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

Spatio-temporal logics for verification and control of networked systems

Emergent behaviors in networks of locally interacting dynamical systems have been a topic of great interest in recent years. As the complexity of these systems increases, so does the range of emergent properties that they exhibit. Due to recent developments in areas such as synthetic biology and multi-agent robotics, there has been a growing necessity for a formal and automated framework for studying global behaviors in such networks. We propose a formal methods approach for describing, verifying, and synthesizing complex spatial and temporal network properties. Two novel logics are introduced in the first part of this dissertation: Tree Spatial Superposition Logic (TSSL) and Spatial Temporal Logic (SpaTeL). The former is a purely spatial logic capable of formally describing global spatial patterns. The latter is a temporal extension of TSSL and is ideal for expressing how patterns evolve over time. We demonstrate how machine learning techniques can be utilized to learn logical descriptors from labeled and unlabeled system outputs. Moreover, these logics are equipped with quantitative semantics and thus provide a metric for distance to satisfaction for randomly generated system trajectories. We illustrate how this metric is used in a statistical model checking framework for verification of networks of stochastic systems. The parameter synthesis problem is considered in the second part, where the goal is to determine static system parameters that lead to the emergence of desired global behaviors. We use quantitative semantics to formulate optimization procedures with the purpose of tuning system inputs. Particle swarm optimization is employed to efficiently solve these optimization problems, and the efficacy of this framework is demonstrated in two applications: biological cell networks and smart power grids. The focus of the third part is the control synthesis problem, where the objective is to find time-varying control strategies. We propose two approaches to solve this problem: an exact solution based on mixed integer linear programming, and an approximate solution based on gradient descent. These algorithms are not restricted to the logics introduced in this dissertation and can be applied to other existing logics in the literature. Finally, the capabilities of our framework are shown in the context of multi-agent robotics and robotic swarms

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

Risk of Stochastic Systems for Temporal Logic Specifications

The wide availability of data coupled with the computational advances in artificial intelligence and machine learning promise to enable many future technologies such as autonomous driving. While there has been a variety of successful demonstrations of these technologies, critical system failures have repeatedly been reported. Even if rare, such system failures pose a serious barrier to adoption without a rigorous risk assessment. This paper presents a framework for the systematic and rigorous risk verification of systems. We consider a wide range of system specifications formulated in signal temporal logic (STL) and model the system as a stochastic process, permitting discrete-time and continuous-time stochastic processes. We then define the STL robustness risk as the risk of lacking robustness against failure. This definition is motivated as system failures are often caused by missing robustness to modeling errors, system disturbances, and distribution shifts in the underlying data generating process. Within the definition, we permit general classes of risk measures and focus on tail risk measures such as the value-at-risk and the conditional value-at-risk. While the STL robustness risk is in general hard to compute, we propose the approximate STL robustness risk as a more tractable notion that upper bounds the STL robustness risk. We show how the approximate STL robustness risk can accurately be estimated from system trajectory data. For discrete-time stochastic processes, we show under which conditions the approximate STL robustness risk can even be computed exactly. We illustrate our verification algorithm in the autonomous driving simulator CARLA and show how a least risky controller can be selected among four neural network lane keeping controllers for five meaningful system specifications