Learning Spatio-Temporal Specifications for Dynamical Systems

Learning dynamical systems properties from data provides important insights that help us understand such systems and mitigate undesired outcomes. In this work, we propose a framework for learning spatio-temporal (ST) properties as formal logic specifications from data. We introduce SVM-STL, an extension of Signal Signal Temporal Logic (STL), capable of specifying spatial and temporal properties of a wide range of dynamical systems that exhibit time-varying spatial patterns. Our framework utilizes machine learning techniques to learn SVM-STL specifications from system executions given by sequences of spatial patterns. We present methods to deal with both labeled and unlabeled data. In addition, given system requirements in the form of SVM-STL specifications, we provide an approach for parameter synthesis to find parameters that maximize the satisfaction of such specifications. Our learning framework and parameter synthesis approach are showcased in an example of a reaction-diffusion system.Comment: 12 pages, submitted to L4DC 202

Neural Network-based Control for Multi-Agent Systems from Spatio-Temporal Specifications

We propose a framework for solving control synthesis problems for multi-agent networked systems required to satisfy spatio-temporal specifications. We use Spatio-Temporal Reach and Escape Logic (STREL) as a specification language. For this logic, we define smooth quantitative semantics, which captures the degree of satisfaction of a formula by a multi-agent team. We use the novel quantitative semantics to map control synthesis problems with STREL specifications to optimization problems and propose a combination of heuristic and gradient-based methods to solve such problems. As this method might not meet the requirements of a real-time implementation, we develop a machine learning technique that uses the results of the off-line optimizations to train a neural network that gives the control inputs at current states. We illustrate the effectiveness of the proposed framework by applying it to a model of a robotic team required to satisfy a spatial-temporal specification under communication constraints.Comment: 8 pages. Submitted to the CDC 202

Learning a Tracking Controller for Rolling μ\mubots

Micron-scale robots ($\mu$bots) have recently shown great promise for emerging medical applications. Accurate controlling $\mu$bots, while critical to their successful deployment, is challenging. In this work, we consider the problem of tracking a reference trajectory using a $\mu$bot in the presence of disturbances and uncertainty. The disturbances primarily come from Brownian motion and other environmental phenomena, while the uncertainty originates from errors in the model parameters. We model the $\mu$bot as an uncertain unicycle that is controlled by a global magnetic field. To compensate for disturbances and uncertainties, we develop a nonlinear mismatch controller. We define the model mismatch error as the difference between our model's predicted velocity and the actual velocity of the $\mu$bot. We employ a Gaussian Process to learn the model mismatch error as a function of the applied control input. Then we use a least-squares minimization to select a control action that minimizes the difference between the actual velocity of the $\mu$bot and a reference velocity. We demonstrate the online performance of our joint learning and control algorithm in simulation, where our approach accurately learns the model mismatch and improves tracking performance. We also validate our approach in an experiment and show that certain error metrics are reduced by up to $40\%$.Comment: 8 pages, 9 figure

Spatio-temporal logics, learning, and synthesis for multi-agent systems

Multi-agent systems (MAS) are used as models for many natural and engineered systems, such as robotic teams and cell-cell interactions. Such systems exhibit time-varying spatial (spatio-temporal) behaviors. As the complexity of MAS increases, there is a need to express their behaviors in formal ways that are interpretable to humans and amenable to rigorous mathematical analysis. In this thesis, we propose using spatio-temporal (ST) logics to write up such expressions. In addition, we address two closely related challenges 1) inferring ST logic expressions from data (the inference problem) and 2) synthesizing system inputs such that the MAS outputs meet specific behavioral requirements given by ST logic expressions (the synthesis problem). We consider two distinct MAS types 1) patterning chemical and biological systems and 2) robotic teams. Overall, this thesis has three main parts. First, we develop ST logics that are (1) capable of describing emerging MAS behaviors and (2) equipped with qualitative and quantitative (robustness metric) semantics. The qualitative semantics address the question "are the requirements satisfied/violated?" while the quantitative semantics address the question "how well are the requirements satisfied/violated?" Second, we develop several techniques for inferring ST logics expressions from executions of patterning systems. The proposed techniques utilize unsupervised and supervised learning techniques to learn the structure and parameters of logical expressions. Third, we propose several methods to solve the synthesis problem when requirements are given by the ST logic formulae. We formulate the synthesis problems as optimization problems where the objective is to maximize the robustness metric, thus satisfying the requirements. We outline our approach for solving optimization problems and learning controllers using optimization and deep learning techniques. We demonstrate the efficacy of the proposed algorithms and tools in simulated examples of patterning systems and robotic teams. We conclude with a discussion about the limitations and future research directions.2025-01-16T00:00:00