John-Josef Leth

Robust helicopter stabilization in the face of wind disturbance

When a helicopter is required to hover with minimum deviations from a desired position without measurements of a persistent wind disturbance, a robustly stabilizing control action is vital. In this paper, the stabilization of the position and translational velocity of a nonlinear helicopter model affected by a wind disturbance is addressed. The wind disturbance is assumed to be a sum of a fixed number of sinusoids with unknown amplitudes, frequencies and phases. An estimate of the disturbance is introduced to be adapted using state measurements for control purposes. A nonlinear controller is then designed based on nonlinear adaptive output regulation and robust stabilization of a chain of integrators by a saturated feedback. Simulation results show the effectiveness of the control design in the stabilization of helicopter motion and the built-in robustness of the controller in handling parameter and model uncertainties.

Model Reduction by Nice Selections for Linear Switched Systems

A moment-matching method for model reduction of linear switched systems (LSSs) is presented. The method can be seen as a non-trivial extension of the Krylov subspace methods for linear time-invariant (LTI) systems. The procedure is based on the so called “nice selections,” which represent a choice of basis in the reachability or observability space of the LSS. The framework can also be used for exact matching of the input-output behavior of an LSS with a reduced order LSS for a specific switching sequence. Conditions for applicability of the method for model reduction are stated and finally the results are illustrated on numerical examples.

Model reduction by moment matching for linear switched systems

A moment-matching method for the model reduction of linear switched systems (LSSs) is developed. The method is based upon a partial realization theory of LSSs and it is similar to the Krylov subspace methods used for moment matching for linear systems. The results are illustrated by a numerical example.

Stochastic stability of systems with semi-Markovian switching

This paper examines stochastic stability of switched dynamics in continuous time. The time evolution of the so called continuous state is at all times, determined by the dynamics indexed by the switching process or discrete state. The main contribution of this paper appears as stochastic stability results for switched dynamics with semi-Markovian switching. The notion of moment stability in the wide sense (MSWS) is applied as a generalization of ? -moment stability. A sufficient criterion for MSWS is presented for the above class of systems, where each subsystem is assumed to be characterized by a Lyapunov function candidate together with an associated growth rate equation. For the set of Lyapunov functions, a compatibility criterion is assumed to be fulfilled, bounding the ratio between pairs of Lyapunov functions.

Optimal production planning of a power plant

This paper addresses the problem of planning the usage of actuators optimally in an economic perspective. The objective is to maximize the profit of operating a given plant during 24 hours of operation. Models of two business objectives are formulated in terms of system states and the monetary value of these objectives is established. Based on these and the cost of using the different actuators a profit function has been formulated. The optimization of the profit is formulated as an optimal control problem where the constraints include the dynamics of the plant as well as a requirement to reference tracking. A power plant is considered in this paper, where the fuel system consists of three different fuels; coal, gas, and oil.

Stochastic Stability of Markovianly Switched Systems

This technical note examines the stochastic stability of noisy dynamics in discrete and continuous time. The notion of moment stability in the wide sense (MSWS) is presented as a generalization of ϵ-moment stability. MSWS is intentionally not based on stochastic convergence properties, since in most practically appearing systems convergence to any equilibrium is not present. A sufficient criterion for both MSWS and ergodicity is presented for a class of systems comprising a finite set of noisy dynamical systems among which switching is governed by a Markov chain. Stability/instability properties for each separate subsystem are assumed to be quantified by a Lyapunov function candidate together with an associated growth rate equation. For the set of Lyapunov functions, a compatibility criterion is assumed to be fulfilled, bounding the ratio between pairs of Lyapunov functions.

A class of stochastic hybrid systems with state-dependent switching noise

In this paper, we develop theoretical results based on a proposed method for modeling switching noise for a class of hybrid systems with piecewise linear partitioned state space, and state-depending switching. We devise a stochastic model of such systems, whose global dynamics is governed by a continuous-time stochastic process. The main result of this paper is that we may identify the realizations of the global dynamics with the solutions of a differential inclusion. Hence, an analysis of switched systems with switching noise can be carried out either based on a non-deterministic method via the differential inclusion, or on a stochastic method via the stochastic process. Furthermore, we describe how to construct intensity plots, which provide a quick overview of the behavior of the system. An example is included to illustrate this.

Demand Response of a TCL Population Using Switching-Rate Actuation

This paper considers the problem of actively managing the power consumption of a large number of thermostatically controlled loads (TCLs), namely, a TCL population and a case study of household refrigerators. Control is performed using a new randomized actuation that consists of switching units ON and OFF at given rates, while at the same time respecting the nominal constraints on each individual unit. Both the free and the controlled behavior of individual TCLs can be aggregated, making it possible to handle a TCL population as if it were a single system. The aggregation method uses the distribution of the TCLs individual states across the population. The distribution approach has two main advantages. It scales excellently, since the computational requirements do not increase with the number of units, and it allows data from individual units to be used anonymously, which solves privacy concerns relevant for consumer adoption.

Nearly cyclic pursuit and its hierarchical variant for multi-agent systems

The rendezvous problem for multiple agents under nearly cyclic pursuit and hierarchical nearly cyclic pursuit is discussed in this paper. The control law designed under nearly cyclic pursuit strategy enables the agents to converge at a point dictated by a beacon. A hierarchical version of the nearly cyclic pursuit is proposed to increase the rate of convergence and also minimizes the communication links between the layers. We provide simulation results to demonstrate the effectiveness of our proposed method.

A Mixed-Integer Linear Programming approach to wind farm layout and inter-array cable routing

A Mixed-Integer Linear Programming (MILP) approach is proposed to optimize the turbine allocation and inter-array offshore cable routing. The two problems are considered with a two steps strategy, solving the layout problem first and then the cable problem. We give an introduction to both problems and present the MILP models we developed to solve them. To deal with interference in the onshore cases, we propose an adaptation of the standard Jensens model, suitable for 3D cases. A simple Stochastic Programming variant of our model allows us to consider different wind scenarios in the optimization. For the inter-array cable routing, we propose a new MILP model able to deal with different constraints arsing in practical application, such as capacity limitations, substation limitations and non-crossing constraints. Computational results on real-world instances prove the practical viability of the approach.