Reservoir computing for system identification and predictive control with limited data

Model predictive control (MPC) is an industry standard control technique that iteratively solves an open-loop optimization problem to guide a system towards a desired state or trajectory. Consequently, an accurate forward model of system dynamics is critical for the efficacy of MPC and much recent work has been aimed at the use of neural networks to act as data-driven surrogate models to enable MPC. Perhaps the most common network architecture applied to this task is the recurrent neural network (RNN) due to its natural interpretation as a dynamical system. In this work, we assess the ability of RNN variants to both learn the dynamics of benchmark control systems and serve as surrogate models for MPC. We find that echo state networks (ESNs) have a variety of benefits over competing architectures, namely reductions in computational complexity, longer valid prediction times, and reductions in cost of the MPC objective function.

Leveraging arbitrary mobile sensor trajectories with shallow recurrent decoder networks for full-state reconstruction

Sensing is one of the most fundamental tasks for the monitoring, forecasting and control of complex, spatio-temporal systems. In many applications, a limited number of sensors are mobile and move with the dynamics, with examples including wearable technology, ocean monitoring buoys, and weather balloons. In these dynamic systems (without regions of statistical-independence), the measurement time history encodes a significant amount of information that can be extracted for critical tasks. Most model-free sensing paradigms aim to map current sparse sensor measurements to the high-dimensional state space, ignoring the time-history all together. Using modern deep learning architectures, we show that a sequence-to-vector model, such as an LSTM (long, short-term memory) network, with a decoder network, dynamic trajectory information can be mapped to full state-space estimates. Indeed, we demonstrate that by leveraging mobile sensor trajectories with shallow recurrent decoder networks, we can train the network (i) to accurately reconstruct the full state space using arbitrary dynamical trajectories of the sensors, (ii) the architecture reduces the variance of the mean-square error of the reconstruction error in comparison with immobile sensors, and (iii) the architecture also allows for rapid generalization (parameterization of dynamics) for data outside the training set. Moreover, the path of the sensor can be chosen arbitrarily, provided training data for the spatial trajectory of the sensor is available. The exceptional performance of the network architecture is demonstrated on three applications: turbulent flows, global sea-surface temperature data, and human movement biomechanics.