1,183 research outputs found
A Parallel Dual Fast Gradient Method for MPC Applications
We propose a parallel adaptive constraint-tightening approach to solve a
linear model predictive control problem for discrete-time systems, based on
inexact numerical optimization algorithms and operator splitting methods. The
underlying algorithm first splits the original problem in as many independent
subproblems as the length of the prediction horizon. Then, our algorithm
computes a solution for these subproblems in parallel by exploiting auxiliary
tightened subproblems in order to certify the control law in terms of
suboptimality and recursive feasibility, along with closed-loop stability of
the controlled system. Compared to prior approaches based on constraint
tightening, our algorithm computes the tightening parameter for each subproblem
to handle the propagation of errors introduced by the parallelization of the
original problem. Our simulations show the computational benefits of the
parallelization with positive impacts on performance and numerical conditioning
when compared with a recent nonparallel adaptive tightening scheme.Comment: This technical report is an extended version of the paper "A Parallel
Dual Fast Gradient Method for MPC Applications" by the same authors submitted
to the 54th IEEE Conference on Decision and Contro
Optimized FPGA Implementation of Model Predictive Control for Embedded Systems Using High-Level Synthesis Tool
Model predictive control (MPC) is an optimization-based strategy for high-performance control that is attracting increasing interest. While MPC requires the online solution of an optimization problem, its ability to handle multivariable systems and constraints makes it a very powerful control strategy specially for MPC of embedded systems, which have an ever increasing amount of sensing and computation capabilities. We argue that the implementation of MPC on field programmable gate arrays (FPGAs) using automatic tools is nowadays possible, achieving cost-effective successful applications on fast or resource-constrained systems. The main burden for the implementation of MPC on FPGAs is the challenging design of the necessary algorithms. We outline an approach to achieve a software-supported optimized implementation of MPC on FPGAs using high-level synthesis tools and automatic code generation. The proposed strategy exploits the arithmetic operations necessaries to solve optimization problems to tailor an FPGA design, which allows a tradeoff between energy, memory requirements, cost, and achievable speed. We show the capabilities and the simplicity of use of the proposed methodology on two different examples and illustrate its advantages over a microcontroller implementation
Custom optimization algorithms for efficient hardware implementation
The focus is on real-time optimal decision making with application in advanced control
systems. These computationally intensive schemes, which involve the repeated solution of
(convex) optimization problems within a sampling interval, require more efficient computational
methods than currently available for extending their application to highly dynamical
systems and setups with resource-constrained embedded computing platforms.
A range of techniques are proposed to exploit synergies between digital hardware, numerical
analysis and algorithm design. These techniques build on top of parameterisable
hardware code generation tools that generate VHDL code describing custom computing
architectures for interior-point methods and a range of first-order constrained optimization
methods. Since memory limitations are often important in embedded implementations we
develop a custom storage scheme for KKT matrices arising in interior-point methods for
control, which reduces memory requirements significantly and prevents I/O bandwidth
limitations from affecting the performance in our implementations. To take advantage of
the trend towards parallel computing architectures and to exploit the special characteristics
of our custom architectures we propose several high-level parallel optimal control
schemes that can reduce computation time. A novel optimization formulation was devised
for reducing the computational effort in solving certain problems independent of the computing
platform used. In order to be able to solve optimization problems in fixed-point
arithmetic, which is significantly more resource-efficient than floating-point, tailored linear
algebra algorithms were developed for solving the linear systems that form the computational
bottleneck in many optimization methods. These methods come with guarantees
for reliable operation. We also provide finite-precision error analysis for fixed-point implementations
of first-order methods that can be used to minimize the use of resources while
meeting accuracy specifications. The suggested techniques are demonstrated on several
practical examples, including a hardware-in-the-loop setup for optimization-based control
of a large airliner.Open Acces
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