-time systems. Here, suboptimality is defined as the deviation between the control provided by MPPI and the optimal solution to the deterministic optimal control problem. Our findings are that in a smooth and unconstrained setting, the growth of suboptimality in the control input trajectory is second-order with the scaling of the MPPI exploration uncertainty. The results indicate that the suboptimality of the MPPI solution can be modulated by tuning the hyperparameters. We illustrate our findings using numerical examples.

In this paper, the performance of a particular state observer algorithm is investigated for concurrently estimating the state of charge of a Li-Ion battery and the deviation of characteristic parameters from their initial values in order to diagnose the aging behavior of the system. The estimation is based on an online minimization approach that has been chosen in particular due to the significant nonlinear behavior of the battery dynamics. The method has been introduced as the “Newtonstep observer” but could also been interpreted as a “sensitivity-based estimation”. The analysis is first made by simulations for comparison with known reference values. Here, we also compare the performance of Newton-type, Gauss-Newton-type and gradient-based optimizations. In a second step, experimental data from a battery that has been subject to an aging process with 400 charging/discharging cycles is used. Despite the fact that for the battery actual reference parameters are unavailable, the results show physically plausible trends. Moreover, the estimated capacity fading is particularly in very good agreement with the data provided by the manufacturer.