Vinayak S. Prabhu

Samira S. Farahani, Rupak Majumdar, Vinayak Prabhu et al.

We present Shrinking Horizon Model Predictive Control (SHMPC) for discrete-time linear systems with Signal Temporal Logic (STL) specification constraints under stochastic disturbances. The control objective is to maximize an optimization function under the restriction that a given STL specification is satisfied with high probability against stochastic uncertainties. We formulate a general solution, which does not require precise knowledge of the probability distributions of the (possibly dependent) stochastic disturbances; only the bounded support intervals of the density functions and moment intervals are used. For the specific case of disturbances that are independent and normally distributed, we optimize the controllers further by utilizing knowledge of the disturbance probability distributions. We show that in both cases, the control law can be obtained by solving optimization problems with linear constraints at each step. We experimentally demonstrate effectiveness of this approach by synthesizing a controller for an HVAC system.

Jyotirmoy V. Deshmukh, Xiaoqing Jin, Rupak Majumdar et al.

Embedded controllers for cyber-physical systems are often parameterized by look-up maps representing discretizations of continuous functions on metric spaces. For example, a non-linear control action may be represented as a table of pre-computed values, and the output action of the controller for a given input is computed by using interpolation. For industrial-scale control systems, several man-hours of effort is spent in tuning the values within the look-up maps, and sub-optimal performance is often associated with inappropriate values in look-up maps. Suppose that during testing, the controller code is found to have sub-optimal performance. The parameter fault localization problem asks which parameter values in the code are potential causes of the sub-optimal behavior. We present a statistical parameter fault localization approach based on binary similarity coefficients and set spectra methods. Our approach extends previous work on software fault localization to a quantitative setting where the parameters encode continuous functions over a metric space and the program is reactive. We have implemented our approach in a simulation workflow for automotive control systems in Simulink. Given controller code with parameters (including look-up maps), our framework bootstraps the simulation workflow to return a ranked list of map entries which are deemed to have most impact on the performance. On a suite of industrial case studies with seeded errors, our tool was able to precisely identify the location of the errors.

Alperen Tercan, Vinayak S. Prabhu

Lexicographic multi-objective problems, which impose a lexicographic importance order over the objectives, arise in many real-life scenarios. Existing Reinforcement Learning work directly addressing lexicographic tasks has been scarce. The few proposed approaches were all noted to be heuristics without theoretical guarantees as the Bellman equation is not applicable to them. Additionally, the practical applicability of these prior approaches also suffers from various issues such as not being able to reach the goal state. While some of these issues have been known before, in this work we investigate further shortcomings, and propose fixes for improving practical performance in many cases. We also present a policy optimization approach using our Lexicographic Projection Optimization (LPO) algorithm that has the potential to address these theoretical and practical concerns. Finally, we demonstrate our proposed algorithms on benchmark problems.

Rayna Dimitrova, Rupak Majumdar, Vinayak S. Prabhu

We present a comprehensive language theoretic causality analysis framework for explaining safety property violations in the setting of concurrent reactive systems. Our framework allows us to uniformly express a number of causality notions studied in the areas of artificial intelligence and formal methods, as well as define new ones that are of potential interest in these areas. Furthermore, our formalization provides means for reasoning about the relationships between individual notions which have mostly been considered independently in prior work; and allows us to judge the appropriateness of the different definitions for various applications in system design. In particular, we consider causality analysis notions for debugging, error resilience, and liability resolution in concurrent reactive systems. Finally, we present automata-based algorithms for computing various causal sets based on our language-theoretic encoding, and derive the algorithmic complexities.

Rayna Dimitrova, Ivan Gavran, Rupak Majumdar et al.

We propose a new model for formalizing reward collection problems on graphs with dynamically generated rewards which may appear and disappear based on a stochastic model. The *robot routing problem* is modeled as a graph whose nodes are stochastic processes generating potential rewards over discrete time. The rewards are generated according to the stochastic process, but at each step, an existing reward disappears with a given probability. The edges in the graph encode the (unit-distance) paths between the rewards' locations. On visiting a node, the robot collects the accumulated reward at the node at that time, but traveling between the nodes takes time. The optimization question asks to compute an optimal (or epsilon-optimal) path that maximizes the expected collected rewards. We consider the finite and infinite-horizon robot routing problems. For finite-horizon, the goal is to maximize the total expected reward, while for infinite horizon we consider limit-average objectives. We study the computational and strategy complexity of these problems, establish NP-lower bounds and show that optimal strategies require memory in general. We also provide an algorithm for computing epsilon-optimal infinite paths for arbitrary epsilon > 0.

Jyotirmoy V. Deshmukh, Rupak Majumdar, Vinayak S. Prabhu

The conformance testing problem for dynamical systems asks, given two dynamical models (e.g., as Simulink diagrams), whether their behaviors are "close" to each other. In the semi-formal approach to conformance testing, the two systems are simulated on a large set of tests, and a metric, defined on pairs of real-valued, real-timed trajectories, is used to determine a lower bound on the distance. We show how the Skorkhod metric on continuous dynamical systems can be used as the foundation for conformance testing of complex dynamical models. The Skorokhod metric allows for both state value mismatches and timing distortions, and is thus well suited for checking conformance between idealized models of dynamical systems and their implementations. We demonstrate the robustness of the system conformance quantification by proving a \emph{transference theorem}: trajectories close under the Skorokhod metric satisfy "close" logical properties. Specifically, we show the result for the timed linear time logic \TLTL augmented with a rich class of temporal and spatial constraint predicates. We provide a window-based streaming algorithm to compute the Skorokhod metric, and use it as a basis for a conformance testing tool for Simulink. We experimentally demonstrate the effectiveness of our tool in finding discrepant behaviors on a set of control system benchmarks, including an industrial challenge problem.