4,045 research outputs found
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
A Semismooth Predictor Corrector Method for Real-Time Constrained Parametric Optimization with Applications in Model Predictive Control
Real-time optimization problems are ubiquitous in control and estimation, and
are typically parameterized by incoming measurement data and/or operator
commands. This paper proposes solving parameterized constrained nonlinear
programs using a semismooth predictor-corrector (SSPC) method. Nonlinear
complementarity functions are used to reformulate the first order necessary
conditions of the optimization problem into a parameterized non-smooth
root-finding problem. Starting from an approximate solution, a semismooth
Euler-Newton algorithm is proposed for tracking the trajectory of the
primal-dual solution as the parameter varies over time. Active set changes are
naturally handled by the SSPC method, which only requires the solution of
linear systems of equations. The paper establishes conditions under which the
solution trajectories of the root-finding problem are well behaved and provides
sufficient conditions for ensuring boundedness of the tracking error. Numerical
case studies featuring the application of the SSPC method to nonlinear model
predictive control are reported and demonstrate the advantages of the proposed
method
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