299 research outputs found
Koopman operator-based model reduction for switched-system control of PDEs
We present a new framework for optimal and feedback control of PDEs using
Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a
linear but infinite-dimensional operator which describes the dynamics of
observables. A numerical approximation of the Koopman operator therefore yields
a linear system for the observation of an autonomous dynamical system. In our
approach, by introducing a finite number of constant controls, the dynamic
control system is transformed into a set of autonomous systems and the
corresponding optimal control problem into a switching time optimization
problem. This allows us to replace each of these systems by a K-ROM which can
be solved orders of magnitude faster. By this approach, a nonlinear
infinite-dimensional control problem is transformed into a low-dimensional
linear problem. In situations where the Koopman operator can be computed
exactly using Extended Dynamic Mode Decomposition (EDMD), the proposed approach
yields optimal control inputs. Furthermore, a recent convergence result for
EDMD suggests that the approach can be applied to more complex dynamics as
well. To illustrate the results, we consider the 1D Burgers equation and the 2D
Navier--Stokes equations. The numerical experiments show remarkable performance
concerning both solution times and accuracy.Comment: arXiv admin note: text overlap with arXiv:1801.0641
Robust de-centralized control and estimation for inter-connected systems
The thesis is concerned with the theoretical development of the control of inter-connected systems to achieve the whole overall stability and specific performance. A special included feature is the Fault-Tolerant Control (FTC) problem for the inter-connected system in terms of local subsystem actuator fault estimation. Hence, the thesis describes the main FTC challenges of distributed control of uncertain non-linear inter-connected systems. The basic principle adopted throughout the work is that the controller has two components, one involving the nominal control with unmatched components including uncertainties and disturbances. The second controller dealing with matched components including uncertainties and actuator faults.The main contributions of the thesis are summarised as follows:- The non-linear inter-connected systems are controlled by two controllers. The linear part via a linear matrix inequality (LMI) technique and the discontinuous part by using Integral Sliding Mode Control (ISMC) based on state feedback control.- The development of a new observer-based state estimate control strategy for non-linear inter-connected systems. The technique is applied either to every individual subsystem or to the whole as one shot system.- A new proposal of Adaptive Output Integral Sliding Mode Control (AOISMC) based only on output information plus static output feedback control is designed via an LMI formulation to control non-linear inter-connected systems. The new method is verified by application to a mathematical example representing an electrical power generator.- The development of a new method to design a dynamic control based on an LMI framework with Output Integral Sliding Mode Control (OISMC) to improve the stability and performance.- Using the above framework, making use of LMI tools and ISMC, a method of on-line actuator fault estimation has been proposed using the Proportional Multiple Integral Observer (PMIO) for fault estimation applicable to non-linear inter-connected systems
Robust de-centralized control and estimation for inter-connected systems
The thesis is concerned with the theoretical development of the control of inter-connected systems to achieve the whole overall stability and specific performance. A special included feature is the Fault-Tolerant Control (FTC) problem for the inter-connected system in terms of local subsystem actuator fault estimation. Hence, the thesis describes the main FTC challenges of distributed control of uncertain non-linear inter-connected systems. The basic principle adopted throughout the work is that the controller has two components, one involving the nominal control with unmatched components including uncertainties and disturbances. The second controller dealing with matched components including uncertainties and actuator faults.
The main contributions of the thesis are summarised as follows:
- The non-linear inter-connected systems are controlled by two controllers. The linear part via a linear matrix inequality (LMI) technique and the discontinuous part by using Integral Sliding Mode Control (ISMC) based on state feedback control.
- The development of a new observer-based state estimate control strategy for non-linear inter-connected systems. The technique is applied either to every individual subsystem or to the whole as one shot system.
- A new proposal of Adaptive Output Integral Sliding Mode Control (AOISMC) based only on output information plus static output feedback control is designed via an LMI formulation to control non-linear inter-connected systems. The new method is verified by application to a mathematical example representing an electrical power generator.
- The development of a new method to design a dynamic control based on an LMI framework with Output Integral Sliding Mode Control (OISMC) to improve the stability and performance.
- Using the above framework, making use of LMI tools and ISMC, a method of on-line actuator fault estimation has been proposed using the Proportional Multiple Integral Observer (PMIO) for fault estimation applicable to non-linear inter-connected systems
Load frequency controllers considering renewable energy integration in power system
Abstract: Load frequency control or automatic generation control is one of the main operations that take place daily in a modern power system. The objectives of load frequency control are to maintain power balance between interconnected areas and to control the power flow in the tie-lines. Electric power cannot be stored in large quantity that is why its production must be equal to the consumption in each time. This equation constitutes the key for a good management of any power system and introduces the need of more controllers when taking into account the integration of renewable energy sources into the traditional power system. There are many controllers presented in the literature and this work reviews the traditional load frequency controllers and those, which combined the traditional controller and artificial intelligence algorithms for controlling the load frequency
Finding unstable periodic orbits for nonlinear dynamical systems using polynomial optimisation
Computing unstable periodic orbits (UPOs) for systems governed by ordinary differential equations (ODEs) is a fundamental problem in the study of nonlinear dynamical systems that exhibit chaotic dynamics. Success of any existing method to compute UPOs relies on the availability of very good initial guesses for both the UPO and its time period. This thesis presents a computational framework for computing UPOs that are extremal, in the sense that they optimise the infinite-time average of a certain observable. Constituting this framework are two novel techniques.
The first is a method to localise extremal UPOs for polynomial ODE systems that does not rely on numerical integration. The UPO search procedure relies on polynomial optimisation to construct nonnegative polynomials whose sublevel sets approximately localise parts of the extremal periodic orbit. Points inside the relevant sublevel sets can then be computed efficiently through direct nonlinear optimisation. Such points provide good initial conditions for UPO computations with existing algorithms.
The second technique involves the addition of a control term to the original polynomial ODE system to reduce the instability of the extremal UPO, and, in some cases, to provably stabilise it. This control methodology produces a family of controlled systems parametrised by a control amplitude, to which existing UPO-finding algorithms are often more easily applied.
The practical potential of these techniques is demonstrated by applying them to find extremal UPOs for a nine-dimensional model of sinusoidally forced shear flow, an extended version of the Lorenz system, and two different three-dimensional chaotic ODE systems. Extensions of the framework to non-polynomial and Hamiltonian ODE systems are also discussed.Open Acces
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