Model Reduction using a Frequency-Limited H2-Cost

We propose a method for model reduction on a given frequency range, without the use of input and output filter weights. The method uses a nonlinear optimization approach to minimize a frequency limited H2 like cost function. An important contribution in the paper is the derivation of the gradient of the proposed cost function. The fact that we have a closed form expression for the gradient and that considerations have been taken to make the gradient computationally efficient to compute enables us to efficiently use off-the-shelf optimization software to solve the optimization problem.Comment: Submitted to Systems and Control Letter

Fast or Cheap: Time and Energy Optimal Control of Ship-to-Shore Cranes

This paper addresses the trade-off between time- and energy-efficiency for the problem of loading and unloading a ship. Container height constraints and energy consumption and regeneration are dealt with. We build upon a previous work that introduced a coordinate system suitable to deal with container avoidance constraints and incorporate the energy related modeling. In addition to changing the coordinate system, standard epigraph reformulations result in an optimal control problem with improved numerical properties. The trade-off is dealt with through the use of weighting of the total time and energy consumption in the cost function. An illustrative example is provided, demonstrating that the energy consumption can be substantially reduced while retaining approximately the same loading time.Comment: Paper accepted for presentation at 22nd IFAC World Congres

The Power of District Judges and the Responsibility of Courts of Appeals

In this paper we have formulated the problem offinding an LPV-approximation to a system as an optimization problem. For this optimization problem we have presented two possible ways to solve this. The problem is posed as a model reduction problem and formulated such that it should try to preserve the input-output behavior of the system. In the two examples in the paper the potential of the new methods are shown. We have also shown the benefits of using model reduction techniques to capture the input-output behavior to obtain accurate low order LPV-approximations. One method uses SDP-optimization to solve the problem. SDP optimization has been a hot topic during the last years, but the problem with the SDP method is that it scales badly with the dimension of the problem. Also here it has bilinear constraint swhich makes the problem really difficult. With the other method we try to use a more general nonlinear approach which seem to be more suitable for this problem. For this method we have also calculated a gradient that can be used to apply a descentor Newton-like method to solve the problem

Approximations of closed-loop minimax MPC Approximations of closed-loop minimax MPC

Abstract Minimax or worst-case approaches have been used frequently recently in model predictive control (MPC) to obtain control laws that are less sensitive to uncertainty. The problem with minimax MPC is that the controller can become overly conservative. An extension to minimax MPC that can resolve this problem is closed-loop minimax MPC. Unfortunately, closed-loop minimax MPC is essentially an intractable problem. In this paper, we introduce a novel approach to approximate the solution to a number of closed-loop minimax MPC problems. The result is convex optimization problems with size growing polynomially in system dimension and prediction horizon. Keywords: Predictive Abstract Minimax or worst-case approaches have been used frequently recently in model predictive control (MPC) to obtain control laws that are less sensitive to uncertainty. The problem with minimax MPC is that the controller can become overly conservative. An extension to minimax MPC that can resolve this problem is closed-loop minimax MPC. Unfortunately, closed-loop minimax MPC is essentially an intractable problem. In this paper, we introduce a novel approach to approximate the solution to a number of closed-loop minimax MPC problems. The result is convex optimization problems with size growing polynomially in system dimension and prediction horizon

A Convex Relaxation of a Minimax MPC Controller

Model predictive control (MPC) for systems with bounded disturbances is studied. A minimax formulation with optimization of the worst-case scenario is defined and conservatively approximated using a relaxation (the S-procedure), yielding a semidefinite optimization problem. Possible extensions are discussed and it is argued that the approach constitutes a promising framework for minimax MPC

Block Diagonalization of Matrix-Valued Sum-of-Squares Programs

Checking non-negativity of polynomials using sum-of-squares has recently been popularized and found many applications in control. Although the method is based on convex programming, the optimization problems rapidly grow and result in huge semidefinite programs. The paper [4] describes how symmetry is exploited in sum-of-squares problems in the MATLAB toolbox YALMIP, but concentrates on the scalar case. This report serves as an addendum, and extends the strategy to matrix-valued sum-of-squares problems.