John Leth

Control for large scale demand response of thermostatic loads

Demand response is an important Smart Grid concept that aims at facilitating the integration of volatile energy resources into the electricity grid. This paper considers a residential demand response scenario and specifically looks into the problem of managing a large number thermostat-based appliances with on/off operation. The objective is to reduce the consumption peak of a group of loads composed of both flexible and inflexible units. The power flexible units are the thermostat-based appliances. We discuss a centralized, model predictive approach and a distributed structure with a randomized dispatch strategy.

Theoretical analysis of balanced truncation for linear switched systems

Abstract In this paper we present a theoretical analysis of the model reduction algorithm for linear switched systems from Shaker and Wisniewski (2011, 2009). This algorithm is based on balanced truncation. More precisely, ( 1 ) we provide a bound on the approximation error in L 2 norm, ( 2 ) we provide a system theoretic interpretation of grammians and their singular values, ( 3 ) we show that the performance of balanced truncation depends only on the input-output map and not on the choice of the state-space representation. In addition, we also show that quadratic stability and LMI estimates of the L 2 gain also depend only on the input-output map.

Estimation of inner-domain temperatures for a freezing process

In this paper a state observer for a distributed parameter system (DPS) with nonconstant parameter functions is presented. The DPS describes the freezing of foodstuff in vertical plate freezers and is a nonlinear heat equation. The observer is based upon the Extended Kalman Filter, meaning that the nonlinear heat equation has been discretized in the spatial domain before designing the observer. We show that the observer is robust with respect to perturbations of parameter functions and noisy measurement signals and that the innerdomain temperatures can be correctly estimated.

Cartesian product-based hierarchical scheme for multi-agent systems

Abstract In this paper, we solve the average-consensus problem using a hierarchical scheme based on Cartesian product of strongly connected balanced graphs — an algebraic approach to design complex networks. We show that the Cartesian product based hierarchical scheme for multi-agent systems outperforms the single-layer control strategies for average-consensus problem in terms of convergence rate, and also the system matrix produced by Cartesian product-based hierarchical (CPH) scheme do not necessarily exhibit block circulant symmetry. We analyze that if the factors graphs in Cartesian product are cyclic pursuit graphs, then the CPH scheme provides the same convergence rate while requiring the same communication links as in the hierarchical cyclic pursuit (HCP). We provide simulation results to demonstrate the key theoretical results.

Leader-following consensus of multi-agent systems under hierarchical nearly cyclic pursuit

In this paper, we solve the leader-following consensus problem using nearly cyclic pursuit (NCP) and a two-layer hierarchical nearly cyclic pursuit (HNCP). First, we design a control strategy based on the nearly cyclic pursuit(NCP) to enable the agents to rendezvous at a point. Second, we propose a two-layer HNCP for a leader-following consensus problem to increase the convergence rate of the network. We show that the two-layer HNCP outperforms the original NCP. Simulations illustrate the key theoretical results.

Stochastic design of switching controller for quadrotor UAV under intermittent localization.

This paper presents a novel methodology for the design of motion controllers for UAVs of quad-rotor type. The developed controllers are of time switching type, where discrete modes are determined by the momentary availability of global positioning information. Relevant application scenarios are found, where the availability of GPS or generally GNSS is scarce, e.g. in case of indoor flight. For indoor flight dedicated indoor positioning technology may be applied, such as the ultra-sound/radio solution from [1]. Even with such technology available, due to reflection, interference and absorption, the required positioning service cannot be provided continuously without intermittency. A control model is presented, for which a general observer based controller framework is suggested. Feedback and observer gains are then allowed to switch according to the availability of positioning information. The mechanical states of the UAV are inherently un-observable in the absence of positioning information. Therefore the controller, in that case, will be unstable. However, by designing a set of feedback/observer gains to obtain stochastic stability under a given stochastic model for the switching process, an overall well functioning controller is obtained.

Local analysis of hybrid systems on polyhedral sets with state-dependent switching

Abstract This paper deals with stability analysis of hybrid systems. Various stability concepts related to hybrid systems are introduced. The paper advocates a local analysis. It involves the equivalence relation generated by reset maps of a hybrid system. To establish a tangible method for stability analysis, we introduce the notion of a chart, which locally reduces the complexity of the hybrid system. In a chart, a hybrid system is particularly simple and can be analyzed with the use of methods borrowed from the theory of differential inclusions. Thus, the main contribution of this paper is to show how stability of a hybrid system can be reduced to a specialization of the well established stability theory of differential inclusions. A number of examples illustrate the concepts introduced in the paper.

Modeling of water supply systems: Circuit theoretic approach

Water leakage is an important component of water losses. Many methods have emerged from urban water supply systems for leakage control, but it still remains a challenge in many countries. To have better understanding of leakage in water supply system (WSS), to control leakage effectively and for optimal design of WSS, suitable modeling is an important prerequisite. In this paper first, the mathematical expression for pressure drop over each component of the water supply system such as pipes, pumps, valves and water towers is presented. Then the network model is derived based on the circuit theory for pressure management in the system. A suitable projection is used to reduce the state vector and to express the model in standard state-space form.

A generalized hierarchical nearly cyclic pursuit for the leader-following consensus problem in multi-agent systems

In this paper, we solve the leader-following consensus problem using a hierarchical nearly cyclic pursuit (HNCP) strategy for multi-agent systems. We extend the nearly cyclic pursuit strategy and the two-layer HNCP to the generalized L-layer HNCP that enables the agents to rendezvous at a point dictated by a beacon. We prove that the convergence rate of the generalized L-layer HNCP for the leader-following consensus problem is faster than that of the nearly cyclic pursuit. Simulation results demonstrate the effectiveness of the proposed method.

A variant of the cyclic pursuit scheme for consensus in multi-agent systems

In this paper, we present a solution to the rendezvous problem using a variant of the cyclic pursuit, in which agent i follows agent i +1 modulo η and in which agent i follows agent i-1 modulo n. With the variant of the cyclic pursuit, we aim to increase the convergence rate compared to the cyclic pursuit A generalized variant of the proposed strategy is also presented to guide mobile agents to rendezvous at a desired point We provide simulation results to illustrate the key theoretical results.