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Solving linear-quadratic optimal control problems on parallel computers
Optimization Methods and Software, 2008We discuss a parallel library of efficient algorithms for the solution of linear-quadratic optimal control problems involving large-scale systems with state-space dimension up to O(104). We survey the numerical algorithms underlying the implementation of the chosen optimal control methods.
Benner, P. ; https://orcid.org/0000-0003-3362-4103 +2 more
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Linear Quadratic Optimal Control Problems
1995In this chapter we consider the optimal control problem with a linear state equation and a quadratic cost functional. Such problems are referred to as linear-quadratic optimal control problems, or LQ problems for short.
Xunjing Li, Jiongmin Yong
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Optimal Dynamic Controller Design for Linear Quadratic Tracking Problems
IEEE Transactions on Automatic ControlzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jianguo Zhao +3 more
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Forward–backward linear quadratic stochastic optimal control problem with delay
Systems & Control Letters, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huang, Jianhui, Li, Xun, Shi, Jingtao
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The linear-quadratic optimal control problem with positive controllers†
International Journal of Control, 1980The linear-quadratic optimal control problem with positive controllers is considered. Specifically, necessary and sufficient conditions are given for the existence of a solution to the optimal control problem ; the form of these conditions is explicit for the case where a trajectory-dependent term in the integrand of the pay-off functional is absent ...
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On positive controllers and linear quadratic optimal control problems†
International Journal of Control, 1982An assumption on the non-negative solutions of quadratic equations has been used to study linear quadratic optimal control problems with positive controllers. This note investigates this assumption in more detail.
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Dynamics and Control, 1997
In the paper, a class of global constrained optimization problems which may be nonconvex in general is studied. A simple approach to their solution is presented. Special attention is paid to the case when the objective and constraints functions are quadratic functionals on a Hilbert space.
Matveev, A., Yakubovich, V.
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In the paper, a class of global constrained optimization problems which may be nonconvex in general is studied. A simple approach to their solution is presented. Special attention is paid to the case when the objective and constraints functions are quadratic functionals on a Hilbert space.
Matveev, A., Yakubovich, V.
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The time-invariant linear-quadratic optimal control problem
Automatica, 1977This paper provides a review of one of the basic problems of systems theory-the general time-invariant optimal control problem involving linear systems and quadratic costs. The problem includes on one hand the regulator problem of optimal control and on the other, the theory of linear dissipative systems, itself central to network theory and to the ...
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A Posteriori Error Estimation for Control-Constrained, Linear-Quadratic Optimal Control Problems
SIAM Journal on Numerical Analysis, 2016Summary: We derive a posteriori error estimates for control-constrained, linear-quadratic optimal control problems. The error is measured in a norm which is motivated by the objective. Our abstract error estimator is separated into three contributions: the error in the variational inequality (i.e., in the optimality condition for the control) and the ...
Schneider, René, Wachsmuth, Gerd
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A Duality Approach for Solving Control-Constrained Linear-Quadratic Optimal Control Problems
SIAM Journal on Control and Optimization, 2014We use a Fenchel duality scheme for solving control-constrained linear-quadratic optimal control problems. We derive the dual of the optimal control problem explicitly, where the control constraints are embedded in the dual objective functional, which turns out to be continuously differentiable.
R. S. Burachik, C. Y. Kaya, S. N. Majeed
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