scholarly journals Fast Model Predictive Control Based on Adaptive Alternating Direction Method of Multipliers

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Yu Li ◽  
Qiming Zou ◽  
Xiaoru Ji ◽  
Chanyuan Zhang ◽  
Ke Lu
Keyword(s):  
Model Predictive Control ◽  
Real Time ◽  
Predictive Control ◽  
Large Scale ◽  
Alternating Direction Method ◽  
Control Input ◽  
Method Of Multipliers ◽  
Time Step ◽  
Prediction Horizon ◽  
Alternating Direction

Model Predictive Control (MPC) can effectively handle control problem with disturbances, multicontrol variables, and complex constraints and is widely used in various control systems. In MPC, the control input at each time step is obtained by solving an online optimization problem, which will cause a time delay in real time on embedded computers with limited computational resources. In this paper, we utilize adaptive Alternating Direction Method of Multipliers (a-ADMM) to accelerate the solution of MPC. This method adaptively adjusts penalty parameter to balance the value of primal residual and dual residual. The performance of this approach is profiled via the control of a quadcopter with 12 states and 4 controls and prediction horizon ranging from 10 to 40. The simulation results demonstrate that the MPC based on a-ADMM has a significant improvement in real-time and convergence performance and thus is more suitable for solving large-scale optimal control problems.

scholarly journals Experimental Validation of a Guaranteed Nonlinear Model Predictive Control

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 248
Author(s):  
Mohamed Fnadi ◽  
Julien Alexandre dit Sandretto
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Nonlinear Model ◽  
Interval Analysis ◽  
Optimization Procedure ◽  
The State ◽  
Nonlinear Model Predictive Control ◽  
Control Input ◽  
Time Step ◽  
Prediction Horizon

This paper combines the interval analysis tools with the nonlinear model predictive control (NMPC). The NMPC strategy is formulated based on an uncertain dynamic model expressed as nonlinear ordinary differential equations (ODEs). All the dynamic parameters are identified in a guaranteed way considering the various uncertainties on the embedded sensors and the system’s design. The NMPC problem is solved at each time step using validated simulation and interval analysis methods to compute the optimal and safe control inputs over a finite prediction horizon. This approach considers several constraints which are crucial for the system’s safety and stability, namely the state and the control limits. The proposed controller consists of two steps: filtering and branching procedures enabling to find the input intervals that fulfill the state constraints and ensure the convergence to the reference set. Then, the optimization procedure allows for computing the optimal and punctual control input that must be sent to the system’s actuators for the pendulum stabilization. The validated NMPC capabilities are illustrated through several simulations under the DynIbex library and experiments using an inverted pendulum.

scholarly journals Model Predictive Control for an Aerial Tree-Pruning Robot Based on Alternating Direction Method of Multipliers

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Changliang Xu ◽  
Zhong Yang ◽  
Hao Xu ◽  
Qiuyan Zhang ◽  
Dongsheng Zhou ◽  
...  
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Uncertain System ◽  
Alternating Direction Method ◽  
Rotational Inertia ◽  
Method Of Multipliers ◽  
Alternating Direction ◽  
Attitude Tracking ◽  
Control Scheme ◽  
Tree Pruning

Obstacles of some trees within the electric power transmission line channel are of great threat to the electricity supply. Nowadays, the tasks of clearing threatening tree branches are still mostly operated by hand and simple tools. In this article, an aerial tree-pruning robot with a novel structure is designed to improve the pruning operation efficiency and enhance the safety of the staff. However, the long arm of the pruning tool results in much higher rotational inertia of the robot, which brings difficulties for the robot to remain stable. Therefore, a control scheme based on model predictive control is proposed for the aerial tree-pruning robot and to deal with an uncertain system during the pruning operation period. One of the main contributions is that an ADMM (alternating direction method of multipliers) algorithm that solves the constrained QP (quadratic programming) is adopted to implement the model predictive control on embedded computers with limited computational power. The dynamic model of the pruning robot is firstly presented. Then, the control scheme of MPC for the pruning robot is presented. Moreover, the QP problem of robot control is addressed with ADMM. Finally, simulation experiments of attitude tracking as well as the antidisturbances capability verification have been conducted. Results for the system of aerial tree-pruning robot are given to demonstrate the effectiveness of the developed attitude tracking control scheme using ADMM-based MPC.

scholarly journals Managing randomization in the multi-block alternating direction method of multipliers for quadratic optimization

2020 ◽  
Author(s):  
Krešimir Mihić ◽  
Mingxi Zhu ◽  
Yinyu Ye
Keyword(s):  
Quadratic Programming ◽  
Large Scale ◽  
Optimization Problems ◽  
Quadratic Optimization ◽  
Alternating Direction Method ◽  
Convex Quadratic Programming ◽  
Method Of Multipliers ◽  
Numerical Tests ◽  
Alternating Direction ◽  
Decision Variables

Abstract The Alternating Direction Method of Multipliers (ADMM) has gained a lot of attention for solving large-scale and objective-separable constrained optimization. However, the two-block variable structure of the ADMM still limits the practical computational efficiency of the method, because one big matrix factorization is needed at least once even for linear and convex quadratic programming. This drawback may be overcome by enforcing a multi-block structure of the decision variables in the original optimization problem. Unfortunately, the multi-block ADMM, with more than two blocks, is not guaranteed to be convergent. On the other hand, two positive developments have been made: first, if in each cyclic loop one randomly permutes the updating order of the multiple blocks, then the method converges in expectation for solving any system of linear equations with any number of blocks. Secondly, such a randomly permuted ADMM also works for equality-constrained convex quadratic programming even when the objective function is not separable. The goal of this paper is twofold. First, we add more randomness into the ADMM by developing a randomly assembled cyclic ADMM (RAC-ADMM) where the decision variables in each block are randomly assembled. We discuss the theoretical properties of RAC-ADMM and show when random assembling helps and when it hurts, and develop a criterion to guarantee that it converges almost surely. Secondly, using the theoretical guidance on RAC-ADMM, we conduct multiple numerical tests on solving both randomly generated and large-scale benchmark quadratic optimization problems, which include continuous, and binary graph-partition and quadratic assignment, and selected machine learning problems. Our numerical tests show that the RAC-ADMM, with a variable-grouping strategy, could significantly improve the computation efficiency on solving most quadratic optimization problems.

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