Prescribed Performance Control for Signal Temporal Logic Specifications

Motivated by the recent interest in formal methods-based control for dynamic robots, we discuss the applicability of prescribed performance control to nonlinear systems subject to signal temporal logic specifications. Prescribed performance control imposes a desired transient behavior on the system trajectories that is leveraged to satisfy atomic signal temporal logic specifications. A hybrid control strategy is then used to satisfy a finite set of these atomic specifications. Simulations of a multi-agent system, using consensus dynamics, show that a wide range of specifications, i.e., formation, sequencing, and dispersion, can be robustly satisfied.Comment: 9 pages - this an extended version of the 56th IEEE Conference on Decision and Control (2017) versio

Coarse-grained Classification of Web Sites by Their Structural Properties

In this paper, we identify and analyze structural properties which reflect the functionality of a Web site. These structural properties consider the size, the organization, the composition of URLs, and the link structure of Web sites. Opposed to previous work, we perform a comprehensive measurement study to delve into the relation between the structure and the functionality of Web sites. Our study focuses on five of the most relevant functional classes, namely Academic, Blog, Corporate, Personal, and Shop. It is based upon more than 1,400 Web sites composed of 7 million crawled and 47 million known Web pages. We present a detailed statistical analysis which provides insight into how structural properties can be used to distinguish between Web sites from different functional classes. Building on these results, we introduce a content-independent approach for the automated coarse-grained classification of Web sites. A naïve Bayesian classifier with advanced density estimation yields a precision of 82% and recall of 80% for the classification of Web sites into the considered classes

Efficient STL Control Synthesis under Asynchronous Temporal Robustness Constraints

In time-critical systems, such as air traffic control systems, it is crucial to design control policies that are robust to timing uncertainty. Recently, the notion of Asynchronous Temporal Robustness (ATR) was proposed to capture the robustness of a system trajectory against individual time shifts in its sub-trajectories. In a multi-robot system, this may correspond to individual robots being delayed or early. Control synthesis under ATR constraints is challenging and has not yet been addressed. In this paper, we propose an efficient control synthesis method under ATR constraints which are defined with respect to simple safety or complex signal temporal logic specifications. Given an ATR bound, we compute a sequence of control inputs so that the specification is satisfied by the system as long as each sub-trajectory is shifted not more than the ATR bound. We avoid combinatorially exploring all shifted sub-trajectories by first identifying redundancy between them. We capture this insight by the notion of instant-shift pair sets, and then propose an optimization program that enforces the specification only over the instant-shift pair sets. We show soundness and completeness of our method and analyze its computational complexity. Finally, we present various illustrative case studies.Comment: This paper was accepted to CDC202

Funktionale Charakterisierung von TRPC-Kanälen bei der Chemotaxis neutrophiler Granulozyten

Der Mechanismus der Chemotaxis umfasst innerhalb der Zelle einen Signalkomplex, der den Zellen ermöglicht, das Signal von Chemoattraktanzien über spezifische Oberflächenrezeptoren innerhalb der Zelle zu verstärken und über Signalkaskaden unter anderem eine gerichtete Bewegung der Zelle einzuleiten. Ein Schlüsselelement innerhalb dieses Signalkomplexes bildet Ca2+. Die molekulare Identität der an der Chemotaxis beteiligten Ca2+-Ionenkanäle konnte aber bisher nur unvollständig geklärt werden und so sollte mit dieser Arbeit die Rolle von zwei TRPC- Kanälen, dem TRPC1 und dem TRPC6, innerhalb der Chemotaxis neutrophiler Granulozyten untersucht werden. Im Rahmen der vorliegenden Arbeit konnte mithilfe von in vitro Chemotaxisstudien die Abhängigkeit von zwei Chemoattraktanz-Rezeptor-Signalwegen von diesen beiden TRPC-Kanälen bei der Chemotaxis muriner neutrophiler Granulozyten nachgewiesen werden

Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference

We consider data-driven reachability analysis of discrete-time stochastic dynamical systems using conformal inference. We assume that we are not provided with a symbolic representation of the stochastic system, but instead have access to a dataset of $K$-step trajectories. The reachability problem is to construct a probabilistic flowpipe such that the probability that a $K$-step trajectory can violate the bounds of the flowpipe does not exceed a user-specified failure probability threshold. The key ideas in this paper are: (1) to learn a surrogate predictor model from data, (2) to perform reachability analysis using the surrogate model, and (3) to quantify the surrogate model's incurred error using conformal inference in order to give probabilistic reachability guarantees. We focus on learning-enabled control systems with complex closed-loop dynamics that are difficult to model symbolically, but where state transition pairs can be queried, e.g., using a simulator. We demonstrate the applicability of our method on examples from the domain of learning-enabled cyber-physical systems

Safe Planning in Dynamic Environments using Conformal Prediction

We propose a framework for planning in unknown dynamic environments with probabilistic safety guarantees using conformal prediction. Particularly, we design a model predictive controller (MPC) that uses i) trajectory predictions of the dynamic environment, and ii) prediction regions quantifying the uncertainty of the predictions. To obtain prediction regions, we use conformal prediction, a statistical tool for uncertainty quantification, that requires availability of offline trajectory data - a reasonable assumption in many applications such as autonomous driving. The prediction regions are valid, i.e., they hold with a user-defined probability, so that the MPC is provably safe. We illustrate the results in the self-driving car simulator CARLA at a pedestrian-filled intersection. The strength of our approach is compatibility with state of the art trajectory predictors, e.g., RNNs and LSTMs, while making no assumptions on the underlying trajectory-generating distribution. To the best of our knowledge, these are the first results that provide valid safety guarantees in such a setting

Conformal Prediction Regions for Time Series using Linear Complementarity Programming

Conformal prediction is a statistical tool for producing prediction regions of machine learning models that are valid with high probability. However, applying conformal prediction to time series data leads to conservative prediction regions. In fact, to obtain prediction regions over $T$ time steps with confidence $1-\delta$, {previous works require that each individual prediction region is valid} with confidence $1-\delta/T$. We propose an optimization-based method for reducing this conservatism to enable long horizon planning and verification when using learning-enabled time series predictors. Instead of considering prediction errors individually at each time step, we consider a parameterized prediction error over multiple time steps. By optimizing the parameters over an additional dataset, we find prediction regions that are not conservative. We show that this problem can be cast as a mixed integer linear complementarity program (MILCP), which we then relax into a linear complementarity program (LCP). Additionally, we prove that the relaxed LP has the same optimal cost as the original MILCP. Finally, we demonstrate the efficacy of our method on a case study using pedestrian trajectory predictors