Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

Delay-independent decentralised output feedback control for large-scale systems with nonlinear interconnections

In this paper, a stabilisation problem for a class of large-scale systems with nonlinear interconnections is considered. All the uncertainties are nonlinear and are subject to the effects of time delay. A decentralised static output feedback variable structure control is synthesised and the stability of the corresponding closed-loop system is analysed based on the Lyapunov Razumikhin approach. A set of conditions is developed to guarantee that the large-scale interconnected system is stabilised uniformly asymptotically. Further study shows that the conservatism can be reduced by employing additive controllers if the known interconnections are separated into matched and mismatched parts. It is not required that the subsystems are square. The designed controller is independent of time delay and thus it does not require memory. Simulation results show the effectiveness of the proposed approach

Low computational complexity model reduction of power systems with preservation of physical characteristics

A data-driven algorithm recently proposed to solve the problem of model reduction by moment matching is extended to multi-input, multi-output systems. The algorithm is exploited for the model reduction of large-scale interconnected power systems and it offers, simultaneously, a low computational complexity approximation of the moments and the possibility to easily enforce constraints on the reduced order model. This advantage is used to preserve selected slow and poorly damped modes. The preservation of these modes has been shown to be important from a physical point of view and in obtaining an overall good approximation. The problem of the choice of the socalled tangential directions is also analyzed. The algorithm and the resulting reduced order model are validated with the study of the dynamic response of the NETS-NYPS benchmark system (68-Bus, 16-Machine, 5-Area) to multiple fault scenarios

Relaxed ISS Small-Gain Theorems for Discrete-Time Systems

In this paper ISS small-gain theorems for discrete-time systems are stated, which do not require input-to-state stability (ISS) of each subsystem. This approach weakens conservatism in ISS small-gain theory, and for the class of exponentially ISS systems we are able to prove that the proposed relaxed small-gain theorems are non-conservative in a sense to be made precise. The proofs of the small-gain theorems rely on the construction of a dissipative finite-step ISS Lyapunov function which is introduced in this work. Furthermore, dissipative finite-step ISS Lyapunov functions, as relaxations of ISS Lyapunov functions, are shown to be sufficient and necessary to conclude ISS of the overall system.Comment: input-to-state stability, Lyapunov methods, small-gain conditions, discrete-time non-linear systems, large-scale interconnection

Feedback stabilization of dynamical systems with switched delays

We analyze a classification of two main families of controllers that are of interest when the feedback loop is subject to switching propagation delays due to routing via a wireless multi-hop communication network. We show that we can cast this problem as a subclass of classical switching systems, which is a non-trivial generalization of classical LTI systems with timevarying delays. We consider both cases where delay-dependent and delay independent controllers are used, and show that both can be modeled as switching systems with unconstrained switchings. We provide NP-hardness results for the stability verification problem, and propose a general methodology for approximate stability analysis with arbitrary precision. We finally give evidence that non-trivial design problems arise for which new algorithmic methods are needed

A multilevel control system for the large space telescope

A multilevel scheme was proposed for control of Large Space Telescope (LST) modeled by a three-axis-six-order nonlinear equation. Local controllers were used on the subsystem level to stabilize motions corresponding to the three axes. Global controllers were applied to reduce (and sometimes nullify) the interactions among the subsystems. A multilevel optimization method was developed whereby local quadratic optimizations were performed on the subsystem level, and global control was again used to reduce (nullify) the effect of interactions. The multilevel stabilization and optimization methods are presented as general tools for design and then used in the design of the LST Control System. The methods are entirely computerized, so that they can accommodate higher order LST models with both conceptual and numerical advantages over standard straightforward design techniques