Differential Dynamic Programming for time-delayed systems

Trajectory optimization considers the problem of deciding how to control a dynamical system to move along a trajectory which minimizes some cost function. Differential Dynamic Programming (DDP) is an optimal control method which utilizes a second-order approximation of the problem to find the control. It is fast enough to allow real-time control and has been shown to work well for trajectory optimization in robotic systems. Here we extend classic DDP to systems with multiple time-delays in the state. Being able to find optimal trajectories for time-delayed systems with DDP opens up the possibility to use richer models for system identification and control, including recurrent neural networks with multiple timesteps in the state. We demonstrate the algorithm on a two-tank continuous stirred tank reactor. We also demonstrate the algorithm on a recurrent neural network trained to model an inverted pendulum with position information only.Comment: 7 pages, 6 figures, conference, Decision and Control (CDC), 2016 IEEE 55th Conference o

A Dynamic Recurrent Neural Network for Wide Area Identification of a Multimachine Power System with a FACTS Device

Multilayer perceptron and radial basis function neural networks have been traditionally used for plant identification in power systems applications of neural networks. While being efficient in tracking the plant dynamics in a relatively small system, their performance degrades as the dimensions of the plant to be identified are increased, for example in supervisory level identification of a multimachine power system for wide area control purposes. Recurrent neural networks can deal with such a problem by modeling the system as a set of differential equations and with less order of complexity. Such a recurrent neural network identifier is designed and implemented for supervisory level identification of a multimachine power system with a FACTS device. Simulation results are provided to show that the neuroidentifier can track the system dynamics with sufficient accuracy

Limited-angle tomographic reconstruction of dense layered objects by dynamical machine learning

Limited-angle tomography of strongly scattering quasi-transparent objects is a challenging, highly ill-posed problem with practical implications in medical and biological imaging, manufacturing, automation, and environmental and food security. Regularizing priors are necessary to reduce artifacts by improving the condition of such problems. Recently, it was shown that one effective way to learn the priors for strongly scattering yet highly structured 3D objects, e.g. layered and Manhattan, is by a static neural network [Goy et al, Proc. Natl. Acad. Sci. 116, 19848-19856 (2019)]. Here, we present a radically different approach where the collection of raw images from multiple angles is viewed analogously to a dynamical system driven by the object-dependent forward scattering operator. The sequence index in angle of illumination plays the role of discrete time in the dynamical system analogy. Thus, the imaging problem turns into a problem of nonlinear system identification, which also suggests dynamical learning as better fit to regularize the reconstructions. We devised a recurrent neural network (RNN) architecture with a novel split-convolutional gated recurrent unit (SC-GRU) as the fundamental building block. Through comprehensive comparison of several quantitative metrics, we show that the dynamic method improves upon previous static approaches with fewer artifacts and better overall reconstruction fidelity.Comment: 12 pages, 7 figures, 2 table

Wireless sensor network modeling using modified recurrent neural network: Application to fault detection

Wireless Sensor Networks (WSNs) consist of a large number of sensors, which in turn have their own dynamics. They interact with each other and the base station, which controls the network. In multi-hop wireless sensor networks, information hops from one node to another and finally to the network gateway or base station. Dynamic Recurrent Neural Networks (RNNs) consist of a set of dynamic nodes that provide internal feedback to their own inputs. They can be used to simulate and model dynamic systems such as a network of sensors. In this dissertation, a dynamic model of wireless sensor networks and its application to sensor node fault detection are presented. RNNs are used to model a sensor node, the node\u27s dynamics, and the interconnections with other sensor network nodes. A neural network modeling approach is used for sensor node identification and fault detection in WSNs. The input to the neural network is chosen to include previous output samples of the modeling sensor node and the current and previous output samples of neighboring sensors. The model is based on a new structure of a backpropagation-type neural network. The input to the neural network (NN) and the topology of the network are based on a general nonlinear sensor model. A simulation example, including a comparison to the Kalman filter method, has demonstrated the effectiveness of the proposed scheme. The simulation with comparison to the Kalman filtering technique was carried out on a network with 15 sensor nodes. A fault such as drift was introduced and successfully detected with the modified recurrent neural net model with no early false alarm that could have resulted when using the Kalman filtering approach. In this dissertation, we also present the real-time implementation of a neural network-based fault detection for WSNs. The method is implemented on a TinyOS operating system. A collection tree network is formed, and multi-hoping data is sent to the base station root. Nodes take environmental measurements every N seconds while neighboring nodes overhear the measurement as it is being forwarded to the base station for recording it. After nodes complete M and receive/store M measurements from each neighboring node, recurrent neural networks are used to model the sensor node, the node\u27s dynamics, and the interconnections with neighboring nodes. The physical measurement is compared to the predicted value and to a given threshold of error to determine a sensor fault. The process of neural network training can be repeated indefinitely to maintain self-aware network fault detection. By simply overhearing network traffic, this implementation uses no extra bandwidth or radio broadcast power. The only costs of the approach are the battery power required to power the receiver for overhearing packets and the processor time to train the RNN

Data-Driven Stability Assessment of Multilayer Long Short-Term Memory Networks

Recurrent Neural Networks (RNNs) are increasingly being used for model identification, forecasting and control. When identifying physical models with unknown mathematical knowledge of the system, Nonlinear AutoRegressive models with eXogenous inputs (NARX) or Nonlinear AutoRegressive Moving-Average models with eXogenous inputs (NARMAX) methods are typically used. In the context of data-driven control, machine learning algorithms are proven to have comparable performances to advanced control techniques, but lack the properties of the traditional stability theory. This paper illustrates a method to prove a posteriori the stability of a generic neural network, showing its application to the state-of-the-art RNN architecture. The presented method relies on identifying the poles associated with the network designed starting from the input/output data. Providing a framework to guarantee the stability of any neural network architecture combined with the generalisability properties and applicability to different fields can significantly broaden their use in dynamic systems modelling and control

Adaptive Noise Cancellation Using Recurrent Radial Basis Function Networks

Radial basis function neural network architectures are introduced for the nonlinear adaptive noise cancellation problem. Both FIR and IIR filter designs are considered and it is shown that by exploiting the duality with system identification that the nonlinear IIR filter can be configured as a recurrent radial basis function network. Details of network training which is based on a combined k-means clustering and Givens routine, the inclusion of linear dynamic network links and metrics for performance monitoring are also discussed. Examples are included to demonstrate the degree of noise suppression that can be achieved based on the new design

System Identification of multi-rotor UAVs using echo state networks

Controller design for aircraft with unusual configurations presents unique challenges, particularly in extracting valid mathematical models of the MRUAVs behaviour. System Identification is a collection of techniques for extracting an accurate mathematical model of a dynamic system from experimental input-output data. This can entail parameter identification only (known as grey-box modelling) or more generally full parameter/structural identification of the nonlinear mapping (known as black-box). In this paper we propose a new method for black-box identification of the non-linear dynamic model of a small MRUAV using Echo State Networks (ESN), a novel approach to train Recurrent Neural Networks (RNN)