This paper proposes a new sampling based nonlinear modelpredictivecontrol (MPC) algorithm, with a bound on complexity quadratic in the prediction horizon N and linear in the number of samples. The idea of the propos...
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This paper proposes a new sampling based nonlinear modelpredictivecontrol (MPC) algorithm, with a bound on complexity quadratic in the prediction horizon N and linear in the number of samples. The idea of the proposed algorithm is to use the sequence of predicted inputs from the previous time step as a warm start, and to iteratively update this sequence by changing its elements one by one, starting from the last predicted input and ending with the first predicted input. This strategy, which resembles the dynamic programming principle, allows for parallelization up to a certain level and yields a suboptimal nonlinear MPC algorithm with guaranteed recursive feasibility, stability and improved cost function at every iteration, which is suitable for real time implementation. The complexity of the algorithm per each time step in the prediction horizon depends only on the horizon, the number of samples and parallel threads, and it is independent of the measured system state. Comparisons with the fmincon nonlinear optimization solver on a benchmark example indicates that, as the simulation time progresses, the proposed algorithm converges rapidly to the "optimal" solution, even when using a small number of samples. (C) 2017, IFAC (International Federation of Automatic control) Hosting by Elsevier Ltd. All rights reserved.
In this paper we analyze the computational complexity of the dual gradient method for solving linearly constrained convex problems. When it is difficult to project on the primal feasible set described by linear constr...
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In this paper we analyze the computational complexity of the dual gradient method for solving linearly constrained convex problems. When it is difficult to project on the primal feasible set described by linear constraints, we use the Lagrangian relaxation to handle the complicated constraints and then, we apply the dual gradient algorithm for solving the corresponding dual. We give a unified convergence rate analysis for the dual gradient algorithm: we provide sublinear or linear estimates on the primal suboptimality and feasibility violation of the generated approximate primal solutions. Our analysis relies on the Lipschitz property of the dual function or an error bound property. Furthermore, the iteration complexity analysis is based on two types of approximate primal solutions: an average primal sequence or the last primal iterate sequence. We also discuss complexity certifications and implementation aspects of the dual gradient algorithm on constrained MPC problems for embedded linear systems. (C) 2015 Elsevier B.V. All rights reserved.
We propose a framework for embedding modelpredictivecontrol for Systems-on-a-Chip applications. In order to allow the implementation of such a computationally expensive controller on chip, we propose reducing the pr...
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We propose a framework for embedding modelpredictivecontrol for Systems-on-a-Chip applications. In order to allow the implementation of such a computationally expensive controller on chip, we propose reducing the precision of the microprocessor to the minimum while maintaining near optimal control performance. Taking advantage of the low precision, a logarithmic number system based microprocessor architecture is used, that allows the design of a reduced size processor, providing further energy and computational cost savings. The design parameters for this high-performance embeddedcontroller are chosen using a combination of finite element method simulations and bit-accurate hardware emulations in a number of parametric tests. We provide the methodology for choosing the design parameters for two particular control problems;the temperature regulation in a wafer cross-section geometry, and the control of temperature in a non-isothermal fluid flow problem in a microdevice. Finally, we provide the microprocessor architecture details and estimates for the performance of the resulting embedded model predictive controller. (c) 2005 Elsevier Ltd. All rights reserved.
We propose a framework for embedding modelpredictivecontrol for Systems-on-a-Chip applications. In order to allow the implementation of such a computationally expensive controller on chip, we propose reducing the pr...
详细信息
We propose a framework for embedding modelpredictivecontrol for Systems-on-a-Chip applications. In order to allow the implementation of such a computationally expensive controller on chip, we propose reducing the precision of the microprocessor to the minimum while maintaining near optimal control performance. Taking advantage of the low precision, a logarithmic number system based microprocessor architecture is used, that allows the design of a reduced size processor, providing further energy and computational cost savings. The design parameters for this high-performance embeddedcontroller are chosen using a combination of finite element method simulations and bit-accurate hardware emulations in a number of parametric tests. We provide the methodology for choosing the design parameters for two particular control problems;the temperature regulation in a wafer cross-section geometry, and the control of temperature in a non-isothermal fluid flow problem in a microdevice. Finally, we provide the microprocessor architecture details and estimates for the performance of the resulting embedded model predictive controller. (c) 2005 Elsevier Ltd. All rights reserved.
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