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Löfberg, Johan
Publications (10 of 73) Show all publications
Bakarac, P., Holaza, J., Kaluz, M., Klauco, M., Löfberg, J. & Kvasnica, M. (2018). Explicit MPC Based on Approximate Dynamic Programming. In: 2018 EUROPEAN CONTROL CONFERENCE (ECC): . Paper presented at 2018 European Control Conference, June 12-15, 2018. Limassol, Cyprus.
Open this publication in new window or tab >>Explicit MPC Based on Approximate Dynamic Programming
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2018 (English)In: 2018 EUROPEAN CONTROL CONFERENCE (ECC), 2018Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we show how to synthesize simple explicit MPC controllers based on approximate dynamic programming. Here, a given MPC optimization problem over a finite horizon is solved iteratively as a series of problems of size one. The optimal cost function of each subproblem is approximated by a quadratic function that serves as a cost-to-go function for the subsequent iteration. The approximation is designed in such a way that closed-loop stability and recursive feasibility is maintained. Specifically, we show how to employ sum-of-squares relaxations to enforce that the approximate cost-to-go function is bounded from below and from above for all points of its domain. By resorting to quadratic approximations, the complexity of the resulting explicit MPC controller is considerably reduced both in terms of memory as well as the on-line computations. The procedure is applied to control an inverted pendulum and experimental data are presented to demonstrate viability of such an approach.

National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-151718 (URN)10.23919/ECC.2018.8550567 (DOI)000467725301032 ()978-3-9524-2698-2 (ISBN)978-1-5386-5303-6 (ISBN)
Conference
2018 European Control Conference, June 12-15, 2018. Limassol, Cyprus
Note

Funding agencies: Scientific Grant Agency of the Slovak Republic [1/0403/15]; Slovak Research and Development Agency [APVV-15-0007]

Available from: 2018-10-03 Created: 2018-10-03 Last updated: 2019-06-28
Ling, G., Lindsten, K., Ljungqvist, O., Löfberg, J., Norén, C. & Larsson, C. A. (2018). Fuel-efficient Model Predictive Control for Heavy Duty Vehicle Platooning using Neural Networks. In: 2018 American Control Conference (ACC): . Paper presented at 2018 American Control Conference (ACC) (pp. 3994-4001). IEEE
Open this publication in new window or tab >>Fuel-efficient Model Predictive Control for Heavy Duty Vehicle Platooning using Neural Networks
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2018 (English)In: 2018 American Control Conference (ACC), IEEE, 2018, p. 3994-4001Conference paper, Published paper (Refereed)
Abstract [en]

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 lowers fuel consumption. We propose a novel Model Predictive Control (MPC) framework for longitudinal control of the follower vehicle in a platoon consisting of two HDVs when no vehicle-to-vehicle communication is available. In the framework, the preceding vehicle's velocity profile is predicted using artificial neural networks which uses a topographic map of the road as input and is trained offline using synthetic data. The gear shifting and mass of consumed fuel for the controlled follower vehicle is modeled and used within the MPC controller. The efficiency of the proposed framework is verified in simulation examples and is benchmarked with a currently available control solution.  

Place, publisher, year, edition, pages
IEEE, 2018
Series
American Control Conference (ACC), E-ISSN 2378-5861
National Category
Control Engineering Robotics
Identifiers
urn:nbn:se:liu:diva-152456 (URN)10.23919/ACC.2018.8431520 (DOI)978-1-5386-5428-6 (ISBN)978-1-5386-5427-9 (ISBN)978-1-5386-5429-3 (ISBN)
Conference
2018 American Control Conference (ACC)
Available from: 2018-11-01 Created: 2018-11-01 Last updated: 2018-11-30
Ljungqvist, O., Axehill, D. & Löfberg, J. (2018). On stability for state-lattice trajectory tracking control. In: 2018 Annual American Control Conference (ACC): . Paper presented at 2018 Annual American Control Conference (ACC) June 27–29, 2018. Wisconsin Center, Milwaukee, USA (pp. 5868-5875). IEEE
Open this publication in new window or tab >>On stability for state-lattice trajectory tracking control
2018 (English)In: 2018 Annual American Control Conference (ACC), IEEE, 2018, p. 5868-5875Conference paper, Published paper (Refereed)
Abstract [en]

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 constructs a feasible trajectory by combining a finite number of precomputed motions. When this local planner is considered, we show that the closed-loop system can be modeled as a nonlinear hybrid system. Based on this, we propose a novel method for analyzing the behavior of the tracking error, how to design the low-level controller and how to potentially impose constraints on the local planner, in order to guarantee that the tracking error is bounded and decays towards zero. The proposed method is applied on a truck and trailer system and the results are illustrated in two simulation examples.

Place, publisher, year, edition, pages
IEEE, 2018
Series
American Control Conference (ACC), E-ISSN 2378-5861
National Category
Control Engineering Robotics
Identifiers
urn:nbn:se:liu:diva-152455 (URN)10.23919/ACC.2018.8430822 (DOI)978-1-5386-5428-6 (ISBN)978-1-5386-5427-9 (ISBN)978-1-5386-5429-3 (ISBN)
Conference
2018 Annual American Control Conference (ACC) June 27–29, 2018. Wisconsin Center, Milwaukee, USA
Available from: 2018-11-01 Created: 2018-11-01 Last updated: 2019-01-17
Korres, G. N., Manousakis, N. M., Xygkis, T. C. & Löfberg, J. (2015). Optimal phasor measurement unit placement for numerical observability in the presence of conventional measurements using semi-definite programming. IET Generation, Transmission & Distribution, 9(15), 2427-2436
Open this publication in new window or tab >>Optimal phasor measurement unit placement for numerical observability in the presence of conventional measurements using semi-definite programming
2015 (English)In: IET Generation, Transmission & Distribution, ISSN 1751-8687, E-ISSN 1751-8695, Vol. 9, no 15, p. 2427-2436Article in journal (Refereed) Published
Abstract [en]

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 their strategic placement across the power system. PMU allocation is optimised here based on measurement observability criteria for achieving solvability of the power system state estimation. Most of the previous work has proposed topological observability based methods for optimal PMU placement (OPP), which may not always ensure numerical observability required for successful execution of state estimation. The proposed OPP method finds out the minimum number and the optimal locations of PMUs required to make the power system numerically observable. The problem is formulated as a binary semi-definite programming (BSDP) model, with binary decision variables, minimising a linear objective function subject to linear matrix inequality observability constraints. The BSDP problem is solved using an outer approximation scheme based on binary integer linear programming. The developed method is conducted on IEEE standard test systems. A large-scale system with 3120 buses is also analysed to exhibit the applicability of proposed model to practical power system cases.

Place, publisher, year, edition, pages
INST ENGINEERING TECHNOLOGY-IET, 2015
Keywords
phasor measurement; numerical analysis; state estimation; linear matrix inequalities; integer programming; linear programming; synchronised phasor measurement units; power system observability; power system state estimation; optimal PMU placement; OPP method; binary semidefinite programming model; BSDP model; linear matrix inequality; binary integer linear programming
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:liu:diva-123135 (URN)10.1049/iet-gtd.2015.0662 (DOI)000364489400038 ()
Available from: 2015-12-07 Created: 2015-12-04 Last updated: 2017-12-01
Petersson, D. & Löfberg, J. (2014). Model reduction using a frequency-limited H2-cost. Systems & control letters (Print), 67(1), 32-39
Open this publication in new window or tab >>Model reduction using a frequency-limited H2-cost
2014 (English)In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 67, no 1, p. 32-39Article in journal (Refereed) Published
Abstract [en]

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 of 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. © 2014 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
Elsevier, 2014
Keywords
H2-norm; Model reduction; Optimization
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:liu:diva-116389 (URN)10.1016/j.sysconle.2014.02.004 (DOI)000335290600006 ()2-s2.0-84896801170 (Scopus ID)
Available from: 2015-03-27 Created: 2015-03-26 Last updated: 2017-12-04
Petersson, D. & Löfberg, J. (2014). Optimisation-based modelling of LPV systems using an -objective. International Journal of Control, 87(8), 1536-1548
Open this publication in new window or tab >>Optimisation-based modelling of LPV systems using an -objective
2014 (English)In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 87, no 8, p. 1536-1548Article in journal (Refereed) Published
Abstract [en]

A method to identify linear parameter varying models through minimisation of an -norm objective is presented. The method uses a direct nonlinear programming approach to a non-convex problem. The reason to use -norm is twofold. To begin with, it is a well-known and widely used system norm, and second, the cost functions described in this paper become differentiable when using the -norm. This enables us to have a measure of first-order optimality and to use standard quasi-Newton solvers to solve the problem. The specific structure of the problem is utilised in great detail to compute cost functions and gradients efficiently. Additionally, a regularised version of the method, which also has a nice computational structure, is presented. The regularised version is shown to have an interesting interpretation with connections to worst-case approaches.

Place, publisher, year, edition, pages
Taylor andamp; Francis: STM, Behavioural Science and Public Health Titles, 2014
Keywords
H2 optimisation; LPV modelling; model reduction
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-107437 (URN)10.1080/00207179.2013.878477 (DOI)000335865400007 ()
Available from: 2014-06-12 Created: 2014-06-12 Last updated: 2017-12-05
Simon, D., Löfberg, J. & Glad, T. (2014). Reference Tracking MPC Using Dynamic Terminal Set Transformation. IEEE Transactions on Automatic Control, 59(10), 2790-2795
Open this publication in new window or tab >>Reference Tracking MPC Using Dynamic Terminal Set Transformation
2014 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 59, no 10, p. 2790-2795Article in journal (Refereed) Published
Abstract [en]

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 technical note our goal is to make minimal changes to the dual mode framework, for the linear polytopic case, in order to develop a flexible reference tracking algorithm with guaranteed stability and low complexity, which is intuitive and easily understood. The main idea is to introduce a scaling variable that dynamically scales the terminal constraint set and therefore allows it to be centered around an arbitrary setpoint without violating the stability conditions. The main benefit of the algorithm is reduced complexity of the resulting QP compared to other state of art methods without loosing performance.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2014
Keywords
Nonlinear control systems; optimal control; optimization
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:liu:diva-112045 (URN)10.1109/TAC.2014.2313767 (DOI)000342924300017 ()
Note

Funding Agencies|Linkoping University; Saab Aeronautics; Swedish Governmental Agency for Innovation Systems (VINNOVA); Center for industrial information technology (CENIIT)

Available from: 2014-11-17 Created: 2014-11-13 Last updated: 2017-12-05
Simon, D., Löfberg, J. & Glad, T. (2013). Nonlinear Model Predictive Control using Feedback Linearization and Local Inner Convex Constraint Approximations. In: Proceedings of the 2013 European Control Conference: . Paper presented at 2013 European Control Conference, July 17-19, Zurich, Switzerland (pp. 2056-2061).
Open this publication in new window or tab >>Nonlinear Model Predictive Control using Feedback Linearization and Local Inner Convex Constraint Approximations
2013 (English)In: Proceedings of the 2013 European Control Conference, 2013, p. 2056-2061Conference paper, Published paper (Refereed)
Abstract [en]

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 linear MPC has been used successfully to control nonlinear systems. The main drawback is that this results in an optimization problem with nonlinear constraints on the control signal.

In this paper we propose a method to handle the nonlinear constraints that arises using a set of dynamically generated local inner polytopic approximations. The main benefits of the proposed method is guaranteed recursive feasibility and convergence.

National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-96743 (URN)000332509702074 ()978-39-5241-734-8 (ISBN)
Conference
2013 European Control Conference, July 17-19, Zurich, Switzerland
Funder
Vinnova, 2010-01255
Available from: 2013-08-26 Created: 2013-08-26 Last updated: 2014-04-25
Löfberg, J. (2012). Automatic Robust Convex Programming. Optimization Methods and Software, 27(1), 115-129
Open this publication in new window or tab >>Automatic Robust Convex Programming
2012 (English)In: Optimization Methods and Software, ISSN 1055-6788, E-ISSN 1029-4937, Vol. 27, no 1, p. 115-129Article in journal (Refereed) Published
Abstract [en]

This paper presents the robust optimization framework in the modelling language YALMIP, which carries out robust modelling 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 modelling and tractability of complex convex uncertain optimization problems.

Place, publisher, year, edition, pages
Taylor & Francis, 2012
Keywords
Robust optimization, Conic programming, Modelling software
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-76971 (URN)10.1080/10556788.2010.517532 (DOI)000302315500007 ()
Available from: 2012-04-27 Created: 2012-04-27 Last updated: 2017-12-07
Rohdin, P., Johansson, M., Löfberg, J. & Ottosson, M. (2012). Energy efficient process ventilation in paint shops in the car industry: experiences and an evaluation of a full scale implementation at Saab Automobile in Sweden. In: : . Paper presented at The 10th International Conference on Industrial Ventilation, Paris, France, 17-19 September 2012.
Open this publication in new window or tab >>Energy efficient process ventilation in paint shops in the car industry: experiences and an evaluation of a full scale implementation at Saab Automobile in Sweden
2012 (English)Conference paper, Published paper (Refereed)
Abstract [en]

Support processes in industrial energy systems, such as heating, ventilation and cooling systems, are important processes in industrial premises as they are related to energy cost, product quality as well as the indoor environment.

 

In the vehicle production process the paint shop is the most energy intensive part, and about 75% of the energy is used in the ovens and spray booths. The spray booth line, which includes paint application and the oven, uses large quantities of air in order to keep the air quality in an optimal range to achieve the desired paint quality. The approach used in paint shops has up to now been to keep as much of steady state conditions as possible to avoid paint defects due to disturbances in the balance. This means that these high air flows are used also at low and non production hours. There is thus a large potential to increase energy efficiency by controlling the air flow and heating without losing the critical balances. This paper will present an initial post-implementation evaluation of the energy efficiency potential and experiences after running this type of system. CFD has been used to investigate the control strategy.

Keywords
industrial ventilation, CFD, evaluation
National Category
Energy Engineering
Identifiers
urn:nbn:se:liu:diva-94003 (URN)
Conference
The 10th International Conference on Industrial Ventilation, Paris, France, 17-19 September 2012
Available from: 2013-06-14 Created: 2013-06-14 Last updated: 2013-08-08Bibliographically approved
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