Johan Löfberg

Johan Löfberg
Linköping University | LiU · Department of Electrical Engineering (ISY)

Phd

About

73
Publications
47,706
Reads
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12,290
Citations
Additional affiliations
October 2006 - present
Linköping University
Position
  • Professor (Associate)
September 2003 - September 2006
ETH Zurich
Position
  • PostDoc Position

Publications

Publications (73)
Preprint
Full-text available
The design of the path-following controller is crucial to enable reliable autonomous vehicle operation. This design problem is especially challenging for a general 2-trailer with a car-like tractor due to the tractor's curvature limitations and the vehicle's structurally unstable joint-angle kinematics in backward motion. Additionally, to make the...
Article
We propose a sequence of pedagogical steps for introducing the Youla-Kucera parametrization, starting from the internal model principle, and introducing the control structures of disturbance observer and internal model control along the way. We provide some background on the concepts and a brief survey of their treatment in textbooks on control.
Article
To optimally compensate for time-varying phase aberrations with adaptive optics, a model of the dynamics of the aberrations is required to predict the phase aberration at the next time step. We model the time-varying behavior of a phase aberration, expressed in Zernike modes, by assuming that the temporal dynamics of the Zernike coefficients can be...
Conference Paper
Full-text available
In order to guarantee that a self-driving vehicle is behaving as expected, stability of the closed-loop system needs to be rigorously analyzed. The key components for the lowest levels of control in self-driving vehicles are the controlled vehicle, the low-level controller and the local planner. The local planner that is considered in this work con...
Conference Paper
Full-text available
The demand for fuel-efficient transport solutions are steadily increasing with the goal of reducing environmental impact and increasing efficiency. Heavy-Duty Vehicle (HDV) platooning is a promising concept where multiple HDVs drive together in a convoy with small intervehicular spacing. By doing this, the aerodynamic drag is reduced which in turn...
Article
In system identification, input selection is a challenging problem. Since less complex models are desireable, non-relevant inputs should be methodically and correctly discarded before or under the estimation process. In this paper we investigate an input selection extension in least-squares ARX estimation and show that better model estimates are ac...
Article
Input selection is an important and oftentimes difficult challenge in system identification. In order to achieve less complex models, irrelevant inputs should be methodically and correctly discarded before or under the estimation process. In this paper we introduce a novel method of input selection that is carried out as a natural extension in a su...
Article
This paper presents a new method to compute upper and lower bounds of any voltage or current of an arbitrary linear electric circuit model with uncertain parameters. The bounds are in the frequency domain, and when compared to a previously proposed method, this novel approach provides a higher level of guarantee. The reason is that the bounds are n...
Article
Devising the planar routes of minimal length that are required to pass through predefined neighborhoods of target points plays an important role in reducing the mission's operating cost. Two versions of the problem are considered. The first one assumes that the ordering of the targets is fixed a priori. In such a case, the optimal route is devised...
Article
Full-text available
It is a well known fact that finite time optimal controllers, such as MPC does not necessarily result in closed loop stable systems. Within the MPC community it is common practice to add a final state constraint and/or a final state penalty in order to obtain guaranteed stability. However, for more advanced controller structures it can be difficult...
Article
This study presents a new approach for optimal placement of synchronised phasor measurement units (PMUs) to ensure complete power system observability in the presence of non-synchronous conventional measurements and zero injections. Currently, financial or technical restrictions prohibit the deployment of PMUs on every bus, which in turn motivates...
Conference Paper
Full-text available
We consider the task of devising a planar route of minimal distance which starts from a given starting point, passes through neighbourhoods of pre-defined target points, e.g. by priorities, and ends at a prescribed finishing location. Two types of routes are considered. A piecewise linear route is of minimal possible length, but introduces sharp tu...
Article
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Among the many different formulations of Model Predictive Control (MPC) with guaranteed stability, one that has attracted significant attention is the formulation with a terminal cost and terminal constraint set, the so called dual mode formulation. In this paper our goal is to make minimal changes to the dual mode framework, for the linear polytop...
Article
Full-text available
A method to identify linear parameter varying models through minimisation of an [Inline formula]-norm objective is presented. The method uses a direct nonlinear programming approach to a non-convex problem. The reason to use [Inline formula]-norm is twofold. To begin with, it is a well-known and widely used system norm, and second, the cost functio...
Conference Paper
Full-text available
Model predictive control (MPC) is one of the most popular advanced control techniques and is used widely in industry. The main drawback with MPC is that it is fairly computationally expensive and this has so far limited its practical use for nonlinear systems. To reduce the computational burden of nonlinear MPC, Feedback Linearization together with...
Article
In the presence of frequent inlet flow upsets, tuning of averaging level controllers is typically quite complicated since not only the size of the individual steps but also the time in between the subsequent steps need to considered. One structured way to achieve optimal filtering for such a case is to use Robust Model Predictive Control. The robus...
Article
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...
Conference Paper
Full-text available
A common assumption when proving stability of linear MPC algorithms for tracking applications is to assume that the desired setpoint is located far into the interior of the feasible set. The reason for this is that the terminal state constraint set which is centered around the setpoint must be contained within the feasible set. In many applications...
Article
This paper considers high-speed control of constrained linear parameter-varying systems using model predictive control. Existing model predictive control schemes for control of constrained linear parameter-varying systems typically require the solution of a semi-definite program at each sampling instance. Recently, variants of explicit model predic...
Article
One of the most fundamental problems in model predictive control (MPC) is the lack of guaranteed stability and feasibility. It is shown how Farkas’ Lemma in combination with bilevel programming and disjoint bilinear programming can be used to search for problematic initial states which lack recursive feasibility, thus invalidating a particular MPC...
Article
Full-text available
This paper presents the robust optimization framework in the modeling language YALMIP, which carries out robust modeling and uncertainty elimination automatically, and allows the user to concentrate on the high-level model. While introducing the software package, a brief summary of robust optimization is given, as well as some comments on modeling...
Chapter
Advanced robustness analysis methods employed in flight control law clearance such as IQC-analysis and μ-analysis, rely on linear fractional representations (LFRs). These models are usually obtained from linear parameter varying (LPV)-models which approximate the behaviour of the underlying parameter uncertain nonlinear aircraft model. The generati...
Conference Paper
Frequent inlet flow changes typically cause problems for averaging level controllers. For a frequently changing inlet flow the upsets do not occur when the system is in steady state and the tank level at its set-point. For this reason the tuning of the level controller gets quite complicated, since not only the size of the upsets but also the time...
Article
A given explicit piecewise affine representation of an MPC feedback law is approximated by a single polynomial, computed using linear programming. This polynomial state feedback control law guarantees closed-loop stability and constraint satisfaction. The polynomial feedback can be implemented in real time even on very simple devices with severe li...
Article
Full-text available
The task of generating time optimal trajectories for a six degrees of freedom industrial robot is discussed in the paper and an existing convex optimization formulation of the problem is extended to include new types of constraints. The new constraints are speed dependent and can be motivated from physical modeling of the motors and the drive syste...
Conference Paper
Full-text available
In this paper we present a regularization of an H<sub>2</sub>-minimization based LPV-model generation algorithm. Our goal is to take care of uncertainties in the data, and obtain more robust models when we have few data. We give an interpretation of the regularization, which shows that the regularization has connections to robust optimization and w...
Conference Paper
Full-text available
Many control related problems can be cast as semidefinite programs but, even though there exist polynomial time algorithms and good publicly available solvers, the time it takes to solve these problems can be long. Something many of these problems have in common, is that some of the variables enter as matrix valued variables. This leads to a low-ra...
Article
Full-text available
This paper addresses the issue of the practical implementation of Model Predictive Con-trollers (MPC) to processes with short sampling times. Given a closed-form solution to an MPC prob-lem, the main idea is to approximate the optimal con-trol law defined over state space regions by a higher degree polynomial which, when applied as a state-feedback...
Conference Paper
Full-text available
This paper addresses the issue of the practical implementation of Model Predictive Controllers (MPC) to processes with short sampling times. Given an explicit solution to an MPC problem, the main idea is to approximate the optimal control law defined over state space regions by a single polynomial of pre-specified degree which, when applied as a st...
Conference Paper
Full-text available
In this paper we use bilevel programming to find the maximum difference between a reference controller and a low-complexity controller in terms of the infinity-norm difference of their control laws. A nominal MPC for linear systems with constraints, and a robust MPC for linear systems with bounded additive noise are considered as reference controll...
Conference Paper
Full-text available
For linear and hybrid systems, constrained time-optimal control was shown to be a low complexity alternative to the explicit solution of the constrained finite-time optimal control problem. In this paper we show how Polya's relaxation can be employed to compute minimum-time controllers for discrete-time LPV systems. Contrary to previous publication...
Article
Recently it was shown how one can reformulate the MPC problem for LPV systems to a series of mpLPs by a closed-loop minimax MPC algorithm based on dynamic programming. A relaxation technique is employed to reformulate constraints which are polynomial in the schedul-ing parameters to parameter-independent constraints. The algorithm allows the comput...
Article
Full-text available
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. Additionally, they often become increasingly ill-conditioned. To alleviate these proble...
Article
Full-text available
Many optimization problems gain from being interpreted and solved in either primal or dual form. For a user with a particular application, one of these forms is usually much more natural to use, but this is not always the most efficient one. This paper presents an implementation in the optimization modelling tool YALMIP that allows the user to defi...
Conference Paper
Full-text available
In this paper we demonstrate how one can reformulate the MPC problem for LPV systems to a series of mpLPs by a closed-loop minimax MPC algorithm based on dynamic programming. A relaxation technique is employed to reformulate constraints which are polynomial in the scheduling parameters to parameter-independent constraints. The algorithm allows the...
Article
Full-text available
In this paper we have formulated the problem of finding 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...
Article
In Ding et al. [A unified approach for circularity and spatial straightness evaluation using semi-definite programming, International Journal of Machine Tools & Manufacture 47(10) (2007) 1646–1650], the authors advocate semidefinite programming-based relaxations of quadratic optimization problems as a vehicle to solve two circularity and straightne...
Article
A considerable amount of optimization problems arising in the control and systems theory field can be seen as special instances of robust optimization. Much of the modeling effort in these cases is spent on converting an uncertain problem to a robust counterpart without uncertainty. Since many of these conversions follow standard procedures, it is...
Conference Paper
Full-text available
Experiment design involving selection of optimal experiment positions for nonlinear gray-box models is studied. From the derived Fisher information matrix, a convex optimization problem is posed. By considering the dual problem, the experiment design is efficiently solved with linear complexity in the number of candidate positions, compared to cubi...
Article
In this paper we propose a closed-loop min-max MPC algorithm based on dynamic programming, to compute explicit control laws for systems with a linear parameter-varying state transition matrix. This enables the controller to exploit parameter information to improve performance compared to a standard robust approach where no uncertainty knowledge is...
Article
Full-text available
We describe a major update of our Matlab freeware GloptiPoly for parsing generalized problems of moments and solving them numerically with semidefinite programming. 1 What is GloptiPoly? Gloptipoly 3 is intended to solve, or at least approximate, the Generalized Problem of Moments (GPM), an infinite-dimensional optimization problem which can be vie...
Conference Paper
A novel machine learning paradigm, i.e. enclosing machine learning based on regular geometric shapes was proposed. It adopted regular minimum volume enclosing and bounding geometric shapes (sphere, ellipsoid, and box) or their unions and so on to obtain one class description model and thus imitate the human “Cognizing” process. A point detection an...
Article
Full-text available
Experiment design involving selection of optimal experiment positions for nonlinear gray-box models is studied. From the derived Fisher information matrix, a convex optimization problem is posed. By considering the dual problem, the experiment design is eciently solved with linear complexity in the number of candidate positions, compared to cubic c...
Conference Paper
Full-text available
An algebraic formulation is proposed for the static output feedback (SOF) problem: the Hermite stability criterion is applied on the closed-loop characteristic polynomial, resulting in a non-convex bilinear matrix inequality (BMI) optimization problem for SIMO or MISO systems. As a result, the BMI problem is formulated directly in the controller pa...
Article
Full-text available
Identification of parametric nonlinear models involves estimating unknown parameters and detecting its underlying structure. Structure computation is concerned with selecting a subset of parameters to give a parsimonious description of the system which may afford greater insight into the functionality of the system or a simpler controller design. I...
Conference Paper
Full-text available
The off-line solution to optimal control problems for linear or piecewise-affine systems with constraints has garnered much attention because the on-line implementation can be realized with a simple look-up table. Specifically, multi-parametric programming techniques can be utilized to compute a piecewise-affine feedback law off-line. Even though t...
Article
Full-text available
Piecewise a-ne (PWA) systems are useful models for describing non- linear and hybrid systems. They also result from LTI systems subject to con- strained optimal control. Recently, stability analysis of PWA systems has received increased interest since it can help to obtain explicit feedback control laws of low complexity (Grieder et al., 2003b; Gri...
Conference Paper
Full-text available
The MATLAB toolbox YALMIP is introduced. It is described how YALMIP can be used to model and solve optimization problems typically occurring in systems and control theory. In this paper, free MATLAB toolbox YALMIP, developed initially to model SDPs and solve these by interfacing eternal solvers. The toolbox makes development of optimization problem...
Conference Paper
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,...
Article
We introduce a new methodology for the numer- ical solution of semidefinite relaxations arising from the sum of squares (SOS) decomposition of multivariate polynomials. The method is based on a novel SOS representation, where polynomials are represented by a finite set of values at discrete sampling points. The techniques have very appealing theo-...
Conference Paper
The use of MATLAB toolbox YALMIP to model and solve optimization problems occuring in systems in control theory was discussed. The toolbox makes development of control oriented SDP problems. Rapid prototyping of an algorithm based on SDP can be done using standard MATLAB commands. YALMIP automatically detects the kind of a problem the user has defi...
Conference Paper
In this paper, we investigate a discrete-time approach to uncertainty modeling for robust control. We show via simulations of one LTI system and experimental data from a one-tank test-bed that a current technique for time-domain uncertainty modeling leads to a feasible linear program. Hence, it is useful for developing robust control solutions.
Conference Paper
Robust synthesis is one of the remaining challenges in model predictive control (MPC). One way to robustify an MPC controller is to formulate a minimax problem, i.e., optimize a worst-case performance measure. For systems modeled with an uncertain gain, there are many results available. Typically, the minimax formulations have given intractable pro...
Article
A new approach to minimax MPC for systems with bounded external system disturbances and measurement errors is introduced. It is shown that joint deterministic state estimation and minimax MPC can be written as an optimization problem with linear and quadratic matrix inequalities. By linearizing the quadratic matrix inequality, a semidefinite progra...
Article
Full-text available
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 consti...
Article
Full-text available
We present a method to increase feasibility in MPC algorithms that use ellipsoidal terminal state constraints and performance bounds from nominal controllers. The method is based on estimating a bound on the achievable performance with a saturated nominal controller and using this bound in the MPC algorithm. The resulting MPC controller can be impl...
Conference Paper
Some previously existing results on locally optimal backstepping controllers are extended to a larger class of nonlinear systems and another performance index. The result is a design procedure that gives a nonlinear controller with LQ performance in the origin and tries to recover the quadratic performance index also globally. As a part of the cont...
Conference Paper
We present a method to increase the feasibility in model predictive control (MPC) algorithms that use ellipsoidal terminal state constraints and performance bounds from nominal controllers. The method is based on estimating a bound on the achievable performance with a saturated nominal controller and using this bound in the MPC algorithm. The resul...
Article
Full-text available
Frequent inlet flow changes, especially in the same direction, typically cause problems for averaging level controllers. To obtain optimal flow filtering while being robust towards future inlet flow upsets closed loop robust MPC has been used. It differs from other averaging controllers in that it does not return the tank level to a fixed set-point...

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