Avishai Weiss

Yuri Shimane, Karl Berntorp, Stefano Di Cairano et al.

This article develops an optical navigation (OPNAV) and station-keeping pipeline for the near-rectilinear halo orbit (NRHO) in high-fidelity ephemeris model dynamics, using synthetic images of the Moon in a non-iterative horizon-based OPNAV algorithm, applying the result in a navigation filter, and using the obtained estimates in a station-keeping control scheme that keeps the spacecraft in the vicinity of a reference orbit. We study differential correction-based and minimization-based implementations of the so-called x-axis and propose an improved targeting prediction scheme by incorporating the filter's state covariance with an unscented transform. We also introduce a hysteresis mechanism, which improves stationkeeping cost and provides insight into the difference in performance between the differential correction-based and minimization-based approaches. We perform Monte-Carlo experiments to assess the pipeline's tracking and Delta-V performances. We report several key findings, including the variability of the filter performance with the sensor field of view and measurement locations, station-keeping cost reduction achieved by the unscented transform-based prediction and hysteresis, as well as the variability of the cumulative Delta-V as a function of maneuver location due to the periodic structure in the OPNAV-based filter's estimation accuracy.

Claus Danielson, Avishai Weiss, Karl Berntorp et al.

We present an algorithm for steering the output of a linear system from a feasible initial condition to a desired target position, while satisfying input constraints and non-convex output constraints. The system input is generated by a collection of local linear state-feedback controllers. The path-planning algorithm selects the appropriate local controller using a graph search, where the nodes of the graph are the local controllers and the edges of the graph indicate when it is possible to transition from one local controller to another without violating input or output constraints. We present two methods for computing the local controllers. The first uses a fixed-gain controller and scales its positive invariant set to satisfy the input and output constraints. We provide a linear program for determining the scale-factor and a condition for when the linear program has a closed-form solution. The second method designs the local controllers using a semi-definite program that maximizes the volume of the positive invariant set that satisfies state and input constraints. We demonstrate our path-planning algorithm on docking of a spacecraft. The semi-definite programming based control design has better performance but requires more computation.

Mouhacine Benosman, Stefano Di Cairano, Avishai Weiss

In this work we study the problem of adaptive MPC for linear time-invariant uncertain models. We assume linear models with parametric uncertainties, and propose an iterative multi-variable extremum seeking (MES)-based learning MPC algorithm to learn on-line the uncertain parameters and update the MPC model. We show the effectiveness of this algorithm on a DC servo motor control example.