Data-Driven Cyberphysical Systems Provably Correct Control in Data Rich/Labels Scarce Scenarios
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The overall goal of this project is to develop theory, methods and tools necessary to take advantage of data in the design, certification, manufacturing and operation of cyberphysical systems. The central question we ask is “How can we, in a data-rich world, design and operate cyberphysical systems differently?” Data-driven techniques will help transform the design process of cyberphysical systems into one in which data and models—and human designers and operators—continuously and fluently interact. This poster addresses the portion of this research carried out at Northeastern University, addressing the issue of provably correct decisions for CPS in scenarios with rich run-time data, but where labeling is expensive and off-line training may not capture rare but potentially catastrophic events. Specifically, we address the following challenges:
- Obtaining space-spanning data, specially for situations involving potentially unsafe operations
- Real-time labeling with certifiable performance, even for data previously unseen
- Synthesizing non-conservative, provably stabilizing control laws
Leveraging Simulations to Handle Scarce Labels: The goal here is to obtain data that spans the space of feasible trajectories by exploiting the ability of simulators to generate data cheaply, while avoiding costly tuning to match the simulator to the actual physical system. We propose to accomplish this by recasting the problem into a Domain Adaptation form, where the goal is to find a transformation that maps the simulation data (source domain) to the actual CPS data (target domain). This problem is solved by jointly finding a transformation that aligns the covariances in both domains and a classifier that optimizes classification accuracy on the combined adapted source and target data. In turn, this leads to an optimization over a Stiefel manifold that can be efficiently solved using recently developed polynomial optimization techniques.
Efficient Data Labeling: While existing state-of-the-art labeling and classification methods are very suc-cessful, they rely on computationally intensive training requiring very large amounts of training data. How-ever, such a training is not always feasible for CPS operating in uncertain environments or subject to failure modes previously unseen. As an alternative, we propose the use of data-driven, statistical classifiers. The main idea here is to construct sum-of-squares polynomials that approximate the support set of the data for different operating regimes. These SoS polynomials can be directly computed from the empirical moment matrices of the data, at the price of a single singular value decomposition, and new data can be incrementally accommodated by simply updating these matrices. Preliminary results show that for the specific case of 3D printing, SoS based classifiers substantially outperform traditional ones.
Non Conservative Data Driven Control Synthesis: The objective of this portion of the research is to synthesize provably stabilizing control laws for cases where an a-priori model of the system is unavailable. Traditionally, this situation is handled through a multi-step process: (i) systems identification, (ii) model (in)validation, and (iii) robust control synthesis. However, this process is computationally involved and the resulting controllers are potentially conservative. As an alternative, we have developed a data-driven approach where the controller is identified directly from the data, by solving a polynomial optimization problem. The resulting controllers are non-conservative and guaranteed to stabilize all plants compatible with existing side-information and experimental data.
Submitted by Mario Sznaier
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The overall goal of this project is to develop theory, methods and tools necessary to take advantage of data in the design, certification, manufacturing and operation of cyberphysical systems. The central question we ask is “How can we, in a data-rich world, design and operate cyberphysical systems differently?” Data-driven techniques will help transform the design process of cyberphysical systems into one in which data and models—and human designers and operators—continuously and fluently interact. This poster addresses the portion of this research carried out at Northeastern University, addressing the issue of provably correct decisions for CPS in scenarios with rich run-time data, but where labeling is expensive and off-line training may not capture rare but potentially catastrophic events. Specifically, we address the following challenges:
- Obtaining space-spanning data, specially for situations involving potentially unsafe operations
- Real-time labeling with certifiable performance, even for data previously unseen
- Synthesizing non-conservative, provably stabilizing control laws
Leveraging Simulations to Handle Scarce Labels: The goal here is to obtain data that spans the space of feasible trajectories by exploiting the ability of simulators to generate data cheaply, while avoiding costly tuning to match the simulator to the actual physical system. We propose to accomplish this by recasting the problem into a Domain Adaptation form, where the goal is to find a transformation that maps the simulation data (source domain) to the actual CPS data (target domain). This problem is solved by jointly finding a transformation that aligns the covariances in both domains and a classifier that optimizes classification accuracy on the combined adapted source and target data. In turn, this leads to an optimization over a Stiefel manifold that can be efficiently solved using recently developed polynomial optimization techniques.
Efficient Data Labeling: While existing state-of-the-art labeling and classification methods are very suc-cessful, they rely on computationally intensive training requiring very large amounts of training data. How-ever, such a training is not always feasible for CPS operating in uncertain environments or subject to failure modes previously unseen. As an alternative, we propose the use of data-driven, statistical classifiers. The main idea here is to construct sum-of-squares polynomials that approximate the support set of the data for different operating regimes. These SoS polynomials can be directly computed from the empirical moment matrices of the data, at the price of a single singular value decomposition, and new data can be incrementally accommodated by simply updating these matrices. Preliminary results show that for the specific case of 3D printing, SoS based classifiers substantially outperform traditional ones.
Non Conservative Data Driven Control Synthesis: The objective of this portion of the research is to synthesize provably stabilizing control laws for cases where an a-priori model of the system is unavailable. Traditionally, this situation is handled through a multi-step process: (i) systems identification, (ii) model (in)validation, and (iii) robust control synthesis. However, this process is computationally involved and the resulting controllers are potentially conservative. As an alternative, we have developed a data-driven approach where the controller is identified directly from the data, by solving a polynomial optimization problem. The resulting controllers are non-conservative and guaranteed to stabilize all plants compatible with existing side-information and experimental data.