5 research outputs found
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
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A comparison of general-purpose optimization algorithms forfinding optimal approximate experimental designs
Several common general purpose optimization algorithms are compared for findingA- and D-optimal designs for different types of statistical models of varying complexity,including high dimensional models with five and more factors. The algorithms of interestinclude exact methods, such as the interior point method, the Nelder–Mead method, theactive set method, the sequential quadratic programming, and metaheuristic algorithms,such as particle swarm optimization, simulated annealing and genetic algorithms.Several simulations are performed, which provide general recommendations on theutility and performance of each method, including hybridized versions of metaheuristicalgorithms for finding optimal experimental designs. A key result is that general-purposeoptimization algorithms, both exact methods and metaheuristic algorithms, perform wellfor finding optimal approximate experimental designs
Optimal control and robust estimation for ocean wave energy converters
This thesis deals with the optimal control of wave energy converters and some associated
observer design problems. The first part of the thesis will investigate model
predictive control of an ocean wave energy converter to maximize extracted power.
A generic heaving converter that can have both linear dampers and active elements
as a power take-off system is considered and an efficient optimal control algorithm
is developed for use within a receding horizon control framework. The optimal
control is also characterized analytically. A direct transcription of the optimal control
problem is also considered as a general nonlinear program. A variation of
the projected gradient optimization scheme is formulated and shown to be feasible
and computationally inexpensive compared to a standard nonlinear program solver.
Since the system model is bilinear and the cost function is not convex quadratic, the
resulting optimization problem is shown not to be a quadratic program. Results are
compared with other methods like optimal latching to demonstrate the improvement
in absorbed power under irregular sea condition simulations.
In the second part, robust estimation of the radiation forces and states inherent in
the optimal control of wave energy converters is considered. Motivated by this, low
order H∞ observer design for bilinear systems with input constraints is investigated
and numerically tractable methods for design are developed. A bilinear Luenberger
type observer is formulated and the resulting synthesis problem reformulated as that
for a linear parameter varying system. A bilinear matrix inequality problem is then
solved to find nominal and robust quadratically stable observers. The performance
of these observers is compared with that of an extended Kalman filter. The robustness
of the observers to parameter uncertainty and to variation in the radiation
subsystem model order is also investigated.
This thesis also explores the numerical integration of bilinear control systems with
zero-order hold on the control inputs. Making use of exponential integrators, exact
to high accuracy integration is proposed for such systems. New a priori bounds
are derived on the computational complexity of integrating bilinear systems with a
given error tolerance. Employing our new bounds on computational complexity, we
propose a direct exponential integrator to solve bilinear ODEs via the solution of
sparse linear systems of equations. Based on this, a novel sparse direct collocation
of bilinear systems for optimal control is proposed. These integration schemes are
also used within the indirect optimal control method discussed in the first part.Open Acces