Multiplexed networks: reservoir computing with virtual and real nodes

The reservoir computing scheme is a machine learning mechanism which utilizes the naturally occurring computational capabilities of dynamical systems. One important subset of systems that has proven powerful both in experiments and theory are delay-systems. In this work, we investigate the reservoir computing performance of hybrid network-delay systems systematically by evaluating the NARMA10 and the Sante Fe task for varying system parameters. We construct ‘multiplexed networks’ that can be seen as intermediate steps on the scale from classical networks to the ‘virtual networks’ of delay systems. We find that the delay approach can be extended to the network case without loss of computational power, enabling the construction of faster reservoir computing systems.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept

Hybrid Electric Distributed Propulsion for Vertical Takeoff and Landing Aircraft

This research effort explores the interactions between aerodynamics and hybridelectric power system (HEPS) design and control for vertical takeoff and landing (VTOL) aircraft applications. Specifically, this research focuses on embedded distributed electric propulsion systems, for which the aerodynamic forces and moments are inextricably linked to power input. This effort begins by characterizing the performance of two similar embedded propulsion systems using computational fluid dynamics (CFD). From this initial analysis, a wind tunnel model is constructed and the systems are tested across the operating conditions required to characterize the performance of a VTOL aircraft, where 0 deg ≤ α ≤ 90 deg. One of these configurations is selected for evaluating the interaction with the hybrid-power system. An experimental HEPS is constructed based on a small two-stroke internal combustion engine as well, with a rated continuous power output of 2kW. This experiment is used to develop a validated dynamical HEPS model in MATLAB and Simulink, where the control systems are refined and the performance of the system is extended to accommodate the VTOL power demand during transitional flight. A robust control design is developed using a second order sliding mode controller (2-SMC), implemented using the super-twisting algorithm and integrated with classical linear control schemes in an interleaved-cascade architecture. The resulting system has a variable voltage output and a robust response to rapid changes in power demand. Additionally, the HEPS is also demonstrated to fully utilize the mechanical power output capability of the two-stroke engine. Ultimately, the HEPS is demonstrated, via the dynamical model, to be capable of supplying power for an embedded propulsion VTOL aircraft. This performance is further extended with the addition of an actively controlled slack bus, utilizing battery energy storage and a buck-converter integrated with the HEPS control system. In this configuration, the peak power demands of the system can exceed the maximum sustained power threshold (MSPT) of the HEPS

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Motion Planning of Uncertain Ordinary Differential Equation Systems

This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems. Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs. The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space

Reachability Analysis of Cyber-Physical Systems Using Symbolic-Numeric Techniques

In this thesis, we address the problem of reachability analysis in cyber-physical systems. These are systems engineered by interfacing computational components with the physical world. They provide partially or fully automated safety-critical services in the form of medical devices, autonomous vehicles, avionics and power systems. We propose techniques to reason about the reachability of such systems, and provide methods for falsifying their safety properties. We model the cyber component as a software program and the physical component as a hybrid dynamical system. Unlike model based analysis, which uses either a purely symbolic or a numerical approach, we argue in favor of using a combination of the two. We justify this by noting that the software program running on a computer is completely specified and has precise semantics. In contrast, the model of the physical system is only an approximation. Hence, we treat the former as a white box, but treat the latter as a black box. Using symbolic methods for the cyber components and numerical methods for hybrid systems, we carefully capture the complex behaviors of software programs and circumvent the difficulty in analyzing complex models developed through first principles. To combine the two techniques, we use a Counterexample Guided Abstraction Refinement (CEGAR) framework. Furthermore, we explore learning techniques like regression and piecewise affine modeling to estimate and represent black box hybrid dynamical systems for the purpose of falsification. We use prototype implementations to demonstrate the effectiveness of presented ideas. Using non-trivial benchmarks, we compare their performance against the state of the art. We also comment on their applicability and discuss ideas for further improvement