12,985 research outputs found
A Warm-start Interior-point Method for Predictive Control
In predictive control, a quadratic program (QP) needs to be solved at each sampling instant. We present a new warm-start strategy to solve a QP with an interior-point method whose data is slightly perturbed from the previous QP. In this strategy, an initial guess of the unknown variables in the perturbed problem is determined from the computed solution of the previous problem. We demonstrate the effectiveness of our warm-start strategy to a number of online benchmark problems. Numerical results indicate that the proposed technique depends upon the size of perturbation and it leads to a reduction of 30β74% in floating point operations compared to a cold-start interior-point method
Sparse preconditioning for model predictive control
We propose fast O(N) preconditioning, where N is the number of gridpoints on
the prediction horizon, for iterative solution of (non)-linear systems
appearing in model predictive control methods such as forward-difference
Newton-Krylov methods. The Continuation/GMRES method for nonlinear model
predictive control, suggested by T. Ohtsuka in 2004, is a specific application
of the Newton-Krylov method, which uses the GMRES iterative algorithm to solve
a forward difference approximation of the optimality equations on every time
step.Comment: 6 pages, 5 figures, to appear in proceedings of the American Control
Conference 2016, July 6-8, Boston, MA, USA. arXiv admin note: text overlap
with arXiv:1509.0286
A Simple and Efficient Algorithm for Nonlinear Model Predictive Control
We present PANOC, a new algorithm for solving optimal control problems
arising in nonlinear model predictive control (NMPC). A usual approach to this
type of problems is sequential quadratic programming (SQP), which requires the
solution of a quadratic program at every iteration and, consequently, inner
iterative procedures. As a result, when the problem is ill-conditioned or the
prediction horizon is large, each outer iteration becomes computationally very
expensive. We propose a line-search algorithm that combines forward-backward
iterations (FB) and Newton-type steps over the recently introduced
forward-backward envelope (FBE), a continuous, real-valued, exact merit
function for the original problem. The curvature information of Newton-type
methods enables asymptotic superlinear rates under mild assumptions at the
limit point, and the proposed algorithm is based on very simple operations:
access to first-order information of the cost and dynamics and low-cost direct
linear algebra. No inner iterative procedure nor Hessian evaluation is
required, making our approach computationally simpler than SQP methods. The
low-memory requirements and simple implementation make our method particularly
suited for embedded NMPC applications
Preconditioned warm-started Newton-Krylov methods for MPC with discontinuous control
We present Newton-Krylov methods for efficient numerical solution of optimal
control problems arising in model predictive control, where the optimal control
is discontinuous. As in our earlier work, preconditioned GMRES practically
results in an optimal complexity, where is a discrete horizon
length. Effects of a warm-start, shifting along the predictive horizon, are
numerically investigated. The~method is tested on a classical double integrator
example of a minimum-time problem with a known bang-bang optimal control.Comment: 8 pages, 10 figures, to appear in Proceedings SIAM Conference on
Control and Its Applications, July 10-12, 2017, Pittsburgh, PA, US
New optimization methods in predictive control
This thesis is mainly concerned with the efficient solution of a linear discrete-time
finite horizon optimal control problem (FHOCP) with quadratic cost and linear constraints
on the states and inputs. In predictive control, such a FHOCP needs to be
solved online at each sampling instant. In order to solve such a FHOCP, it is necessary
to solve a quadratic programming (QP) problem. Interior point methods (IPMs) have
proven to be an efficient way of solving quadratic programming problems. A linear system
of equations needs to be solved in each iteration of an IPM. The ill-conditioning
of this linear system in the later iterations of the IPM prevents the use of an iterative
method in solving the linear system due to a very slow rate of convergence; in some cases
the solution never reaches the desired accuracy. A new well-conditioned IPM, which increases
the rate of convergence of the iterative method is proposed. The computational
advantage is obtained by the use of an inexact Newton method along with the use of
novel preconditioners.
A new warm-start strategy is also presented to solve a QP with an interior-point
method whose data is slightly perturbed from the previous QP. The effectiveness of
this warm-start strategy is demonstrated on a number of available online benchmark
problems. Numerical results indicate that the proposed technique depends upon the
size of perturbation and it leads to a reduction of 30-74% in floating point operations
compared to a cold-start interior point method.
Following the main theme of this thesis, which is to improve the computational efficiency
of an algorithm, an efficient algorithm for solving the coupled Sylvester equation
that arises in converting a system of linear differential-algebraic equations (DAEs) to
ordinary differential equations is also presented. A significant computational advantage
is obtained by exploiting the structure of the involved matrices. The proposed algorithm
removes the need to solve a standard Sylvester equation or to invert a matrix. The
improved performance of this new method over existing techniques is demonstrated by
comparing the number of floating-point operations and via numerical examples
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