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Publication Computer-Aided Design for Safe Autonomous Vehicles(2017-05-01) O'Kelly, Matthew; Abbas, Houssam; Mangharam, RahulThis paper details the design of an autonomous vehicle CAD toolchain, which captures formal descriptions of driving scenarios in order to develop a safety case for an autonomous vehicle (AV). Rather than focus on a particular component of the AV, like adaptive cruise control, the toolchain models the end-to-end dynamics of the AV in a formal way suitable for testing and verification. First, a domain-specific language capable of describing the scenarios that occur in the day-to-day operation of an AV is defined. The language allows the description and composition of traffic participants, and the specification of formal correctness requirements. A scenario described in this language is an executable that can be processed by a specification-guided automated test generator (bug hunting), and by an exhaustive reachability tool. The toolchain allows the user to exploit and integrate the strengths of both testing and reachability, in a way not possible when each is run alone. Finally, given a particular execution of the scenario that violates the requirements, a visualization tool can display this counter-example and generate labeled sensor data. The effectiveness of the approach is demonstrated on five autonomous driving scenarios drawn from a collection of 36 scenarios that account for over 95% of accidents nationwide. These case studies demonstrate robustness-guided verification heuristics to reduce analysis time, counterexample visualization for identifying controller bugs in both the discrete decision logic and low-level analog (continuous) dynamics, and identification of modeling errors that lead to unrealistic environment behavior.Publication Technical Report: Control Using the Smooth Robustness of Temporal Logic(2017-03-01) Pant, Yash Vardhan; Abbas, Houssam; Mangharam, RahulCyber-Physical Systems must withstand a wide range of errors, from bugs in their software to attacks on their physical sensors. Given a formal specification of their desired behavior in Metric Temporal Logic (MTL), the robust semantics of the specification provides a notion of system robustness that can be calculated directly on the output behavior of the system, without explicit reference to the various sources or models of the errors. The robustness of the MTL specification has been used both to verify the system offline (via robustness minimization) and to control the system online (to maximize its robustness over some horizon). Unfortunately, the robustness objective function is difficult to work with: it is recursively defined, non-convex and non-differentiable. In this paper, we propose smooth approximations of the robustness. Such approximations are differentiable, thus enabling us to use powerful off-the- shelf gradient descent algorithms for optimizing it. By using them we can also offer guarantees on the performance of the optimization in terms of convergence to minima. We show that the approximation error is bounded to any desired level, and that the approximation can be tuned to the specification. We demonstrate the use of the smooth robustness to control two quad-rotors in an autonomous air traffic control scenario, and for temperature control of a building for comfort.Publication Relaxed decidability and the robust semantics of Metric Temporal Logic(2017-02-16) Abbas, Houssam; O'Kelly, Matthew; Mangharam, RahulRelaxed notions of decidability widen the scope of automatic verification of hybrid systems. In quasi-decidability and $\delta$-decidability, the fundamental compromise is that if we are willing to accept a slight error in the algorithm's answer, or a slight restriction on the class of problems we verify, then it is possible to obtain practically useful answers. This paper explores the connections between relaxed decidability and the robust semantics of Metric Temporal Logic formulas. It establishes a formal equivalence between the robustness degree of MTL specifications, and the imprecision parameter $\delta$ used in $\delta$-decidability when it is used to verify MTL properties. We present an application of this result in the form of an algorithm that generates new constraints to the $\delta$-decision procedure from falsification runs, which speeds up the verification run. We then establish new conditions under which robust testing, based on the robust semantics of MTL, is in fact a quasi-semidecision procedure. These results allow us to delimit what is possible with fast, robustness-based methods, accelerate (near-)exhaustive verification, and further bridge the gap between verification and simulation.Publication Data Predictive Control for building energy management(2017-02-01) Jain, Achin; Behl, Madhur; Mangharam, RahulDecisions on how to best optimize energy systems operations are becoming ever so complex and conflicting, that model-based predictive control (MPC) algorithms must play an important role. However, a key factor prohibiting the widespread adoption of MPC in buildings, is the cost, time, and effort associated with learning first-principles based dynamical models of the underlying physical system. This paper introduces an alternative approach for implementing finite-time receding horizon control using control-oriented data-driven models. We call this approach Data Predictive Control (DPC). Specifically, by utilizing separation of variables, two novel algorithms for implementing DPC using a single regression tree and with regression trees ensembles (random forest) are presented. The data predictive controller enables the building operator to trade off energy consumption against thermal comfort without having to learn white/grey box models of the systems dynamics. We present a comprehensive numerical study which compares the performance of DPC with an MPC based energy management strategy, using a single zone building model. Our results demonstrate that performance of DPC is comparable to an MPC controller, with only 3.8% additional cost in terms of optimal objective function and within 95% in terms of R2 score, thereby making it an alluring alternative to MPC, whenever the associated cost of learning the model is high.Publication High-Level Modeling for Computer-Aided Clinical Trials of Medical Devices(2016-08-16) Abbas, Houssam; Jiang, Zhihao; Jang, Kuk Jin; Beccani, Marco; Liang, Jackson; Dixit, Sanjay; Mangharam, RahulPublication Robust Model Predictive Control for Non-Linear Systems with Input and State Constraints Via Feedback Linearization(2016-01-01) Pant, Yash Vardhan; Abbas, Houssam; Mangharam, RahulRobust predictive control of non-linear systems under state estimation errors and input and state constraints is a challenging problem, and solutions to it have generally involved solving computationally hard non-linear optimizations. Feedback linearization has reduced the computational burden, but has not yet been solved for robust model predictive control under estimation errors and constraints. In this paper, we solve this problem of robust control of a non-linear system under bounded state estimation errors and input and state constraints using feedback linearization. We do so by developing robust constraints on the feedback linearized system such that the non-linear system respects its constraints. These constraints are computed at run-time using online reachability, and are linear in the optimization variables, resulting in a Quadratic Program with linear constraints. We also provide robust feasibility, recursive feasibility and stability results for our control algorithm. We evaluate our approach on two systems to show its applicability and performance.Publication Data Predictive Control for Peak Power Reduction(2016-11-15) Jain, Achin; Behl, Madhur; Mangharam, RahulDecisions on how best to optimize today's energy systems operations are becoming ever so complex and conflicting such that model-based predictive control algorithms must play a key role. However, learning dynamical models of energy consuming systems such as buildings, using grey/white box approaches is very cost and time prohibitive due to its complexity. This paper presents data-driven methods for making control-oriented model for peak power reduction in buildings. Specifically, a data predictive control with regression trees (DPCRT) algorithm, is presented. DPCRT is a finite receding horizon method, using which the building operator can optimally trade off peak power reduction against thermal comfort without having to learn white/grey box models of the systems dynamics. We evaluate the performance of our method using a DoE commercial reference virtual test-bed and show how it can be used for learning predictive models with 90% accuracy, and for achieving 8.6% reduction in peak power and costs.Publication Computer Aided Clinical Trials for Implantable Cardiac Devices(2016-08-19) Abbas, Houssam; Jiang, Zhihao; Jang, Kuk Jin; Beccani, Marco; Liang, Jackson; Dixit, Sanjay; Mangharam, RahulIn this effort we investigate the design and use of physiological and device models to conduct pre-clinical trials to provide early insight in the design and execution of the actual clinical trial. Computer models of physiological phenomena like cardiac electrical activity can be extremely complex. However, when the purpose of the model is to interact with a medical device, then it becomes sufficient to model the measurements that the device makes, e.g. the intra-cardiac electrograms (EGMs) that an Implantable Cardioverter Defibrillator (ICD) measures. We present a probabilistic generative model of EGMs, capable of generating exemplars of various arrhythmias. The model uses deformable shape templates, or motifs, to capture the variability in EGM shapes within one EGM channel, and a cycle length parameter to capture the variability in cycle length in one EGM channel. The relation between EGM channels, which is essential for determining whether the current arrhythmia is potentially fatal, is captured by a time-delayed Markov chain, whose states model the various combinations of (learned) motifs. The heart model is minimally parameterized and is learned from real patient data. Thus the statistics of key features reflect the statistics of a real cohort, but the model can also generate rare cases and new combinations from the inferred probabilities. On the device end, algorithms for signal sensing, detection and discrimination for major ICD manufacturers have been implemented both in simulation and on hardware platforms. The generated arrhythmia episodes are used as input to both the modeled ICD algorithms and real ICDs as part of a Computer Aided Clinical Trial (CACT). In a CACT, a computer model simulates the inputs to the device (such as a new, investigational ICD), and the device’s performance is evaluated. By incorporating these results into the appropriate statistical framework, the Computer Aided Clinical Trial results can serve as regulatory evidence when planning and executing an actual clinical trial. We demonstrate this by conducting a mock trial similar to the 2005-2010 RIGHT trial which compared the discrimination algorithms from two major ICD manufacturers. The results of the CACT clearly demonstrate that the failed outcome of the RIGHT trial could have been predicted and provides statistical support for deeper results that could have been captured prior to the trial.Publication Co-Design of Anytime Computation and Robust Control(2015-01-01) Pant, Yash Vardhan; Mohta, Kartik; Abbas, Houssam; Nghiem, Truong; Deveitti, Joesph; Mangharam, RahulPublication Benchmark: Nonlinear Hybrid Automata Model of Excitable Cardiac Tissue(2016-03-20) Abbas, Houssam; Jang, Kuk Jin; Mangharam, RahulImplantable cardiac devices like pacemakers and defibrillators are life-saving medical devices. To verify their functionality, there is a need for heart models that can simulate interesting phenomena and are relatively computationally tractable. In this benchmark we implement a model of the electrical activity in excitable cardiac tissue as a network of nonlinear hybrid automata. The model has previously been shown to simulate fast arrhythmias. The hybrid automata are arranged in a square n-by-n grid and communicate via their voltages. Our Matlab implementation allows the user to specify any size of model $n$, thus rendering it ideal for benchmarking purposes since we can study tool efficiency as a function of size. We expect the model to be used to analyze parameter ranges and network connectivity that lead to dangerous heart conditions. It can also be connected to device models for device verification.