Formal adjoints of linear DAE operators and their role in optimal control.
Free end-point linear-quadratic control subject to implicit continuous- time systems: Necessary and sufficient conditions for solvability
Guaranteed control policy with arbitrary set of correction points for linear-quadratic system with delay
Linear-quadratic optimization and some general hypotheses on optimal control.
Minimax LQG control
This paper presents an overview of some recent results concerning the emerging theory of minimax LQG control for uncertain systems with a relative entropy constraint uncertainty description. This is an important new robust control system design methodology providing minimax optimal performance in terms of a quadratic cost functional. The paper first considers some standard uncertainty descriptions to motivate the relative entropy constraint uncertainty description. The minimax LQG problem under...
Multitime linear-quadratic regulator problem based on curvilinear integral.
New results in subspace-stabilization control theory.
On a criterion of Yakubovich type for the absolute stability of nonautonomous control processes.
On adaptive control for the continuous time-varying JLQG problem
In this paper the adaptive control problem for a continuous infinite time-varying stochastic control system with jumps in parameters and quadratic cost is investigated. It is assumed that the unknown coefficients of the system have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Under these assumptions it is shown that the optimal value of the quadratic cost can be reached based only on the values of these limits, which, in turn, can be estimated...
On an infinite dimensional linear-quadratic problem with fixed endpoints: the continuity question
In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.
On Fredholm alternative for certain quasilinear boundary value problems
On Fredholm alternative for certain quasilinear boundary value problems
We study the Dirichlet boundary value problem for the -Laplacian of the form where is a bounded domain with smooth boundary , , , and is the first eigenvalue of . We study the geometry of the energy functional and show the difference between the case and the case . We also give the characterization of the right hand sides for which the above Dirichlet problem is solvable and has multiple solutions.
On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints
In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated and...
On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints
In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated and...
On the Accuracy of Regularized Solutions to Quadratic Minimization Problems on a Half-Space, in Case of a Normally Solvable Operator
On the infinite time horizon linear-quadratic regulator problem under a fractional brownian perturbation
In this paper we solve the basic fractional analogue of the classical infinite time horizon linear-quadratic gaussian regulator problem. For a completely observable controlled linear system driven by a fractional brownian motion, we describe explicitely the optimal control policy which minimizes an asymptotic quadratic performance criterion.
On the infinite time horizon linear-quadratic regulator problem under a fractional Brownian perturbation
In this paper we solve the basic fractional analogue of the classical infinite time horizon linear-quadratic Gaussian regulator problem. For a completely observable controlled linear system driven by a fractional Brownian motion, we describe explicitely the optimal control policy which minimizes an asymptotic quadratic performance criterion.
On the parameter selection problem in the Newton-ADI iteration for large-scale Riccati equations.
On the smoothness of solutions of linear-quadratic regulator for degenerate diffusions.
One possibility of multidimensional control system design