8,437 research outputs found
Computer Architectures to Close the Loop in Real-time Optimization
© 2015 IEEE.Many modern control, automation, signal processing and machine learning applications rely on solving a sequence of optimization problems, which are updated with measurements of a real system that evolves in time. The solutions of each of these optimization problems are then used to make decisions, which may be followed by changing some parameters of the physical system, thereby resulting in a feedback loop between the computing and the physical system. Real-time optimization is not the same as fast optimization, due to the fact that the computation is affected by an uncertain system that evolves in time. The suitability of a design should therefore not be judged from the optimality of a single optimization problem, but based on the evolution of the entire cyber-physical system. The algorithms and hardware used for solving a single optimization problem in the office might therefore be far from ideal when solving a sequence of real-time optimization problems. Instead of there being a single, optimal design, one has to trade-off a number of objectives, including performance, robustness, energy usage, size and cost. We therefore provide here a tutorial introduction to some of the questions and implementation issues that arise in real-time optimization applications. We will concentrate on some of the decisions that have to be made when designing the computing architecture and algorithm and argue that the choice of one informs the other
Predictive control using an FPGA with application to aircraft control
Alternative and more efficient computational methods can extend the applicability of MPC to systems with tight real-time requirements. This paper presents a “system-on-a-chip” MPC system, implemented on a field programmable gate array (FPGA), consisting of a sparse structure-exploiting primal dual interior point (PDIP) QP solver for MPC reference tracking and a fast gradient QP solver for steady-state target calculation. A parallel reduced precision iterative solver is used to accelerate the solution of the set of linear equations forming the computational bottleneck of the PDIP algorithm. A numerical study of the effect of reducing the number of iterations highlights the effectiveness of the approach. The system is demonstrated with an FPGA-inthe-loop testbench controlling a nonlinear simulation of a large airliner. This study considers many more manipulated inputs than any previous FPGA-based MPC implementation to date, yet the implementation comfortably fits into a mid-range FPGA, and the controller compares well in terms of solution quality and latency to state-of-the-art QP solvers running on a standard PC
Bundle-based pruning in the max-plus curse of dimensionality free method
Recently a new class of techniques termed the max-plus curse of
dimensionality-free methods have been developed to solve nonlinear optimal
control problems. In these methods the discretization in state space is avoided
by using a max-plus basis expansion of the value function. This requires
storing only the coefficients of the basis functions used for representation.
However, the number of basis functions grows exponentially with respect to the
number of time steps of propagation to the time horizon of the control problem.
This so called "curse of complexity" can be managed by applying a pruning
procedure which selects the subset of basis functions that contribute most to
the approximation of the value function. The pruning procedures described thus
far in the literature rely on the solution of a sequence of high dimensional
optimization problems which can become computationally expensive.
In this paper we show that if the max-plus basis functions are linear and the
region of interest in state space is convex, the pruning problem can be
efficiently solved by the bundle method. This approach combining the bundle
method and semidefinite formulations is applied to the quantum gate synthesis
problem, in which the state space is the special unitary group (which is
non-convex). This is based on the observation that the convexification of the
unitary group leads to an exact relaxation. The results are studied and
validated via examples
Convolutional Dictionary Learning: Acceleration and Convergence
Convolutional dictionary learning (CDL or sparsifying CDL) has many
applications in image processing and computer vision. There has been growing
interest in developing efficient algorithms for CDL, mostly relying on the
augmented Lagrangian (AL) method or the variant alternating direction method of
multipliers (ADMM). When their parameters are properly tuned, AL methods have
shown fast convergence in CDL. However, the parameter tuning process is not
trivial due to its data dependence and, in practice, the convergence of AL
methods depends on the AL parameters for nonconvex CDL problems. To moderate
these problems, this paper proposes a new practically feasible and convergent
Block Proximal Gradient method using a Majorizer (BPG-M) for CDL. The
BPG-M-based CDL is investigated with different block updating schemes and
majorization matrix designs, and further accelerated by incorporating some
momentum coefficient formulas and restarting techniques. All of the methods
investigated incorporate a boundary artifacts removal (or, more generally,
sampling) operator in the learning model. Numerical experiments show that,
without needing any parameter tuning process, the proposed BPG-M approach
converges more stably to desirable solutions of lower objective values than the
existing state-of-the-art ADMM algorithm and its memory-efficient variant do.
Compared to the ADMM approaches, the BPG-M method using a multi-block updating
scheme is particularly useful in single-threaded CDL algorithm handling large
datasets, due to its lower memory requirement and no polynomial computational
complexity. Image denoising experiments show that, for relatively strong
additive white Gaussian noise, the filters learned by BPG-M-based CDL
outperform those trained by the ADMM approach.Comment: 21 pages, 7 figures, submitted to IEEE Transactions on Image
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