dynamic response optimization using an active set rqp algorithm a recently developed recursive quadratic programming rqp algorithm is applied to dynamic response design problems the algorithm incorporates updated hessians of the lagrange function and uses an active set strategy in which only a subset of the constraints is included in the direction finding qp subproblem hessian updating with dynamic response constraints presents some difficulties the primary difficulty is that the total number of constraints and the location of time points where they have to be imposed can change from iteration to iteration this can cause inconsistencies in hessian updating if proper numerical procedures are not used a numerical procedure to handle the situation is developed implemented and evaluated automatic restarting procedures are necessary for proper convergence of the algorithm the new algorithm is robust as well as more efficient than the purely linear algorithm the active set strategy plays an important role for application to dynamic response problems the rqp algorithms that do not use such a strategy are not applicable to this class of problems

optimization of mechanical systems on strategy of non linear first order approximation the paper presents an extended approach to non linear first order approximation of non linear programming problems and it explains how to transform an approximate problem into a strictly convex one the essence of the proposed approximation technique is to rewrite each given function hj as a composite gjo j the function j has to be chosen the paper explains how to do this while gj is linear approximated with gj the approximation of hj is then obtained as gjo j this approach enables one to obtain approximate functions with variable conservativeness which implies an adjustable approximate problem a solution procedure which replaces the original problem with a sequence of approximate problems can therefore adjust each succeeding approximate problem to improve the convergence properties the theory is illustrated with a three parameters controlled approximation this technique represents together with an optimality criteria based solution procedure a powerful and economic tool for solving nonlinear programming problems the three parameters which influence to a great extent the conservativeness of the approximate functions are under full control of the optimizer they are varied automatically during the process of optimization to speed up the convergence or to prevent oscillations the benefits gained from the proposed approach are demonstrated on several numerical examples involving structures and a dynamic multibody system

extension criterion via two components of vorticity on strong solutions to the 3 d navier stokes equations we shall show that only two components of vorticity play an essential role to determine possibility of extension of the time interval for the local strong solution to the navier stokes equations then we shall apply our extension theorem to regularity criterion on weak solutions due to serrin and beirao da veiga chae choe proved the same criterion as beirao da veiga only by means of the two components of vorticity we deal with the critical case which they excluded our criterion may be regarded as the generalization of the result of beal kato majda from l to bmo

generic solvability of the axisymmetric 3 d euler equations and the 2 d boussinesq equations abstract in this paper we first prove a new criterion of global solvability for smooth axisymmetric solutions of the 3 d euler equations for a cylindrical type of domain which can be whole r3 then using this result we obtain generic solvability of the equations in the cylindrical domain which does not include the axis of symmetry by a similar method we also obtain generic solvability of the 2 d boussinesq system

control of nonlinear systems with output tracking error constraints and its application to magnetic bearings a constructive method is presented to design controllers that force the output of nonlinear systems in a strict feedback form to track a bounded and sufficiently smooth reference trajectory asymptotically under a suitable condition on the initial output tracking error the proposed controllers guarantee the output tracking error within a symmetric or an asymmetric pre specified limit range and boundedness of all signals of the closed loop system a transformation is introduced to take care of the output tracking error constraint smooth and or p times differentiable step functions are proposed and incorporated in the output tracking error transformation to overcome difficulties due to the asymmetric limit range on the output tracking error as a result there are no switchings in the proposed controllers despite the asymmetric limit range the proposed control design is then applied to design a tracking controller for active magnetic bearings as an illustrating application

optimum design of systems for dynamics and controls using sequentialquadratic programming this paper describes application of a sequential quadratic programming method for dynamic response optimization and optimal control problems several methods to treat time dependent constraints are described

generalized mhd equations abstract solutions of the d dimensional generalized mhd gmhd equations t u u u p b b u t b u b b u b are studied in this paper we pay special attention to the impact of the parameters and on the regularity of solutions our investigation is divided into three major cases 1 0 and 0 2 0 and 0 and 3 0 and 0 when 0 and 0 the gmhd equations with any 0 and 0 possess a global weak solution corresponding to any l2 initial data furthermore weak solutions associated with 1 2 d 4 and 1 2 d 4 are actually global classical solutions when their initial data are sufficiently smooth as a special consequence smooth solutions of the 3d gmhd equations with 5 4 and 5 4 do not develop finite time singularities the study of the gmhd equations with 0 and 0 is motivated by their potential applications in magnetic reconnection a local existence result of classical solutions and several global regularity conditions are established for this case these conditions are imposed on either the vorticity u or the current density j b but not both and are weaker than some of current existing ones when 0 and 0 the gmhd equations reduce to the ideal mhd equations it is shown here that the ideal mhd equations admit a unique local solution when the prescribed initial data is in a holder space cr with r 1

lyapunov design of stabilizing controllers for cascaded systems the design of a state feedback law for an affine nonlinear system to render a as small as possible compact neighborhood of the equilibrium of interest globally attractive is discussed following z artstein s theorem 1983 the problem can be solved by designing a so called control lyapunov function for systems which are in a cascade form a lyapunov function meeting artstein s conditions is designed assuming the knowledge of a control law stabilizing the equilibrium of the head nonlinear subsystem in particular for planar systems this gives sufficient and necessary conditions for a compact neighborhood of the equilibrium to be stabilized

maximizing regions of attraction via backstepping and clfs with singularities when a nonlinear control law contains a singularity that is becomes unbounded on a set of points in the state space the region of attraction is often only a subset of the region of feasibility of this control law a method which is well known to suffer from this difficulty is feedback linearization we show that the backstepping design in its standard form has an inherent ability to make the regions of feasibility and attraction coincide thus maximizing the latter the key observation that this paper provides is that a standard backstepping style control lyapunov function which grows unbounded on the set where the control law becomes unbounded has level sets that always remain in the feasibility region which makes the feasibility region positively invariant a simulation comparison with a feedback linearization design shows a dramatic improvement of the region of attraction with backstepping since our theorem imposes a strong assumption that the feasibility region for the first subsystem in the backstepping problem is positively invariant we present examples ranging from simple to fairly difficult which demonstrate how this condition can be satisfied

design sensitivity analysis and optimization of dynamic response abstract the paper presents methods of design sensitivity analysis and optimization of dynamic response of mechanical and structural systems a key feature of the paper is the development of procedures to handle point wise state variable constraints difficulties with a previous treatment where such constraints were transformed to equivalent integral constraints are noted and explained from theoretical as well as engineering standpoints an alternate treatment of such constraints is proposed developed and evaluated in this treatment each point wise state variable constraint is replaced by several constraints that are imposed at all the local max points for the original constraint function the differential equations of motion are formulated in the first order form so as to handle more general problems the direct differentiation and adjoint variable methods of design sensitivity analysis to deal with the point wise constraints are presented with the adjoint variable methods there are two ways of calculating design sensitivity coefficients the first approach uses an impulse load and the second approach uses a step load for the corresponding adjoint equation since the adjoint variable methods are better for a large class of problems an efficient computational algorithm with these methods is presented in detail optimum results for several problems are obtained and compared with those available in the literature the new formulation works extremely well as precise optimum designs are obtained

stabilization of nonlinear systems in the plane abstract it is shown that every small time locally controllable system in the plane can locally be asymptotically stabilized by employing locally holder continuous feedback laws as essentially was conjectured by e sontag an explicit algorithm for the construction of such feedback laws is given

on the regularity of weak solutions to the magnetohydrodynamic equations abstract in this paper we study the regularity of weak solution to the incompressible magnetohydrodynamic equations we obtain some sufficient conditions for regularity of weak solutions to the magnetohydrodynamic equations which is similar to that of incompressible navier stokes equations moreover our results demonstrate that the velocity field of the fluid plays a more dominant role than the magnetic field does on the regularity of solution to the magneto hydrodynamic equations

constrained conjugate directions methods for design optimization of large systems the constrained steepest descent directions obtained as the solution of a quadratic programming subproblem are used to generate the constrained conjugate directions the resulting algorithm is quite simple and its finite convergence and other properties have been proved for convex quadratic programing problems for general problems instart procedures step size determination and potential constraint strategy are discussed

two regularity criteria for the 3d mhd equations this work establishes two regularity criteria for the 3d incompressible mhd equations the first one is in terms of the derivative of the velocity field in one direction while the second one requires suitable boundedness of the derivative of the pressure in one direction

navier stokes equations with lower bounds on the pressure we prove that weak solutions of the three dimensional incompressible navier stokes equations are smooth if the negative part of the pressure is controlled or if the positive part of the quantity v 2 2p is controlled

asymptotic stabilization of a class of smooth two dimensional systems this paper studies the asymptotic stabilizability of two dimensional control systems the class under consideration includes c infty systems that satisfy a certain genericity assumption and all real analytic systems necessary and sufficient conditions for feedback stabilization using continuous feedback and a sufficient condition for c 1 feedback stabilization are given this latter condition is given in terms of an inequality involving two indices if the direction of the inequality is changed an obstruction to c infty feedback stabilizability is obtained a subclass of polynomial systems is also studied and given complete necessary and sufficient conditions for global asymptotic stabilization using c 1 feedback

partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations in this paper we study the local behavior of the solutions to the three dimensional magnetohydrodynamic equations we are interested in both the uniform gradient estimates for smooth solutions and regularity of weak solutions it is shown that in some neighborhood of x0 t0 the gradients of the velocity field u and the magnetic field b are locally uniformly bounded in l norm as long as that either the scaled local l2 norm of the gradient or the scaled local total energy of the velocity field is small and the scaled local total energy of the magnetic field is uniformly bounded these estimates indicate that the velocity field plays a more dominant role than that of the magnetic field in the regularity theory as an immediately corollary we can derive an estimates of hausdorff dimension on the possible singular set of a suitable weak solution as in the case of pure fluid various partial regularity results are obtained as consequences of our blow up estimates

remarks on singularities dimension and energy dissipation for ideal hydrodynamics and mhd for weak solutions of the incompressible euler equations there is energy conservation if the velocity is in the besov space b 3 s with s greater than 1 3 b 3 s consists of functions that are lip s i e holder continuous with exponent s measured in the l p norm here this result is applied to a velocity field that is lip 0 except on a set of co dimension on which it is lip agr 1 with uniformity that will be made precise below we show that the frisch parisi multifractal formalism is valid at least in one direction for such a function and that there is energy conservation if analogous conservation results are derived for the equations of incompressible ideal mhd i e zero viscosity and resistivity for both energy and helicity in addition a necessary condition is derived for singularity development in ideal mhd generalizing the beale kato majda condition for ideal hydrodynamics

a recursive quadratic programming method with active set strategy for optimal design recursive quadratic programming methods have become popular in the field of mathematical programming owing to their excellent convergence characteristics there are two recursive quadratic programming methods that have been published in the literature one is by han and the other is by pshenichny published in 1977 and 1970 respectively the algorithm of pshenichny had been undiscovered until now and is examined here for the first time it is found that the proof of global convergence by han requires computing sensitivity coefficients derivatives of all constraint functions of the problem at every iteration this is prohibitively expensive for large scale applications in optimal design in contrast pshenichny has proved global convergence of his algorithm using only an active set strategy this is clearly preferable for large scale applications the method of pshenichny has been coded into a fortran program applications of this method to four example problems are presented the method is found to be very reliable however the method is found to be very sensitive to local minima i e it converges to a local minimum nearest to the starting design thus for optimal design problems which usually possess multiple local minima it is suggested that pshenichny s method be used as part of a hybrid method

several simultaneous formulations for transient dynamic response optimization an evaluation several simultaneous formulations for transient dynamic response optimization are described analyzed and compared a key feature of the formulations is that the state variables in addition to the real design variables are treated as independent variables in the optimization process the state variables include different combinations of generalized displacements velocities and accelerations formulations based on different discretization techniques for first order and second order differential equations are presented finite difference newmark s method and methods based on collocation are all discussed similar to the simultaneous analysis and design approach used for the optimization of structures subjected to static loads and the direct collocation transcription method for optimal control the equations of motion are treated as equality constraints a major advantage of these formulations is that special design sensitivity analysis methods are no longer needed however the formulations have larger numbers of variables and constraints therefore sparsity of the problem functions must be exploited in all the calculations advantages and disadvantages of the formulations are discussed the numerical results for an example problem and performance features of the formulations are compared all the formulations converge to the optimum solution for the example problem they are quite efficient for a smaller number of time grid points however the computational times increase as the number of grid points is increased copyright 2009 john wiley sons ltd

performance of some sqp algorithms on structural design problems this paper describes the basic ideas of sequential quadratic programming sqp algorithms for design optimization there are two fundamental differences between the various algorithms i the difinition of the qp subproblem solved at each iteration and ii the descent function used during step size determination the performances of the algorithms can change dramatically depending on how the two steps are executed numerical implementation details of various computational steps are discussed three programs based on sqp algorithms are used to solve 17 structural design problems having 7 to 96 design variables and 10 to 1051 performance constraints besides design variable bounds based on the performance of these programs efficient procedures to execute various steps of the sqp methods are determined it is concluded that the potential constraint strategy where only a subset of the constraints is used to define the qp subproblem is essential for large scale engineering design applications with this strategy the sqp methods are quite robust and have great potential for routine application in engineering design

alternative formulations for transient dynamic response optimization three alternative formulations for transient dynamic response optimization of mechanical systems are presented analyzed and evaluated the basic idea of these formulations is to treat various state variables as independent variables in the optimization process in addition to the real design variables that is generalized displacements velocities and accelerations because all functions of the optimization problem become explicit in terms of the variables in these formulations their gradients can be calculated easily as compared to the conventional approach where special design sensitivity analysis methods need to be used also the equations of motion are not integrated explicitly they are imposed as equality constraints for the alternative formulations the optimization problem is quite large in terms of the numbers of variables and constraints however the problem functions are quite sparse which is exploited in the optimization process advantages and disadvantages of the formulations are discussed several cases of two example problems are solved to study the performance of the formulations based on the extensive numerical experiments it is concluded that the proposed formulations work well for the example problems and have potential for further development for practical applications

nonexistence of self similar singularities in the viscous magnetohydrodynamics with zero resistivity abstract we are concerned on the possibility of finite time singularity in a partially viscous magnetohydrodynamic equations in r n n 2 3 namely the mhd with positive viscosity and zero resistivity in the special case of zero magnetic field the system reduces to the navier stokes equations in r n in this paper we exclude the scenario of finite time singularity in the form of self similarity under suitable integrability conditions on the velocity and the magnetic field we also prove the nonexistence of asymptotically self similar singularity this provides us information on the behavior of solutions near possible singularity of general type as described in corollary 1 1

the critical sobolev inequalities in besov spaces and regularity criterion to some semi linear evolution equations we show the critical sobolev inequalities in the besov spaces with the logarithmic form such as brezis gallouet wainger and beale kato majda as an application of those inequalities the regularity problem under the critical condition to the navier stokes equations the euler equations in mathbb r n and the gradient flow to the harmonic map to the sphere are discussed namely the serrin ohyama type regularity criteria are improved in the terms of the besov spaces

structural shape optimization using equivalent static loads transformed from dynamic loads in structural optimization static loads are generally utilized although real external forces are dynamic dynamic loads have been considered only in small scale problems recently an algorithm for dynamic response optimization using transformation of dynamic loads into equivalent static loads has been proposed the transformation is conducted to match the displacement fields from dynamic and static analyses this algorithm can be applied to large scale problems however the application has been limited to size optimization the present study applies the algorithm to shape optimization because the number of degrees of freedom of finite element models is usually very large in shape optimization it is difficult to conduct dynamic response optimization with conventional methods that directly treat dynamic response in the time domain the optimization process is carried out by interfacing an optimization system and an analysis system for structural dynamics various examples are solved to verify the algorithm the results are compared to the results from static loads it is found that the algorithm using static loads transformed from dynamic loads based on displacement is valid for very large scale shape optimization problems copyright 2005 john wiley sons ltd

control of nonlinear systems with partial state constraints using a barrier lyapunov function this article addresses the problem of control design for strict feedback systems with constraints on the states to prevent the states from violating the constraints we employ a barrier lyapunov function blf which grows to infinity whenever its arguments approaches some finite limits based on blf based backstepping we show that asymptotic output tracking is achieved without violation of any constraint provided that the initial states and control parameters are feasible we also establish sufficient conditions to ensure feasibility which can be checked offline without precise knowledge of the initial states the feasibility conditions are relaxed when handling the partial state constraint problem as compared to the full state constraint problem in the presence of parametric uncertainties blf based adaptive backstepping is useful in preventing the states from transgressing the constrained region during the transient stages of online parameter adaptation to relax the feasibility conditions asymme

adding an integrator for the stabilization problem abstract we study the relationship between the following two properties p1 the system x f x y y v is locally asymptotically stabilizable and p2 the system x f x u is locally asymptotically stabilizable where x r n y r dayawansa martin and knowles have proved that these properties are equivalent if the dimension n 1 here using the so called control lyapunov function approach a we propose another more constructive and somewhat simpler proof of dayawansa martin and knowles s result b we show that in general p1 does not imply p2 for dimensions n larger than 1 c we prove that p2 implies p1 if some extra assumptions are added like homogeneity of the system by using the latter result recursively we obtain a sufficient condition for the local asymptotic stabilizability of systems in a triangular form

regularity criterion via two components of vorticity on weak solutions to the navier stokes equations in r 3 we consider the regularity of weak solutions to the navier stokes equations in r3 let u be a weak solution in r3 0 t w curlu and w w1 w2 0 it is proved that u becomes a classical solution if w lq 0 t b r 0 for 2 q 3 r 2 32 r and 2r 3 this is an improvement of the result given by kozono yatsu extension criterion via two components of vorticity on strong solution to the 3d navier stokes equations math z 246 2003 55 68

remarks on the breakdown of smooth solutions for the 3 d euler equations the authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3 d euler equations in other words if a solution of the euler equations is initially smooth and loses its regularity at some later time then the maximum vorticity necessarily grows without bound as the critical time approaches equivalently if the vorticity remains bounded a smooth solution persists

isogeometric shape optimization for quasi static processes summary a framework to solve shape optimization problems for quasi static processes is developed and implemented numerically within the context of isogeometric analysis iga recent contributions in shape optimization within iga have been limited to static or steady state loading conditions in the present contribution the formulation of shape optimization is extended to include time dependent loads and responses a general objective functional is used to accommodate both structural shape optimization and passive control for mechanical problems an adjoint sensitivity analysis is performed at the continuous level and subsequently discretized within the context of iga the methodology and its numerical implementation are tested using benchmark static problems of optimal shapes of orifices in plates under remote bi axial tension and pure shear under quasi static loading conditions the method is validated using a passive control approach with an a priori known solution several applications of time dependent mechanical problems are shown to illustrate the capabilities of this approach in particular a problem is considered where an external load is allowed to move along the surface of a structure the shape of the structure is modified in order to control the time dependent displacement of the point where the load is applied according to a pre specified target copyright 2015 john wiley sons ltd

barrier lyapunov functions for the control of output constrained nonlinear systems in this paper we present control designs for single input single output siso nonlinear systems in strict feedback form with an output constraint to prevent constraint violation we employ a barrier lyapunov function which grows to infinity when its arguments approach some limits by ensuring boundedness of the barrier lyapunov function in the closed loop we ensure that those limits are not transgressed besides the nominal case where full knowledge of the plant is available we also tackle scenarios wherein parametric uncertainties are present asymptotic tracking is achieved without violation of the constraint and all closed loop signals remain bounded under a mild condition on the initial output furthermore we explore the use of an asymmetric barrier lyapunov function as a generalized approach that relaxes the requirements on the initial conditions we also compare our control with one that is based on a quadratic lyapunov function and we show that our control requires less restrictive initial conditions a numerical example is provided to illustrate the performance of the proposed control