A primal-dual interior-point linear programming algorithm for MPC

Edlund, Kristian; Sokoler, Leo Emil; Jørgensen, John Bagterp

doi:10.1109/cdc.2009.5400440

Cited by 11 publications

(5 citation statements)

References 13 publications

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“…We use a damping parameter, ν, to keep the iterates well inside the interior of the non-negative orthant (w,s,τ,κ) ≥ 0, as they approach the solution. To speed-up numerical computations and reduce the storage requirements of LPempc, operations involving the structured matrices F and H are implemented as specialized linear algebra routines [28].…”

Section: A Interior Point Methodsmentioning

confidence: 99%

A warm-started homogeneous and self-dual interior-point method for linear economic model predictive control

Sokoler

Skajaa

Frison

et al. 2013

52nd IEEE Conference on Decision and Control

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In this paper, we present a warm-started homogenous and self-dual interior-point method (IPM) for the linear programs arising in economic model predictive control (MPC) of linear systems. To exploit the structure in the optimization problems, our algorithm utilizes a Riccati iteration procedure which is adapted to the non-standard system solved in homogenous and self-dual IPMs, and specifically tailored to economic MPC. Fast convergence is further achieved by means of a recent warm-starting strategy for homogenous and self-dual IPMs that has not previously been applied to MPC. We implement our algorithm in MATLAB and its performance is analyzed based on a smart grid power management case study. Closed loop simulations show that 1) our algorithm is significantly faster than state-of-the-art IPMs based on sparse linear algebra routines, and 2) warm-starting reduces the number of iterations by approximately 15-35%.

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Section: A Interior Point Methodsmentioning

confidence: 99%

A warm-started homogeneous and self-dual interior-point method for linear economic model predictive control

Sokoler

Skajaa

Frison

et al. 2013

52nd IEEE Conference on Decision and Control

Self Cite

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“…e above optimization problem is a typical convex quadratic programming problem with linear constraints. Some previous works [32,33] have provided the methods to solve this kind of problem, and we will not repeat them here.…”

Section: Objective Function and Optimization Problemmentioning

confidence: 99%

Path Tracking Method Based on Model Predictive Control and Genetic Algorithm for Autonomous Vehicle

Wang¹,

Chen²,

Yang

et al. 2022

Mathematical Problems in Engineering

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Model predictive control (MPC) is often used for controlling the autonomous vehicle tracking the target path. But to apply MPC schemes, the nonlinear model of vehicle kinematics needs to be approximately converted to a linear format, and the path tracking problem has to be converted into certain formats in order to implement the solver of convex quadratic programming. To solve these issues, a control strategy combining MPC and genetic algorithm (GA) is put forward. The nonlinear predictive model is adopted to predict the future movement of a controlled vehicle. The objective function is established according to the future movement and target path. Instead of using a convex quadratic programming solver, GA is applied to solve the optimization problem. The proposed MPC-GA method can handle the arbitrary nonlinear problem and make the objective function more comprehensible and flexible. This method is applied in solving the path tracking problem of an autonomous vehicle. Both simulations and on-field tests are conducted. The results validate the efficiency of the proposed MPC-GA path tracking method in comparison with traditional methods. With the MPC-GA controller, the automatic driving on the park road is basically realized. The control strategy can be considered as an alternative method to solve the path tracking problem for an autonomous vehicle.

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“…Traditionally, MPC is designed using objective functions penalizing deviations from a given set-point. MPC based on optimizing economic objectives has only recently emerged as a general methodology with efficient numerical implementations and provable stability properties [10]- [13]. The idea of utilizing load shifting capabilities to reduce total energy consumption is slowly gaining acceptance (see [14], [15]).…”

Section: Introductionmentioning

confidence: 99%

The potential of Economic MPC for power management

Hovgaard

Edlund

Jørgensen

2010

49th IEEE Conference on Decision and Control (CDC)

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Abstract-Economic Model PredictiveControl is a receding horizon controller that minimizes an economic objective function rather than a weighted least squares objective function as in Model Predictive Control (MPC). We use Economic MPC to operate a portfolio of power generators and consumers such that the cost of producing the required power is minimized. The power generators are controllable power generators such as combined heat and power generators (CHP), coal and gas fired power generators, as well as a significant share of uncontrollable power generators such as parks of wind turbines. In addition, some of the power consumers are controllable. In this paper, the controllable power consumers are exemplified by large cold rooms or aggregations of super markets with refrigeration systems. We formulate the Economic MPC as a linear program. By simulation, we demonstrate the performance of Economic MPC for a small conceptual example.

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A primal-dual interior-point linear programming algorithm for MPC

Cited by 11 publications

References 13 publications

A warm-started homogeneous and self-dual interior-point method for linear economic model predictive control

A warm-started homogeneous and self-dual interior-point method for linear economic model predictive control

Path Tracking Method Based on Model Predictive Control and Genetic Algorithm for Autonomous Vehicle

The potential of Economic MPC for power management

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