Controlling continuous-time dynamical systems is generally a two step process: first, identify or model the system dynamics with differential equations, then, minimize the control objectives to achieve optimal control function and optimal state trajectories. However, any inaccuracy in dynamics modeling will lead to sub-optimality in the resulting control function. To address this, we propose a neural ODE based method for controlling unknown dynamical systems, denoted as Neural Control (NC), which combines dynamics identification and optimal control learning using a coupled neural ODE. Through an intriguing interplay between the two neural networks in coupled neural ODE structure, our model concurrently learns system dynamics as well as optimal controls that guides towards target states. Our experiments demonstrate the effectiveness of our model for learning optimal control of unknown dynamical systems.

We develop a novel computational framework to approximate solution operators of evolution partial differential equations (PDEs). By employing a general nonlinear reduced-order model, such as a deep neural network, to approximate the solution of a given PDE, we realize that the evolution of the model parameters is a control problem in the parameter space. Based on this observation, we propose to approximate the solution operator of the PDE by learning the control vector field in the parameter space. From any initial value, this control field can steer the parameter to generate a trajectory such that the corresponding reduced-order model solves the PDE. This allows for substantially reduced computational cost to solve the evolution PDE with arbitrary initial conditions. We also develop comprehensive error analysis for the proposed method when solving a large class of semilinear parabolic PDEs. Numerical experiments on different high-dimensional evolution PDEs with various initial conditions demonstrate the promising results of the proposed method.

We propose a novel way to integrate control techniques with reinforcement learning (RL) for stability, robustness, and generalization: leveraging contraction theory to realize modularity in neural control, which ensures that combining stable subsystems can automatically preserve the stability. We realize such modularity via signal composition and dynamic decomposition. Signal composition creates the latent space, within which RL applies to maximizing rewards. Dynamic decomposition is realized by coordinate transformation that creates an auxiliary space, within which the latent signals are coupled in the way that their combination can preserve stability provided each signal, that is, each subsystem, has stable self-feedbacks. Leveraging modularity, the nonlinear stability problem is deconstructed into algebraically solvable ones, the stability of the subsystems in the auxiliary space, yielding linear constraints on the input gradients of control networks that can be as simple as switching the signs of network weights. This minimally invasive method for stability allows arguably easy integration into the modular neural architectures in machine learning, like hierarchical RL, and improves their performance. We demonstrate in simulation the necessity and the effectiveness of our method: the necessity for robustness and generalization, and the effectiveness in improving hierarchical RL for manipulation learning.

In a Bayesian framework, we give a principled account of how domain(cid:173) specific prior knowledge such as imperfect analytic domain theories can be optimally incorporated into networks of locally-tuned units: by choosing a specific architecture and by applying a specific training regimen. Our method proved successful in overcoming the data deficiency problem in a large-scale application to devise a neural control for a hot line rolling mill. It achieves in this application significantly higher accuracy than optimally-tuned standard algorithms such as sigmoidal backpropagation, and outperforms the state-of-the-art solution.

A neural network based approach is presented for controlling two distinct types of nonlinear systems. The first corresponds to nonlinear systems with parametric uncertainties where the parameters occur nonlinearly. The second corresponds to systems for which stabilizing control struc(cid:173) tures cannot be determined. The proposed neural controllers are shown to result in closed-loop system stability under certain conditions.

We present a novel methodology for control of neural circuits based on deep reinforcement learning. Our approach achieves aimed behavior by generating external continuous stimulation of existing neural circuits (neuromodulation control) or modulations of neural circuits architecture (connectome control). Both forms of control are challenging due to nonlinear and recurrent complexity of neural activity. To infer candidate control policies, our approach maps neural circuits and their connectome into a grid-world like setting and infers the actions needed to achieve aimed behavior. The actions are inferred by adaptation of deep Q-learning methods known for their robust performance in navigating grid-worlds. We apply our approach to the model of \textit{C. elegans} which simulates the full somatic nervous system with muscles and body. Our framework successfully infers neuropeptidic currents and synaptic architectures for control of chemotaxis. Our findings are consistent with in vivo measurements and provide additional insights into neural control of chemotaxis. We further demonstrate the generality and scalability of our methods by inferring chemotactic neural circuits from scratch.

Controlling sensori-motor systems in higher animals or complex robots is a challenging combinatorial problem, because many sensory signals need to be simultaneously coordinated into a broad behavioural spectrum. To rapidly interact with the environment, this control needs to be fast and adaptive. Current robotic solutions operate with limited autonomy and are mostly restricted to few behavioural patterns. Here we introduce chaos control as a new strategy to generate complex behaviour of an autonomous robot. In the presented system, 18 sensors drive 18 motors via a simple neural control circuit, thereby generating 11 basic behavioural patterns (e.g., orienting, taxis, self-protection, various gaits) and their combinations. The control signal quickly and reversibly adapts to new situations and additionally enables learning and synaptic long-term storage of behaviourally useful motor responses. Thus, such neural control provides a powerful yet simple way to self-organize versatile behaviours in autonomous agents with many degrees of freedom.

Neural motor prostheses (NMPs) require the accurate decoding of motor cortical population activity for the control of an artificial motor system. Previous work on cortical decoding for NMPs has focused on the recovery of hand kinematics. Human NMPs however may require the control of computer cursors or robotic devices with very different physical and dynamical properties. Here we show that the firing rates of cells in the primary motor cortex of nonhuman primates can be used to control the parameters of an artificial physical system exhibiting realistic dynamics. The model represents 2D hand motion in terms of a point mass connected to a system of idealized springs. The nonlinear spring coefficients are estimated from the firing rates of neurons in the motor cortex. We evaluate linear and a nonlinear decoding algorithms using neural recordings from two monkeys performing two different tasks. We found that the decoded spring coefficients produced accurate hand trajectories compared with state-of-the-art methods for direct decoding of hand kinematics. Furthermore, using a physically-based system produced decoded movements that were more "natural" in that their frequency spectrum more closely matched that of natural hand movements.

Neural motor prostheses (NMPs) require the accurate decoding of motor cortical population activity for the control of an artificial motor system. Previous work on cortical decoding for NMPs has focused on the recovery of hand kinematics. Human NMPs however may require the control of computer cursors or robotic devices with very different physical and dynamical properties. Here we show that the firing rates of cells in the primary motor cortex of nonhuman primates can be used to control the parameters of an artificial physical system exhibiting realistic dynamics. The model represents 2D hand motion in terms of a point mass connected to a system of idealized springs. The nonlinear spring coefficients are estimated from the firing rates of neurons in the motor cortex. We evaluate linear and a nonlinear decoding algorithms using neural recordings from two monkeys performing two different tasks. We found that the decoded spring coefficients produced accurate hand trajectories compared with state-of-the-art methods for direct decoding of hand kinematics. Furthermore, using a physically-based system produced decoded movements that were more "natural" in that their frequency spectrum more closely matched that of natural hand movements.

Neural motor prostheses (NMPs) require the accurate decoding of motor cortical population activity for the control of an artificial motor system. Previous work on cortical decoding for NMPs has focused on the recovery of hand kinematics. Human NMPs however may require the control of computer cursors or robotic devices with very different physical and dynamical properties. Here we show that the firing rates of cells in the primary motor cortex of nonhuman primates can be used to control the parameters of an artificial physical system exhibiting realistic dynamics. The model represents 2D hand motion in terms of a point mass connected to a system of idealized springs. The nonlinear spring coefficients are estimated from the firing rates of neurons in the motor cortex. We evaluate linear and a nonlinear decoding algorithms using neural recordings from two monkeys performing two different tasks. We found that the decoded spring coefficients produced accurate hand trajectories compared with state-of-the-art methods for direct decoding of hand kinematics. Furthermore, using a physically-based system produced decoded movements that were more "natural" in that their frequency spectrum more closely matched that of natural hand movements.