Continuous-time integral dynamics for Aggregative Game equilibrium seeking

In this paper, we consider continuous-time semi-decentralized dynamics for the equilibrium computation in a class of aggregative games. Specifically, we propose a scheme where decentralized projected-gradient dynamics are driven by an integral control law. To prove global exponential convergence of the proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov function argument. We derive a sufficient condition for global convergence that we position within the recent literature on aggregative games, and in particular we show that it improves on established results

Demand response from thermostatically controlled loads: modelling, control and system-level value

The research area of this thesis concerns the efficient and secure operation of the future low-carbon power system, where alternative sources of control and flexibility will progressively replace the traditional providers of ancillary services i.e. conventional generators. Various options are engaged in this challenge and suit the innovative concept of Smart Grid. Specifically, this thesis investigates the potential of demand side response support by means of thermostatically controlled loads (TCLs). This thesis aims to quantify the impact that a population of thermostatically controlled loads has on the commitment and dispatch of a future power system characterized by a large penetration of renewable energy sources (e.g. wind) that are variable and intermittent. Thanks to their relative insensitivity to temperature fluctuations, thermostatic loads would be able to provide frequency response services and other forms of system services, such as energy arbitrage and congestion relief. These actions in turn enhance the power system operation and support the strict compliance with system security standards. However, the achievement of this transition requires addressing two challenges. The first deals with the design of accurate device models. Significant differences affect the devices’ design included in the same class, leading to different system-level performances. In addition, the flexibility associated to TCLs would be handled more easily by means of models that describes the TCLs dynamics directly as a cluster rather than considering the appliances individually. Second, it is not straightforward achieving satisfactory controllability of a cluster of TCLs for the considered applications. The complexity lies in the typical operation of these devices that has only two power states (on and off) whereas the desired response is continuous. Moreover the control strategy has always to comply with strict device-level temperature constraints as the provision of ancillary services cannot affect the quality of the service of the primary function of TCLs. This thesis addresses the challenges exhibited. Detailed thermal dynamic models are derived for eight classes of domestic and commercial refrigeration units. In addition, a heterogeneous population of TCLs is modelled as a leaky storage unit; this unit describes the aggregate flexibility of a large population of TCLs as a single storage unit incorporating the devices’ physical thermal models and their operational temperature limits. The control problem is solved by means of an initial hybrid controller for frequency response purposes that is afterwards replaced by an advanced controller for various applications. Provided these two elements, a novel demand side response model is designed considering the simultaneous provision of a number of system services and taking into account the effect of the load energy recovery. The model, included in a stochastic scheduling routine, quantifies the system-level operational cost and wind curtailment savings enabled by the TCLs support.Open Acces

Robust Engineering of Dynamic Structures in Complex Networks

Populations of nearly identical dynamical systems are ubiquitous in natural and engineered systems, in which each unit plays a crucial role in determining the functioning of the ensemble. Robust and optimal control of such large collections of dynamical units remains a grand challenge, especially, when these units interact and form a complex network. Motivated by compelling practical problems in power systems, neural engineering and quantum control, where individual units often have to work in tandem to achieve a desired dynamic behavior, e.g., maintaining synchronization of generators in a power grid or conveying information in a neuronal network; in this dissertation, we focus on developing novel analytical tools and optimal control policies for large-scale ensembles and networks. To this end, we first formulate and solve an optimal tracking control problem for bilinear systems. We developed an iterative algorithm that synthesizes the optimal control input by solving a sequence of state-dependent differential equations that characterize the optimal solution. This iterative scheme is then extended to treat isolated population or networked systems. We demonstrate the robustness and versatility of the iterative control algorithm through diverse applications from different fields, involving nuclear magnetic resonance (NMR) spectroscopy and imaging (MRI), electrochemistry, neuroscience, and neural engineering. For example, we design synchronization controls for optimal manipulation of spatiotemporal spike patterns in neuron ensembles. Such a task plays an important role in neural systems. Furthermore, we show that the formation of such spatiotemporal patterns is restricted when the network of neurons is only partially controllable. In neural circuitry, for instance, loss of controllability could imply loss of neural functions. In addition, we employ the phase reduction theory to leverage the development of novel control paradigms for cyclic deferrable loads, e.g., air conditioners, that are used to support grid stability through demand response (DR) programs. More importantly, we introduce novel theoretical tools for evaluating DR capacity and bandwidth. We also study pinning control of complex networks, where we establish a control-theoretic approach to identifying the most influential nodes in both undirected and directed complex networks. Such pinning strategies have extensive practical implications, e.g., identifying the most influential spreaders in epidemic and social networks, and lead to the discovery of degenerate networks, where the most influential node relocates depending on the coupling strength. This phenomenon had not been discovered until our recent study