Formal methods paradigms for estimation and machine learning in dynamical systems
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Formal methods are widely used in engineering to determine whether a system exhibits a certain property (verification) or to design controllers that are guaranteed to drive the system to achieve a certain property (synthesis). Most existing techniques require a large amount of accurate information about the system in order to be successful. The methods presented in this work can operate with significantly less prior information. In the domain of formal synthesis for robotics, the assumptions of perfect sensing and perfect knowledge of system dynamics are unrealistic. To address this issue, we present control algorithms that use active estimation and reinforcement learning to mitigate the effects of uncertainty. In the domain of cyber-physical system analysis, we relax the assumption that the system model is known and identify system properties automatically from execution data. First, we address the problem of planning the path of a robot under temporal logic constraints (e.g. "avoid obstacles and periodically visit a recharging station") while simultaneously minimizing the uncertainty about the state of an unknown feature of the environment (e.g. locations of fires after a natural disaster). We present synthesis algorithms and evaluate them via simulation and experiments with aerial robots. Second, we develop a new specification language for tasks that require gathering information about and interacting with a partially observable environment, e.g. "Maintain localization error below a certain level while also avoiding obstacles.'' Third, we consider learning temporal logic properties of a dynamical system from a finite set of system outputs. For example, given maritime surveillance data we wish to find the specification that corresponds only to those vessels that are deemed law-abiding. Algorithms for performing off-line supervised and unsupervised learning and on-line supervised learning are presented. Finally, we consider the case in which we want to steer a system with unknown dynamics to satisfy a given temporal logic specification. We present a novel reinforcement learning paradigm to solve this problem. Our procedure gives "partial credit'' for executions that almost satisfy the specification, which can lead to faster convergence rates and produce better solutions when the specification is not satisfiable.