@article{ito_ravindran_2001, title={Reduced basis method for optimal control of unsteady viscous flows}, volume={15}, ISSN={["1061-8562"]}, DOI={10.1080/10618560108970021}, abstractNote={Abstract In this article we discuss the reduced basis method (RBM) for optimal control of unsteady viscous flows. RBM is a reduction method in which one can achieve the versatility of the finite element method or another for that matter and gain significant reduction in the number of degrees of freedom. The essential idea in this method is to define a reduced order subspace spanned by few basis elements and then obtain the solution via a Galerkin projection. We present several ways to define this subspace. Feasibility of the approach is demonstrated on two boundary control problems in cavity and wall bounded channel flows. Control action is effected through boundary surface movement on part of the solid wall. Application of RBM to the control problems leads to finite dimensional optimal control problems which are solved using Newton's method. Through computational experiments we demonstrate the feasibility and applicability of the reduced basis method for control of unsteady viscous flows.}, number={2}, journal={INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS}, author={Ito, K and Ravindran, SS}, year={2001}, pages={97–113} }
 @article{hou_ravindran_1998, title={A penalized Neumann control approach for solving an optimal Dirichlet control problem for the Navier-Stokes equations}, volume={36}, ISSN={["0363-0129"]}, DOI={10.1137/S0363012996304870}, abstractNote={We introduce a penalized Neumann boundary control approach for solving an optimal Dirichlet boundary control problem associated with the two- or three-dimensional steady-state Navier--Stokes equations. We prove the convergence of the solutions of the penalized Neumann control problem, the suboptimality of the limit, and the optimality of the limit under further restrictions on the data. We describe the numerical algorithm for solving the penalized Neumann control problem and report some numerical results.}, number={5}, journal={SIAM JOURNAL ON CONTROL AND OPTIMIZATION}, author={Hou, LS and Ravindran, SS}, year={1998}, month={Sep}, pages={1795–1814} }
 @article{ito_ravindran_1998, title={A reduced-order method for simulation and control of fluid flows}, volume={143}, ISSN={["1090-2716"]}, DOI={10.1006/jcph.1998.5943}, abstractNote={This article presents a reduced-order modeling approach for simulation and control of viscous incompressible flows. The reduced-order models suitable for control and which capture the essential physics are developed using the reduced-basis method. The so-called Lagrange approach is used to define reduced bases and the basis functions in this approach are obtained from the numerical solutions. The feasibility of this method for flow control is demonstrated on boundary control problems in closed cavity and in wall-bounded channel flows. Control action is effected through boundary surface movement on a part of the solid wall. Our formulation of the reduced-order method applied to flow control problems leads to a constrained minimization problem and is solved by applying Newton-like methods to the necessary conditions of optimality. Through our computational experiments we demonstrate the feasibility and applicability of the reduced-order method for simulation and control of fluid flows.}, number={2}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Ito, K and Ravindran, SS}, year={1998}, month={Jul}, pages={403–425} }
 @article{ito_ravindran_1998, title={Optimal control of thermally convected fluid flows}, volume={19}, ISSN={["1064-8275"]}, DOI={10.1137/S1064827596299731}, abstractNote={We examine the optimal control of stationary thermally convected fluid flows from the theoretical and numerical point of view. We use thermal convection as control mechanism; that is, control is effected through the temperature on part of the boundary. Control problems are formulated as constrained minimization problems. Existence of optimal control is given and a first-order necessary condition of optimality from which optimal solutions can be obtained is established. We develop numerical methods to solve the necessary condition of optimality and present computational results for control of cavity- and channel-type flows showing the feasibility of the proposed approach.}, number={6}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Ito, K and Ravindran, SS}, year={1998}, month={Nov}, pages={1847–1869} }
 @article{gunzburger_hou_ravindran_1997, title={Analysis and approximation of optimal control problems for a simplified Ginzburg-Landau model of superconductivity}, volume={77}, ISSN={["0029-599X"]}, DOI={10.1007/s002110050285}, number={2}, journal={NUMERISCHE MATHEMATIK}, author={Gunzburger, MD and Hou, LS and Ravindran, SS}, year={1997}, month={Aug}, pages={243–268} }
 @article{hou_ravindran_yan_1997, title={Numerical solution of optimal distributed control problems for incompressible flows}, volume={8}, ISSN={["1029-0257"]}, DOI={10.1080/10618569708940798}, abstractNote={Abstract We study the numerical solution of optimal control problems associated with the two-dimensional viscous incompressible flows which are governed by the Navier-Stokes equations. Although the techniques apply to more general settings, the presentation is confined to the objectives of minimizing the vorticity in the steady-state case with distributed controls and tracking the velocity field in the nonstationary case with piecewise distributed controls. In the steady-state case, we develop a systematic way to use the Lagrange multiplier rules to derive an optimality system of equations from which an optimal solution can be computed; finite element methods are used to find approximate solutions for the optimality system of equations. In the time-dependent case, a piecewise-in-time optimal control approach is proposed and the fully discrete approximation algorithm for solving the piecewise optimal control problem is defined. Numrical results are presented for both the steady-state and time-dependent opt...}, number={2}, journal={INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS}, author={Hou, LS and Ravindran, SS and Yan, Y}, year={1997}, pages={99–114} }
 @article{ravindran_1997, title={Numerical solutions of optimal control for thermally convective flows}, volume={25}, number={2}, journal={International Journal for Numerical Methods in Fluids}, author={Ravindran, S. S.}, year={1997}, pages={205–223} }