Gautam Kumar

Suruchi Sharma, Volodymyr Makarenko, Gautam Kumar et al.

Control of a dynamical system without the knowledge of dynamics is an important and challenging task. Modern machine learning approaches, such as deep neural networks (DNNs), allow for the estimation of a dynamics model from control inputs and corresponding state observation outputs. Such data-driven models are often utilized for the derivation of model-based controllers. However, in general, there are no guarantees that a model represented by DNNs will be controllable according to the formal control-theoretical meaning of controllability, which is crucial for the design of effective controllers. This often precludes the use of DNN-estimated models in applications, where formal controllability guarantees are required. In this proof-of-the-concept work, we propose a control-theoretical method that explicitly enhances models estimated from data with controllability. That is achieved by augmenting the model estimation objective with a controllability constraint, which penalizes models with a low degree of controllability. As a result, the models estimated with the proposed controllability constraint allow for the derivation of more efficient controllers, they are interpretable by the control-theoretical quantities and have a lower long-term prediction error. The proposed method provides new insights on the connection between the DNN-based estimation of unknown dynamics and the control-theoretical guarantees of the solution properties. We demonstrate the superiority of the proposed method in two standard classical control systems with state observation given by low resolution high-dimensional images.

Benjamin Plaster, Gautam Kumar

Modeling brain dynamics to better understand and control complex behaviors underlying various cognitive brain functions are of interests to engineers, mathematicians, and physicists from the last several decades. With a motivation of developing computationally efficient models of brain dynamics to use in designing control-theoretic neurostimulation strategies, we have developed a novel data-driven approach in a long short-term memory (LSTM) neural network architecture to predict the temporal dynamics of complex systems over an extended long time-horizon in future. In contrast to recent LSTM-based dynamical modeling approaches that make use of multi-layer perceptrons or linear combination layers as output layers, our architecture uses a single fully connected output layer and reversed-order sequence-to-sequence mapping to improve short time-horizon prediction accuracy and to make multi-timestep predictions of dynamical behaviors. We demonstrate the efficacy of our approach in reconstructing the regular spiking to bursting dynamics exhibited by an experimentally-validated 9-dimensional Hodgkin-Huxley model of hippocampal CA1 pyramidal neurons. Through simulations, we show that our LSTM neural network can predict the multi-time scale temporal dynamics underlying various spiking patterns with reasonable accuracy. Moreover, our results show that the predictions improve with increasing predictive time-horizon in the multi-timestep deep LSTM neural network.