53,932 research outputs found
Infinite horizon control and minimax observer design for linear DAEs
In this paper we construct an infinite horizon minimax state observer for a
linear stationary differential-algebraic equation (DAE) with uncertain but
bounded input and noisy output. We do not assume regularity or existence of a
(unique) solution for any initial state of the DAE. Our approach is based on a
generalization of Kalman's duality principle. The latter allows us to transform
minimax state estimation problem into a dual control problem for the adjoint
DAE: the state estimate in the original problem becomes the control input for
the dual problem and the cost function of the latter is, in fact, the
worst-case estimation error. Using geometric control theory, we construct an
optimal control in the feed-back form and represent it as an output of a stable
LTI system. The latter gives the minimax state estimator. In addition, we
obtain a solution of infinite-horizon linear quadratic optimal control problem
for DAEs.Comment: This is an extended version of the paper which is to appear in the
proceedings of the 52nd IEEE Conference on Decision and Control, Florence,
Italy, December 10-13, 201
Model order reduction approaches for infinite horizon optimal control problems via the HJB equation
We investigate feedback control for infinite horizon optimal control problems
for partial differential equations. The method is based on the coupling between
Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is
well-known that HJB equations suffer the so called curse of dimensionality and,
therefore, a reduction of the dimension of the system is mandatory. In this
report we focus on the infinite horizon optimal control problem with quadratic
cost functionals. We compare several model reduction methods such as Proper
Orthogonal Decomposition, Balanced Truncation and a new algebraic Riccati
equation based approach. Finally, we present numerical examples and discuss
several features of the different methods analyzing advantages and
disadvantages of the reduction methods
Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem
An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed
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