We present a new deep learning-based adaptive control framework for nonlinear systems with multiplicatively-separable parametric uncertainty, called an adaptive Neural Contraction Metric (aNCM). The aNCM uses a neural network model of an optimal adaptive contraction metric, the existence of which guarantees asymptotic stability and exponential boundedness of system trajectories under the parametric uncertainty. In particular, we exploit the concept of a Neural Contraction Metric (NCM) to obtain a nominal provably stable robust control policy for nonlinear systems with bounded disturbances, and combine this policy with a novel adaptation law to achieve stability guarantees. We also show that the framework is applicable to adaptive control of dynamical systemsmodeled via basis function approximation  . Furthermore, the use of neural networks in the aNCM permits its real-time implementation, resulting in broad applicability to a variety of systems. Its superiority to the state-of-the-art is illustrated with a simple cart-pole balancing task.
We present a deep learning-based adaptive control framework for nonlinear systems with multiplicatively separable parametrization, called aNCM - for adaptive Neural Contraction Metric . The framework utilizes a deep neural network to approximate a stabilizing adaptive control law parameterized by an optimal contraction metric. The use of deep networks permits real-time implementation of the control law and broad applicability to a variety of systems, including systems modeled with basis function approximation methods. We show using contraction theory that aNCM ensures exponential boundedness of the distance between the target and controlled trajectories even under the presence of the parametric uncertainty, robustly to the learning errors caused by aNCM approximation as well as external additive disturbances . Its superiority to the existing robust and adaptive control methods is demonstrated in a simple cart-pole balancing task.
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multiplicatively-separable parametric uncertainty, called an
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(aNCM). The aNCM uses a neural network model of an optimal adaptive contraction metric, the existence of which guarantees asymptotic stability and exponential boundedness of system trajectories under the parametric uncertainty. In particular, we exploit the concept of a Neural Contraction Metric (NCM) to obtain a nominal provably stable robust control policy for nonlinear systems with bounded disturbances, and combine this policy with a novel adaptation law to achieve stability guarantees. We also show that the framework is applicable to adaptive control of dynamical systemsmodeled via
. The framework utilizes a deep neural network to approximate a stabilizing adaptive control law parameterized by an optimal contraction metric. The use of deep networks permits real-time implementation of the control law and broad applicability to a variety of systems, including systems modeled with
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methods. We show using contraction theory that aNCM ensures exponential boundedness of the distance between the target and controlled trajectories even under the presence of the parametric uncertainty, robustly to the learning errors caused by aNCM approximation as well as external additive disturbances
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Furthermore, the use of neural networks in the aNCM permits its real-time implementation, resulting in broad applicability to a variety of systems.
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