Optimal semiactive control of structures with isolated base

The paper investigates the benefits of implementing the semiactive control systems in relation to passive viscous damping in the context of seismically isolated structures. Frequency response functions are compiled from the computed time history response to pulse-like seismic excitation. A simple semiactive control policy is evaluated in regard to passive linear viscous damping and an optimal non-causal semiactive control strategy. The optimal control strategy minimizes the integral of the squared absolute accelerations subject to the constraint that the nonlinear equations of motion are satisfied. The optimization procedure involves a numerical solution to the Euler-Lagrange equations Published in Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 129–135, February 2006.     

Optimal obstacle control problem

In the paper we discuss some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality.Existence,uniqueness and regularity of the optimal control,problem are established.In addition,the approximation of the optimal obstacle problem is also studied.     

Optimal control of film casting processes

We present an optimal control approach for the isothermal film casting process with free surfaces described by averaged Navier–Stokes equations. We control the thickness of the film at the take‐up point using the shape of the nozzle and the initial thickness. The control goal consists in finding an even thickness profile. To achieve this goal, we minimize an appropriate cost functional. The resulting minimization problem is solved numerically by a steepest descent method. The gradient of the cost functional is approximated using the adjoint variables of the problem with fixed film width. Numerical simulations show the applicability of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimal control of unsteady compressible viscous flows

The control of complex, unsteady flows is a pacing technology for advances in fluid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical flow control systems. However, most of the prior work in this area has focused on incompressible flow which precludes many of the important physical flow phenomena that must be controlled in practice including the coupling of fluid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two‐dimensional compressible Navier–Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter‐rotating viscous vortices above an infinite wall which, due to the self‐induced velocity field, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall‐normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the influence of control regularization for each case. Copyright © 2002 John Wiley & Sons, Ltd.     

An Optimal control least-squares method for the solution of advection dispersion problems

This paper discusses the numerical solution of advection dispersion equations using an Optimal control,H ¹, least-squares formulation, associated with a quasi-Newton conjugate gradient algorithm. The suggested algorithm represents an extension of the method proposed by Bristeauxet al., for the solution of nonlinear fluid flow problems.At each time step, the discretized differential equation is transformed into an optimal control problem. This problem is then stated as an equivalent minimization one, whose objective function allows the capture of the advective behavior of the equation for high values of the P_e number.A general presentation is made of the optimization algorithm. Validation runs, for a one-dimensional example, show fairly accurate results for a wide range of Péclet and Courant numbers. Comparisons with several numerical schemes are also presented.     

Optimal flow control for Navier–Stokes equations: drag minimization

Optimal control and shape optimization techniques have an increasing role in Fluid Dynamics problems governed by partial differential equations (PDEs). In this paper, we consider the problem of drag minimization for a body in relative motion in a fluid by controlling the velocity through the body boundary. With this aim, we handle with an optimal control approach applied to the steady incompressible Navier–Stokes equations. We use the Lagrangian functional approach and we consider the Lagrangian multiplier method for the treatment of the Dirichlet boundary conditions, which include the control function itself. Moreover, we express the drag coefficient, which is the functional to be minimized, through the variational form of the Navier–Stokes equations. In this way, we can derive, in a straightforward manner, the adjoint and sensitivity equations associated with the optimal control problem, even in the presence of Dirichlet control functions. The problem is solved numerically by an iterative optimization procedure applied to state and adjoint PDEs which we approximate by the finite element method. Copyright © 2007 John Wiley & Sons, Ltd.     

Navier-Stokes analysis of a circulation control airfoil

The two-dimensional, compressible, mass-averaged Navier-Stokes equations are used to investigate flows about a typical circulation control airfoil. The governing equations are solved using the implicit approximate-factorization algorithm of Beam-Warming with a modified algebraic eddy viscosity model. Results are compared with experimental data, and excellent agreement is obtained. The effects of different jet momentum coefficients and angles of attack on the flow are studied. The mechanism of genenating large lift by circulation control is discussed.     

Optimal Control in Navier-Stokes Equations

This paper presents a formulation for optimal control of a forced convection flow. The state equation that governs the forced convection flow can be expressed as the incompressible Navier-Stokes equations and energy equation. The optimal control can be formulated as finding a control force to minimize a performance function that is defined to evaluate a control object. The stabilized finite element method is used for the spatial discretization, while the Crank-Nicolson scheme is used for the temporal discretization. The Sakawa-Shindo method, which is an iterative procedure, is applied for minimizing the performance function.     

Optimal control of quadratic functionals for affine nonlinear systems

In this paper we analyze the optimal control problem for a class of affine nonlinear systems under the assumption that the associated Lie algebra is nilpotent. The Lie brackets generated by the vector fields which define the nonlinear system represent a remarkable mathematical instrument for the control of affine systems. We determine the optimal control which corresponds to the nilpotent operator of the first order. In particular, we obtain the control that minimizes the energy of the given nonlinear system. Applications of this control to bilinear systems with first order nilpotent operator are considered.     

Optimal control of hyperbolic H-hemivariational inequalities with state constraints

The optimal control problems of hyperbolic H-hemivariational inequalities with the state constraints and nonnornotone multivalued mapping term are considered. The optimal solutions are obtained. In addition, their approximating problems are also studied.     

Stochastic Optimal Control of Nonlinear Systems via Short-Time Gaussian Approximation and Cell Mapping

A novel strategy to obtain global solutions of stochasticoptimal control problems with fixed state terminal conditions and controlbounds is proposed in this paper. The solution is global in the sense that theoptimal control solutions for all the initial conditions in a region of thestate space are obtained. The method makes use of Bellman's principle ofoptimality, the cumulant neglect closure method and the short-time Gaussianapproximation. A Markov chain with a control dependent transition probabilitymatrix is built using the generalized cell mapping method. This allows toevaluate the transient and steady state response of the controlled system. Themethod is applied to several linear and nonlinear systems leading to excellentcontrol performances.     

Multi-fluid modelling of pulsed discharges for flow control applications

Experimental evidence suggests that short-pulse dielectric barrier discharge actuators are effective for speeds corresponding to take-off and approach of large aircraft, and thus are a fruitful direction for flow control technology development. Large-eddy simulations have reproduced some of the main fluid dynamic effects. The plasma models used in such simulations are semi-empirical, however, and need to be tuned for each flowfield under consideration. In this paper, the discharge physics is examined in more detail with multi-fluid modelling, comparing a five-moment model (continuity, momentum, and energy equations) to a two-moment model (continuity and energy equations). A steady-state, one-dimensional discharge was considered first, and the five-moment model was found to predict significantly lower ionisation rates and number densities than the two-moment model. A two-dimensional, transient discharge problem with an elliptical cathode was studied next. Relative to the two-moment model, the five-moment model predicted a slower response to the activation of the cathode, and lower electron velocities and temperatures as the simulation approached steady-state. The primary reason for the differences in the predictions of the two models can be attributed to the effects of particle inertia, particularly electron inertia in the cathode layer. The computational cost of the five-moment model is only about twice that of the simpler variant, suggesting that it may be feasible to use the more sophisticated model in practical calculations for flow control actuator design.     

Optimal control of shallow water flow using time-delay function

This paper presents an optimal control system that includes a time-delay function for application to flood control setups with a retardation area. This system consists of the present and past controls that express flow behaviour in the retardation area. Optimal control theory is used to obtain a control discharge that satisfies the state equation including the time-delay function and minimizes the performance function. The optimal control and the delayed control discharges are obtained by the solution of an adjoint equation. The weighted gradient method is employed as a minimization algorithm. The Galerkin finite element procedure is employed to discretize the state and adjoint equations in the spatial direction. The bubble function interpolation, originated by the authors' group, using a stabilized term, is employed for the discretization in space. The flood flow in the Tsurumi river is presented as a numerical model. We show in this paper that floods can be controlled by means of a time-delay function.     

Optimal control of nonholonomic motion planning for a flee-falling cat

The nonholonomic motion phnning of a free-falling cat is investigated.Nonholonomicity arises in a free-falling cat subject to nonintegrable angle velocity constraints or nonintegrable conservation laws.When the total angular momentum is zero,the motion equation of a free-falling cat is established based on the model of two symmetric rigid bodies and conservation of angular momentum.The control of system can be converted to the problem of nonholonomic motion planning for a free-falling cat.Based on Ritz approximation theory,the Gauss-Newton method for motion planning by a falling cat is proposed.The effectiveness of the numerical algorithm is demonstrated through simulation on model of a free-falling cat.     

Optimal control of parabolic variational inequalities with state constraint

1　IntroductionandProblemWeshallstudytheoptimalcontrolproblemsgovernedbynonlinearparabolicvariationalinequalitiesoftheformy′+Ay +β(y) ∈Bu+f(a.e .(x,t)∈Q =Ω× [0 ,t]) ,y(0 ) =y0 , ( )withthestateconstraintF(y) S ,andthecostfunctionalI(y,u) .Whereβisadiscontinuous,nonlinearandnonmonotonemulti_valuedmapping .Theoptimalcontrolproblemsofthedifferentialsystemshavebeenstudiedforalongtime.Manyscholars,suchasJ.L .Lions ,V .Barbu ,D .Tiba,andF .Mignotetal.,haveresearchedtheoptimalcontrolpr…     

Optimal control of nonholonomic motion planning for a free-falling cat

The nonholonomic motion planning of a free-falling cat is investigated. Non-holonomicity arises in a free-falling cat subject to nonintegrable angle velocity constraints or nonintegrable conservation laws. When the total angular momentum is zero, the motion equation of a free-falling cat is established based on the model of two symmetric rigid bodies and conservation of angular momentum. The control of system can be converted to the problem of nonholonomic motion planning for a free-falling cat. Based on Ritz approximation theory, the Gauss-Newton method for motion planning by a falling cat is proposed. The effectiveness of the numerical algorithm is demonstrated through simulation on model of a free-falling cat.     

KUHN-TUCKER CONDITION AND WOLFE DUALITY OF PREINVEX SET-VALUED OPTIMIZATION

The optimality Kuhn-Tucker condition and the wolfe duality for the prein-vex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.     

Dynamics of cantilever plates and its hybrid vibration control

Applying Lagrange–Germain’s theory of elastic thin plates and Hamiltonian formulation, the dynamics of cantilever plates and the problem of its vibration control are studied, and a general solution is finally given. Based on Hamiltonian and Lagrangian density function, we can obtain the flexural wave equation of the plate and the relationship between the transverse and the longitudinal eigenvalues.Based on eigenfunction expansion, dispersion equations of propagation mode of cantilever plates are deduced. By satisfying the boundary conditions of cantilever plates, the natural frequencies of the cantilever plate structure can be given.Then, analytic solution of the problem in plate structure is obtained. An hybrid wave/mode control approach, which is based on both independent modal space control and wave control methods, is described and adopted to analyze the active vibration control of cantilever plates. The low-order(controlled by modal control) and the high-order(controlled by wave control) frequency response of plates are both improved. The control spillover is avoided and the robustness of the system is also improved. Finally, simulation results are analyzed and discussed.     

Optimal control of drainage basin considering moving boundary

The purpose of this article is to present a technique to optimally control river flood using a drainage basin considering a moving boundary. The main theme of this article is to obtain outflow discharge from the drainage basin that maintains the water level at a downstream point and empties the drainage basin as soon as possible. The water flow phenomenon inside the drainage basin when a river flood occurs is considered. This phenomenon can be analysed by the finite element method considering a moving boundary. The optimal control theory can be implemented to obtain the optimal control discharge. The finite element analysis with a moving boundary is introduced in the optimal control theory. A new boundary condition on the downstream side of the river is proposed. This condition is formulated by the solitary wave condition based on the basic water level being capable of representing natural water surface. As a numerical study, optimal control of shallow water flow is carried out for the Tsurumi River and its drainage basin model.     

An indirect shooting method based on the POD/DEIM technique for distributed optimal control of the wave equation

This paper presents a fast numerical method, based on the indirect shooting method and Proper Orthogonal Decomposition (POD) technique, for solving distributed optimal control of the wave equation. To solve this problem, we consider the first‐order optimality conditions and then by using finite element spatial discretization and shooting strategy, the solution of the optimality conditions is reduced to the solution of a series of initial value problems (IVPs). Generally, these IVPs are high‐order and thus their solution is time‐consuming. To overcome this drawback, we present a POD indirect shooting method, which uses the POD technique to approximate IVPs with smaller ones and faster run times. Moreover, in the presence of the nonlinear term, to reduce the order of the nonlinear calculations, a discrete empirical interpolation method (DEIM) is applied and a POD/DEIM indirect shooting method is developed. We investigate the performance and accuracy of the proposed methods by means of 4 numerical experiments. We show that the presented POD and POD/DEIM indirect shooting methods dramatically reduce the CPU time compared to the full indirect shooting method, whereas there is no significant difference between the accuracy of the reduced and full indirect shooting methods.