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Abstract This article presents an extremum‐seeking control (ESC) algorithm for unmodeled nonlinear systems with known steady‐state gain and generally non‐convex cost functions with bounded curvature. The main contribution of this article is a novel gradient estimator, which uses a polyhedral set that characterizes all gradient estimates consistent with the collected data. The gradient estimator is posed as a quadratic program, which selects the gradient estimate that provides the best worst‐case convergence of the closed‐loop Lyapunov function. We show that the polyhedral‐based gradient estimator ensures the stability of the closed‐loop system formed by the plant and optimization algorithm. Furthermore, the estimated gradient provably produces the optimal robust convergence. We demonstrate our ESC controller through three benchmark examples and one practical example, which shows our ESC has fast and robust convergence to the optimal equilibrium. 

This paper experimentally validates the invariant-set motion planner (ISMP) for the spacecraft attitude motion planning problem. Three novel results are presented that enable the experimental implementation: i) a method for gridding quaternions from the keep-in cone, ii) a method for scaling the invariant sets to enforce angular velocity constraints, and iii) a method for scaling the sets used by the ISMP to ensure their positive invariance despite this torque constraint. The ISMP is experimentally validated through three experimental scenarios. In the first scenario, the spacecraft must perform a re-orientation maneuver that caused it to move toward a keep-out cone. The ISMP manages the momentum of the spacecraft to prevent it from overshooting into the keep-out cone. In the second scenario, the spacecraft performs a slalom maneuver to avoid a pair of keep-out cones. The ISMP must reverse the momentum of the spacecraft to transition from avoiding the first keep-out cone to the second. The final scenario is an unrealistically difficult scenario designed to stress-test the capabilities of the ISMP where the spacecraft must escape from a maze of keep-out cones. These results demonstrate the ability of the ISMP to control the spacecraft attitude while enforcing state and input constraints.