Control Methodologies for Systems with Set-Valued Uncertainties

Abstract

This dissertation develops control methodologies for systems with set-valued uncertainties in modeling and estimation, with applications spanning spacecraft navigation and neuromodulation. The work is organized into two major parts. The first part addresses estimation-related uncertainties in vision-guided navigation and their integration into planning and control. The second part focuses on modeling uncertainty in neuronal systems, presenting a controller design and model inference framework for neuromodulation.In the context of spacecraft navigation, we design a pose-estimation pipeline supported by a photorealistic simulation environment for satellite rendezvous operations. A Machine Learning (ML)-based platform is developed to detect the pose of a target spacecraft, and the simulation environment is used to generate test and validation data with a minimal simulation-to-reality (sim2real) gap. The platform also serves as a tool for modeling ML-based uncertainties, thereby enabling robust controller design. Building on this foundation, two approaches are proposed for incorporating ML-based estimation into navigation systems. The first introduces a controller design methodology that constructs invariant funnels for slope-bounded uncertainty models around nominal trajectories. The second employs a passivity-based framework to characterize uncertainties that define a family of feasible controllers. Furthermore, we demonstrate that multi-agent consensus, viewed as an interconnection of passive agents, can enhance estimation performance in distributed settings. We further investigate estimation-aware trajectory design for improving the performance of state-dependent sensors such as perception maps. A class of state-dependent, set-valued output uncertainty models is formalized as state-to-output uncertainty set maps. An observability-based metric is introduced to quantify the estimator’s sensitivity to output perturbations, and this metric is optimized to generate trajectories that improve estimation performance. Extensions of this framework to multi-agent trajectory planning are also presented. The final part of the dissertation develops a feedback control framework for neuromodulation. By analyzing neuronal system trajectories during experimental sessions, we show that average neuronal dynamics in closed-loop scenarios can be approximated as a linear parameter-dependent system, with parameter-dependent internal processes. For a fixed parameter, the trial-averaged dynamics exhibit closed-loop linear behavior. A proportional–integral (PI) feedback controller is demonstrated to effectively track reference signals over a finite horizon, outperforming feedforward control in both tracking accuracy and disturbance rejection, while also reducing trial-to-trial variability. Moreover, in a ``reward-induced'' brain state with more consistent parameters, a sample-based approach is shown to enable controller optimization. Together, these contributions advance the integration of machine learning, robust control, and trajectory optimization in the presence of set-valued uncertainty, providing new methodologies for controlling uncertain dynamical systems in both engineering and biological domains.