1,452 research outputs found
Second-order analysis and numerical approximation for bang-bang bilinear control problems
We consider bilinear optimal control problems whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient secondorder conditions for bang-bang controls, which guarantee local quadratic growth of the objective functional in L1 . In addition, we prove that for controls that are not bang-bang, no such growth can be expected. Finally, we study the finite-element discretization and prove error estimates of bang-bang controls in L1 -norms.The first author was partially supported by the Spanish Ministerio de Economía Industria y Competitividad under research projects MTM2014-57531-P and MTM2017-83185-P. The second author was partially supported by DFG under grant Wa 3626/1-1
Total variation regularization of multi-material topology optimization
This work is concerned with the determination of the diffusion coefficient
from distributed data of the state. This problem is related to homogenization
theory on the one hand and to regularization theory on the other hand. An
approach is proposed which involves total variation regularization combined
with a suitably chosen cost functional that promotes the diffusion coefficient
assuming prespecified values at each point of the domain. The main difficulty
lies in the delicate functional-analytic structure of the resulting
nondifferentiable optimization problem with pointwise constraints for functions
of bounded variation, which makes the derivation of useful pointwise optimality
conditions challenging. To cope with this difficulty, a novel reparametrization
technique is introduced. Numerical examples using a regularized semismooth
Newton method illustrate the structure of the obtained diffusion coefficient.
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
Order reduction and eigenstructure assignment for nonsmooth vibrating systems: a nonlinear normal modes approach
Thesis (M.S.) University of Alaska Fairbanks, 2002Two related problems are addressed in this thesis. The first one is for order reduction of conservative vibrating systems with piecewise linear nonsmooth nonlinearities of arbitrary dimension. Linear-based, PMM-based and LELSM-based order reduction transformations are applied. The technique is applied to multi-degree-of-freedom systems with nonsmooth clearance, deadzone, bang-bang, and saturation nonlinearities. The resulting approximate frequencies are compared with those obtained from numerical simulations. The second technique is eigenstructure assignment of n-degree-of-freedom conservative vibrating systems with nonsmooth nonlinearities. Three distinct control strategies which utilize methods for approximating the NNM frequencies and mode shapes are employed. First, PMM for approximating NNM frequencies is used to determine n constant actuator gains for eigenvalue placement. Second, an approximate single-degree-of-freedom reduced model is found with one actuator gain for the mode to be controlled. The third strategy allows the frequencies and mode shapes (eigenstructure) to be placed by using a full n x n matrix of actuator gains and employing LELSM for approximating NNM frequencies and mode shapes
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