Avishai Weiss

Extremum seeking-based iterative learning linear MPC

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 online the uncertain parameters and update the MPC model. We show the effectiveness of this algorithm on a DC servo motor control example.

Path planning using positive invariant sets

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 nonconvex 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.

MPC for coupled station keeping, attitude control, and momentum management of low-thrust geostationary satellites

This paper develops a model predictive control (MPC) policy for simultaneous station keeping, attitude control, and momentum management of a nadir-pointing geostationary satellite equipped with three reaction wheels and four gimbaled electric thrusters that are located on the anti-nadir face of the satellite. The MPC policy works in combination with an inner-loop SO(3)-based attitude controller that ensures the satellite maintains a nadir-pointing attitude. The MPC policy is able to maintain the satellites position within a prescribed latitude and longitude window, while minimizing the Δv required by the thrusters. The MPC policy also enforces thruster pointing constraints and manages the satellites stored momentum. With reference to simulation results, we explain how the MPC is tuned for station keeping, the need for an inner-loop attitude controller, and how these separate systems work together to achieve all the controllers objectives.

Opportunities and potential of model predictive control for low-thrust spacecraft station-keeping and momentum-management

While electric propulsion generates fuel-efficient thrust for spacecraft control, it can only produce low levels of thrust, necessitating continuous actuation to impart an equivalent impulse to that of chemical thrusters. Thus, many of the standard open-loop propulsion scheduling techniques, developed for impulsive thrust, do not transfer to low-thrust architectures. Continuous actuation, together with tighter anticipated requirements for spacecraft station keeping, e.g., in geostationary Earth orbit (GEO), provides great opportunity for the application of feedback control. We demonstrate that model predictive control (MPC) can provide significant advantages as a control strategy for station keeping of low-thrust spacecraft, provided that its features, such as the capability to enforce output constraints, and the use of a prediction model for the plant and disturbances, are fully exploited. We develop a basic MPC design for station keeping in GEO, and compare its performance with an advanced MPC design that includes output constraints and disturbance prediction. We show that the basic MPC achieves precise regulation, albeit with unsustainable fuel consumption, whereas the advanced MPC satisfies the target mission requirements with fuel consumption in line with that of carefully designed open-loop strategies.

Motion planning with invariant set trees

This paper introduces the planning algorithm Sa-feRRT, which extends the rapidly-exploring random tree (RRT) algorithm by using feedback control and positively invariant sets to guarantee collision-free closed-loop path tracking. The SafeRRT algorithm steers the output of a system from a feasible initial value to a desired goal, while satisfying input constraints and non-convex output constraints. The algorithm constructs a tree of local state-feedback controllers, each with a randomly sampled reference equilibrium and corresponding positively invariant set. The positively invariant sets indicate when it is possible to safely transition from one local controller to another without violating constraints. The tree is expanded from the desired goal until it contains the initial condition, at which point traversing the tree yields a dynamically feasible and safe closed-loop trajectory. We demonstrate SafeRRT on a spacecraft rendezvous example.

MPC for coupled station keeping, attitude control, and momentum management of GEO satellites using on-off electric propulsion

This paper develops a model predictive control (MPC) policy for simultaneous station keeping, attitude control, and momentum management of a nadir-pointing geostationary satellite equipped with three reaction wheels and four on-off electric thrusters mounted on two boom assemblies attached to the anti-nadir face of the satellite. A closed-loop pulse-width modulation (PWM) scheme is implemented in conjunction with the MPC policy in order to generate on-off commands to the thrusters. The MPC policy is shown to satisfy all station keeping and attitude constraints while managing stored momentum, enforcing thruster constraints, and minimizing required delta-v.