In this thesis, the problem of designing model discrimination algorithms for unknown nonlinear systems is considered, where only raw experimental data of the system is available. This kind of model discrimination techniques finds one of its application in the estimation of the system or intent models under consideration, where all incompatible models are invalidated using new data that is available at run time. The proposed steps to reach the end goal of the algorithm for intention estimation involves two steps: First, using available experimental data of system trajectories, optimization-based techniques are used to over-approximate/abstract the dynamics of the system by constructing an upper and lower function which encapsulates/frames the true unknown system dynamics. This over-approximation is a conservative preservation of the dynamics of the system, in a way that ensures that any model which is invalidated against this approximation is guaranteed to be invalidated with the actual model of the system. The next step involves the use of optimization-based techniques to investigate the distinguishability of pairs of abstraction/approximated models using an algorithm for 'T-Distinguishability', which gives a finite horizon time 'T', within which the pair of models are guaranteed to be distinguished, and to eliminate incompatible models at run time using a 'Model Invalidation' algorithm. Furthermore, due the large amount of data under consideration, some computation-aware improvements were proposed for the processing of the raw data and the abstraction and distinguishability algorithms.The effectiveness of the above-mentioned algorithms is demonstrated using two examples. The first uses the data collected from the artificial simulation of a swarm of agents, also known as 'Boids', that move in certain patterns/formations, while the second example uses the 'HighD' dataset of naturalistic trajectories recorded on German Highways for vehicle intention estimation.

JOOEE is a cube-shaped lunar robot with a simple yet robust design. JOOEE ishermetically sealed from its environment with no external actuators. Instead, JOOEE spins three internal orthogonal flywheels to accumulate angular momentum and uses a solenoid brake at each wheel to transfer the angular momentum to the body. This procedure allows JOOEE to jump and hop along the lunar surface. The sudden transfer in angular momentum during braking causes discontinuities in JOOEE’s dynamics that are best described using a hybrid control framework. Due to the irregular methods of locomotion, the limited resources on the lunar surface, and the unique mission objectives, optimal control profiles are desired to minimize performance metrics such as time, energy, and impact velocity during different maneuvers. This paper details the development of an optimization tool that can handle JOOEE’s dynamics including the design of a hybrid control framework, dynamics modeling and discretization, optimization cost functions and constraints, model validation, and code acceleration techniques.

This thesis proposes novel set-theoretic approaches for polytopic state estimationin bounded- error discrete-time nonlinear systems with nonlinear observations or constraints. Specically, our approaches rely on two equivalent representations of polytopic sets known as zonotope bundles (ZB) and constrained zonotopes (CZ), which allows us to transform the state space to the space of the generators of the ZB/CZ that are generally interval-valued. This transformation enables us to leverage a recent result on remainder-form mixed-monotone decomposition functions for interval propagation to compute the propagated set estimate, i.e., a polytope that is guaranteed to enclose the set of the state trajectories of a nonlinear dynamical system. Furthermore, a similar procedure with state transformation and remainderform decomposition functions can be applied to the nonlinear observation function to compute the updated set estimate, i.e., an enclosing polytope of the set of states from the propagated set estimate that are compatible/consistent with the observations/ constraints. In addition, we also show that a mean value extension result for computing the propagated set estimate in the literature can also be extended to compute the updated set estimation when the observation/constraint function is nonlinear. Finally, the eectiveness of our proposed techniques is demonstrated using two simulation examples and compared with existing methods in the literature.