Lars Imsland

Model Predictive Load-Frequency Control

A model predictive controller (MPC) for load frequency control (LFC) of an interconnected power system is investigated. The MPC is based on a simplified system model of the Nordic power system, and it takes into account limitations on tie-line power flow, generation capacity, and generation rate of change. The participation factors for each generator are optimization variables, and suggestions are made as to how one can ensure tie-line power transfer margins through slack-variables, and pricing information through the objective function. The solution of MPC for LFC is completed by including a Kalman filter for state estimation. The presented MPC is compared against a conventional LFC/AGC scheme with proportional integral (PI) controllers. Simulations show that the MPC gives better frequency response while using cheaper resources. This paper illustrates that MPC could be a realistic solution to some of the LFC problems power systems are facing today.

Monitoring Moving Objects Using Aerial Mobile Sensors

We propose an optimization-based path-planning framework for an aerial mobile sensor network. The purpose of the path planning is to monitor a set of moving surface objects. The algorithm provides collision-free mobile sensor trajectories that are feasible with respect to user-defined vehicle dynamics. The objective of the resulting optimal control problem is to minimize the uncertainty of the objects, represented as the trace of the augmented state and parameter estimation error covariance. The dynamic optimization problem is discretized into a large-scale nonlinear programming problem using the direct transcription method known as simultaneous collocation. The optimization problem is solved with a receding horizon and both a field experiment and a numerical simulation illustrate the approach.

Combined economic and regulatory predictive control

A combined economic and regulatory Model Predictive Control (MPC) framework, referred to as dual-objective MPC, is presented. Economic and regulatory cost objectives are combined using an explicitly defined dynamic weight function. The features embedded in the weight function allow for increased economic online performance during process transients, while simultaneously steering the process to an optimal economic steady-state. The proposed strategy gives an online optimization problem of same type as typical nonlinear MPC formulations, with the same number of variables. Increased economic transient performance is illustrated for an acetylene hydrogenation case, when compared to regulatory MPC. A link to dissipativity theory for the presented dual-objective MPC strategy concludes the work.

Monitoring an Advection-Diffusion Process Using Aerial Mobile Sensors

A path planning framework for regional surveillance of a planar advection-diffusion process by aerial mobile sensors is proposed. The goal of the path planning is to produce feasible and collision-free trajectories for a set of aerial mobile sensors that minimize some uncertainty measure of the process under observation. The problem is formulated as a dynamic optimization problem and discretized into a large-scale nonlinear programming (NLP) problem using the Petrov–Galerkin finite element method in space and simultaneous collocation in time. Receding horizon optimization problems are solved in simulations with an advection-dominated ice concentration field. Simulations illustrate the usefulness of the proposed method.

On convergence of the unscented Kalman–Bucy filter using contraction theory

Contraction theory entails a theoretical framework in which convergence of a nonlinear system can be analysed differentially in an appropriate contraction metric. This paper is concerned with utilising stochastic contraction theory to conclude on exponential convergence of the unscented Kalman–Bucy filter. The underlying process and measurement models of interest are Itô-type stochastic differential equations. In particular, statistical linearisation techniques are employed in a virtual–actual systems framework to establish deterministic contraction of the estimated expected mean of process values. Under mild conditions of bounded process noise, we extend the results on deterministic contraction to stochastic contraction of the estimated expected mean of the process state. It follows that for the regions of contraction, a result on convergence, and thereby incremental stability, is concluded for the unscented Kalman–Bucy filter. The theoretical concepts are illustrated in two case studies.

Iterative algorithms for computing the feedback Nash equilibrium point for positive systems

ABSTRACT The paper studies N-player linear quadratic differential games on an infinite time horizon with deterministic feedback information structure. It introduces two iterative methods (the Newton method as well as its accelerated modification) in order to compute the stabilising solution of a set of generalised algebraic Riccati equations. The latter is related to the Nash equilibrium point of the considered game model. Moreover, we derive the sufficient conditions for convergence of the proposed methods. Finally, we discuss two numerical examples so as to illustrate the performance of both of the algorithms.

Forecasting using multivariate empirical mode decomposition — Applied to iceberg drift forecast

The prediction of the movement of a floating object in the ocean, such as an iceberg, is a challenging problem. Large uncertainties in the driving forces and possibly in the geometry of the object itself prevent accurate forecasts. However, if observations of the past trajectory of the object are available the forecast can be improved considerably. This article proposes an adaptive data-driven forecast algorithm using multivariate empirical mode decomposition to handle these kinds of forecast problems. The algorithm identifies the common oscillatory modes and noise in the velocity of the floating object and its driving forces. Thereafter, it decides which mode contributes to the movement and how the future movement of each mode can be predicted best with the available information. The efficacy of the proposed forecast algorithm is shown on a real iceberg drift data set.

The moving horizon estimator used in iceberg drift estimation and Forecast

Iceberg drift forecast is a challenging process. Large uncertainties in iceberg geometry and driving forces prevent accurate forecasts. In this work, a moving horizon estimation approach that uses past drift information of the iceberg to correct the uncertainties is proposed to improve the forecast. Simple criteria are introduced to aid the decision of which uncertain parameters are most beneficial to estimate. In addition, it is discussed why other choices result in a lower prediction performance after the estimation process. Based on these considerations, the moving horizon estimator is implemented on a drift trajectory of an iceberg surveyed during a research expedition Offshore Newfoundland in 2015. It is demonstrated that the iceberg drift forecast improves significantly within a short-time frame. Furthermore, it is shown that the approach will in general also improve 24 hour iceberg drift predictions.

A Study on an Iceberg Drift Trajectory

Iceberg drift forecast is a challenging process. Large uncertainties in iceberg geometry and in the driving forces current, wind and waves make accurate forecasts difficult. This article illustrates from a data set that even if the uncertainties in current, wind and waves are reduced the forecast using a dynamic iceberg models stays difficult, because of the sensitivity of the model to different parameters and inputs. Nevertheless, if the uncertainty of the current driving force on the iceberg is reduced by measuring the current at the iceberg location, it is possible under specific conditions to estimate the approximate iceberg shape. This iceberg shape geometry can be used directly in the dynamic iceberg model. NOMENCLATURE a Major axis of ellipse [m] A Iceberg layer cross sectional area [m2] b Minor axis of ellipse [m] Fa Air drag force [N] Fc Water drag force [N] Fcor Coriolis force [N] Fp Pressure gradient force [N] Fr Wave radiation force [N] h Iceberg layer height [m] k Ratio between minor and major axis [−] m Iceberg mass [kg] ∗Address all correspondence to this author. p Vector of parameters r Iceberg layer radius [m] R Measurement noise covariance [−] u Vector of inputs v Measurement noise V Iceberg velocity [m/s] Vkeel Iceberg keel volume [m3] Vsail Iceberg sail volume [m3] x Vector of differential states y Vector of outputs ρice Iceberg density [kg/m3] ρw Water density [kg/m3] INTRODUCTION Icebergs are a threat to navigation and offshore installations. Good operational iceberg drift forecasts are important for marine operations such as station keeping in areas subjected to drifting icebergs. Mechanistic dynamic models, which model the drift of an iceberg by considering the forces that act on the iceberg, have been developed by [1–3]. An operational iceberg drift model was developed at the Canadian Ice Service [4]. The model uses environmental inputs as winds, waves and currents and detailed description of the iceberg keel geometry to simulate the iceberg trajectory. Currents are usually identified as the most important driving force for the iceberg drift [4–7]. However, current direction and speed are identified as the most uncertain iceberg model param1 Copyright c

Stochastic NMPC of Batch Processes Using Parameterized Control Policies

Abstract Nonlinear model predictive control (NMPC) is an effective method for optimal operation of batch processes. Most dynamic models however contain significant uncertainties. It is therefore important to take these uncertainties into account in the formulation of the open-loop MPC problem to prevent infeasibilities or worse performance. An issue of such formulations is the disregard of feedback in the predictions, which leads to overly conservative control actions. The introduction of feedback through parametrized control policies is one way to solve this issue. In this work we compare the performance of affine feedback policies against more complex policies given by radial basis function networks. We incorporate these feedback policies into a polynomial chaos based stochastic NMPC algorithm to gauge their efficiency. The parameters of the feedback policies are either determined online by the NMPC algorithm or are pre-computed offline.