recovering the initial state of an infinite dimensional system using observers let a be the generator of a strongly continuous semigroup t on the hilbert space x and let c be a linear operator from d a to another hilbert space y possibly unbounded with respect to x not necessarily admissible we consider the problem of estimating the initial state z 0 d a with respect to the norm of x from the output function y t ct tz 0 given for all t in a bounded interval 0 t we introduce the concepts of estimatability and backward estimatability for a c in a more general way than currently available in the literature we introduce forward and backward observers and we provide an iterative algorithm for estimating z 0 from y this algorithm generalizes various algorithms proposed recently for specific classes of systems and it is an attractive alternative to methods based on inverting the gramian our results lead also to a very general formulation of russell s principle i e estimatability and backward estimatability imply exact observability this general formulation of the principle does not require t to be invertible we illustrate our estimation algorithms on systems described by wave and schrodinger equations and we provide results from numerical simulations

brief paper the strong stabilization of a one dimensional wave equation by non collocated dynamic boundary feedback control the stabilization of a one dimensional wave equation with non collocated observation at its unstable free end and control at another end is considered the controller comprises a state estimator which is designed in the case where the velocity is not available the method of backstepping is adopted in our design of the feedback law we use the theory of c 0 semigroups and lyapunov functionals to prove the strong stability of the resulting closed loop system

a new mutation operator for real coded genetic algorithms abstract in this paper a new mutation operator called power mutation pm is introduced for real coded genetic algorithms rcga the performance of pm is compared with two other existing real coded mutation operators taken from literature namely non uniform mutation num and makinen periaux and toivanen mutation mptm using the various combinations of two crossovers laplace crossover kusum deep manoj thakur a new crossover operator for real coded genetic algorithms applied mathematics and computations accepted for publication doi 10 1016 j amc 2006 10 047 and heuristic crossover z michalewicz genetic algorithms data structures evolution programs springer verlag new york 1992 a h wright genetic algorithms for real parameter optimization in g j e rawlins ed foundations of genetic algorithms i morgan kaufmann san mateo 1991 pp 205 218 and three mutation operators the newly defined mutation in this paper pm num and mptm six generational real coded gas are compared on a set of 20 benchmark global optimization test problems various performance criterion are used to judge the efficiency accuracy and reliability of all the rcgas the results show that the rcga using the proposed power mutation when used in conjunction with the earlier defined laplace crossover outperforms all other gas considered in this study

optimizability and estimatability for infinite dimensional linear systems an infinite dimensional linear system described by dot x t ax t bu t t geq 0 is said to be optimizable if for every initial state x 0 an input u in l 2 can be found such that x in l 2 here a is the generator of a strongly continuous semigroup on a hilbert space and b is an admissible control operator for this semigroup in this paper we investigate optimizability also known as the finite cost condition and its dual estimatability we explore the connections with stabilizability and detectability we give a very general theorem about the equivalence of input output stability and exponential stability of well posed linear systems the two are equivalent if the system is optimizable and estimatable we conclude that a well posed system is exponentially stable if and only if it is dynamically stabilizable and input output stable we illustrate the theory by two examples based on pdes in two or more space dimensions the wave equation and a structural acoustics model

how to get a conservative well posed linear system out of thin air part ii controllability and stability let a0 be a possibly unbounded positive operator on the hilbert space h which is boundedly invertible let c0 be a bounded operator from cal d a 0 1 2 with the norm z 1 2 2 langle

a directed genetic algorithm for global optimization within the framework of real coded genetic algorithms this paper proposes a directed genetic algorithm dga that introduces a directed crossover operator and a directed mutation operator the operation schemes of these operators borrow from the reflection and the expansion search mode of the nelder mead s simplex method first the taguchi method is employed to study the influence analysis of the parameters in the dga the results show that the parameters in the dga have strong robustness for solving the global optimal solution then several strategies are proposed to enhance the solution accuracy capability of the dga all of the strategies are applied to a set of 30 100 dimensional benchmark functions to prove their superiority over several genetic algorithms finally a cantilevered beam design problem with constrained conditions is used as a practical structural optimization example for demonstrating the very good performance of the proposed method

soccer game optimization with substitute players metaheuristic methods are powerful optimization methods to solve various problems and have been used widely in this paper a player substitution mechanism to enhance the performance of the soccer game optimization sgo is proposed the substitution mechanism refers to the competition concept existing in the evolutionary algorithm the substitute players are continuously updated to keep up with a set of best solutions so far this paper discusses the sensitivity of its parameters as well as assesses the performance of the proposed method using unconstraint continuous problems the proposed method is compared to the sgo without player substitution biogeography based optimization bbo ant colony optimization aco differential evolution de evolutionary strategies es genetic algorithm ga and particle swarm optimization pso the experiment results show that the proposed method performs better than other algorithms used in this paper player substitution mechanism is proposed to enhance the soccer games optimization the proposed method is compared to sgo without substitution the experiment results confirm the proposed method is better we investigate the method sensitivity for unimodal and multimodal functions

uniform controllability of semidiscrete approximations of parabolic control systems controlling an approximation model of a controllable infinite dimensional linear control system does not necessarily yield a good approximation of the control needed for the continuous model in the present paper under the main assumptions that the discretized semigroup is uniformly analytic and that the control operator is mildly unbounded we prove that the semidiscrete approximation models are uniformly controllable moreover we provide a computationally efficient way to compute the approximation controls an example of application is implemented for the one and two dimensional heat equation with neumann boundary control

infinite dimensional luenberger like observers for a rotating body beam system the paper proposes luenberger like observers for a rotating body beam system the latter is described by a partial differential equation and its dynamic is governed a unitary group the observers proposed in the paper are able to reconstitute the dynamic evolution of the beam profile by measuring the moment force on the boundary only meanwhile we propose a reliable numerical scheme based on a finite element method in order to simulate the observation system and the observers the efficiency of our proposed scheme and the performances of the observers are illustrated with numerical simulation results

rapid exponential feedback stabilization with unbounded control operators we study the wellposedness and the main features of a class of feedback control systems the involved control system is composed of the generator of a strongly continuous group for the free part and of an unbounded control operator so that the results can be applied to boundary or point control problems for partial differential equations of hyperbolic or petrowski type the feedback operator is explicit and one can achieve an arbitrary large decay rate for the closed loop system these results are proved under a controllability assumption and the proofs rely on general results about the algebraic riccati equation associated with the linear quadratic regulator problem

rapid boundary stabilization of linear distributed systems we prove that under rather general assumptions an exactly controllable problem is uniformly stabilizable with arbitrarily prescribed decay rates our approach is direct and constructive and avoids many of the technical difficulties associated with the usual methods based on riccati equations we give several applications for the wave equation and for petrovsky systems

quasi random initial population for genetic algorithms the selection of the initial population in a population based heuristic optimizationmethod is important since it affects the search for several iterations and often has an influence on the final solution if no a priori information about the optima is available the initial population is often selected randomly using pseudorandom numbers usually however it is more important that the points are as evenly distributed as possible than that they imitate random points in this paper we study the use of quasi random sequences in the initial population of a genetic algorithm sample points in a quasi random sequence are designed to have good distribution properties here a modified genetic algorithm using quasi random sequences in the initial population is tested by solving a large number of continuous benchmark problems from the literature the numerical results of two implementations of genetic algorithms using different quasi random sequences are compared to those of a traditional implementation using pseudorandom numbers the results obtained are promising

optimal filtration for the approximation of boundary controls for the one dimensional wave equation using a finite difference method we consider a finite differences semi discrete scheme for the approximation of boundary controls for the one dimensional wave equation the high frequency numerical spurious oscillations lead to a loss of the uniform with respect to the mesh size controllability property of the semi discrete model in the natural setting we prove that by filtering the high frequencies of the initial data in an optimal range we restore the uniform controllability property moreover we obtain a relation between the range of filtration and the minimal time of control needed to ensure the uniform controllability

modifications of real code genetic algorithm for global optimization a series of modifications to the real coded genetic algorithm for the task of locating the global minimum of multidimensional functions are presented here these modifications include a new stopping rule a novel mutation mechanism and a periodically application of a local search procedure the proposed modifications are tested on a series of optimization problems and the results are reported

reconstructing initial data using observers error analysis of the semi discrete and fully discrete approximations a new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in ramdani et al automatica 46 10 1616 1625 2010 based on the concept of observers also called luenberger observers this algorithm covers a large class of abstract evolution pde s in this paper we are concerned with the convergence analysis of this algorithm more precisely we provide a complete numerical analysis for semi discrete in space and fully discrete approximations derived using finite elements in space and an implicit euler method in time the analysis is carried out for abstract schrodinger and wave conservative systems with bounded observation locally distributed

electromagnetic scattering by rough conducting circular cylinders ii axial corrugation for pt i see ibid vol 36 no 5 p 651 1988 the coherent and incoherent responses of conducting axially corrugated surfaces which are on the average circular cylinders are calculated the calculation encompasses second order perturbation the general approach used is to apply the extinction theorem to write an integral equation for the surface current density and then to use the perturbation theory to solve it the results are recast by using pade approximants to achieve a significant extension of the domain of validity of the original formulation

an approximation method for exact controls of vibrating systems we propose a new method for the approximation of exact controls of a second order infinite dimensional system with bounded input operator the algorithm combines russell s stabilizability implies controllability principle with the galerkin method the main new feature of this work consists of giving precise error estimates in order to test the efficiency of the method we consider two illustrative examples with the finite element approximations of the wave and the beam equations and describe the corresponding simulations

analysis of the hum control operator and exact controllability for semilinear waves in uniform time we present a regularity result for the hum optimal control associated with the interior control of linear waves we use this analysis together with strichartz inequalities to get results on the exact controllability for subcritical nonlinear waves in a bounded domain of mathbb r 3

solving inverse source problems using observability applications to the euler bernoulli plate equation the aim of this paper is to provide a general framework for solving a class of inverse source problems by using exact observability of infinite dimensional systems more precisely we show that if a system is exactly observable then a source term in this system can be identified by knowing its intensity and appropriate observations which often correspond to measurements of some boundary traces this abstract theory is then applied to obtain new identifiability results for a system governed by the euler bernoulli plate equation using a different methodology we show that exact observability can be used to identify both the locations and the intensities of combinations of point sources in the plate equation

propagation observation and control of waves approximated by finite difference methods this paper surveys several topics related to the observation and control of wave propagation phenomena modeled by finite difference methods the main focus is on the property of observability corresponding to the question of whether the total energy of solutions can be estimated from partial measurements on a subregion of the domain or boundary the mathematically equivalent property of controllability corresponds to the question of whether wave propagation behavior can be controlled using forcing terms on that subregion as is often desired in engineering applications observability controllability of the continuous wave equation is well understood for the scalar linear constant coefficient case that is the focus of this paper however when the wave equation is discretized by finite difference methods the control for the discretized model does not necessarily yield a good approximation to the control for the original continuous problem in other words the classical convergence consistency stability property of a numerical scheme does not suffice to guarantee its suitability for providing good approximations to the controls that might be needed in applications observability controllability may be lost under numerical discretization as the mesh size tends to zero due to the existence of high frequency spurious solutions for which the group velocity vanishes this phenomenon is analyzed and several remedies are suggested including filtering tychonoff regularization multigrid methods and mixed finite element methods we also briefly discuss these issues for the heat beam and schrodinger equations to illustrate that diffusive and dispersive effects may help to retain the observability controllability properties at the discrete level we conclude with a list of open problems and future subjects for research

time reversal focusing of the initial state for kirchhoff plate consider a kirchhoff plate partial t 2 u delta 2 u partial t 2 delta u 0 in omega times 0 t with boundary data u delta u 0 on partial omega times 0 t and unknown initial data u cdot 0 u 0 and partial t u cdot 0 u 1 in omega we study an inverse problem of determining u 0 u 1 from an interior observation u omega times 0 t here omega is a bounded domain omega a nonempty open subset of omega and t 0 a suitable time duration by means of an iterative time reversal technique we derive an asymptotic formula of reconstructing u 0 u 1 approximately with a logarithmical convergence rate for smooth initial data the convergence becomes uniform and exponential when omega omega t satisfies the geometric control condition introduced by bardos lebeau and rauch

electromagnetic scattering by rough conduction circular cylinders i angular corrugation the coherent and incoherent responses of perfectly conducting angularly corrugated surfaces which are infinite circular cylinders on the average are calculated using a second order perturbation method the general approach used is to apply the extinction theorem to write an integral equation for the surface current density and then to use perturbation theory to solve it these results are recast by using the only nontrivial pade approximant for this approximation this recasting yield a considerable qualitative improvement which at least in one special case is shown to be quantitative as well

a modified real coded genetic algorithm for constrained optimization abstract the performance of a genetic algorithm ga largely depends upon crossover and mutation operators deep and thakur 2007 14 15 proposed a real coded genetic algorithm rcga incorporating laplace crossover lx and power mutation pm operator and shown that the resulting ga named lx pm outperforms many existing rcgas on a large set of scalable test problems of varying difficulty level in this paper lx pm is modified by improving the lx operator the modified lx operator named as bounded exponential crossover bex operator always creates offspring within the variable bounds a new rcga named bex pm incorporating bex and pm operator is proposed the performance of the modified ga is tested against the original algorithm lx pm and three other popular constrained optimization algorithms hx num hx mptm and sbx pol over a test suite containing twenty five constrained optimization problems collected from global optimization literature the performance of all rcgas and quality of solution obtained is compared on the basis of standard criteria used in ga literature the comparative study shows that bex pm performs significantly better than the original algorithm lx pm and outperforms all rcgas considered in this study

output error minimizing back and forth nudging method for initial state recovery abstract we show that for linear dynamical systems with skew adjoint generators the initial state estimate given by the back and forth nudging method with colocated feedback converges to the minimizer of the discrepancy between the measured and simulated outputs given that the observer gains are chosen suitably and the system is exactly observable if the system s generator a is essentially skew adjoint and dissipative with not too much dissipation the colocated feedback has to be corrected by the operator e a t e a t in order to obtain such convergence in some special cases a feasible approximation for this operator can be found analytically the case with wave equation with constant dissipation will be presented

hybridizing harmony search algorithm with different mutation operators for continuous problems abstract harmony search hs is a recent ea inspired by musical improvisation process to seek a pleasing harmony mutation is a vital component used in evolutionary algorithms ea where a value in the population is randomly selected to be altered to improve the evolution process the original hs algorithm applies an operation similar to mutation during the random consideration operator during random selection operator a value within the range of the decision variable is selected randomly to explore different areas in the search space this paper aims at experimentally evaluating the performance of hs algorithm after replacing the random consideration operator in the original hs with five different mutation methods the different variations of hs are experimented on standard benchmark functions in terms of final obtained solution and convergence speed the results show that using polynomial mutation improves the performance of the hs algorithm for most of the used functions

stabilization of an abstract second order system with application to wave equations under non collocated control and observations abstract the objective of this paper is to deal with the stabilization of multi dimensional wave equations under non collocated control and observation with the following cases a locally internal distributed control and observation b internal distributed control and boundary observation c boundary control and internal distributed observation d locally internal distributed control and boundary observation we first discuss the stability of an abstract second order infinite dimensional system under the estimated state feedback control the well posedness in the sense of d salamon is specially emphasized the result is then applied to the multi dimensional wave equations with the aforementioned three different non collocated control and observations a c finally we prove the stabilizability of a wave equation with non collocated control and observation d by using the same idea although it cannot be cast into the abstract setting

uniform exponential long time decay for the space semi discretization of a locally damped wave equation via an artificial numerical viscosity we consider the finite difference space semi discretization of a locally damped wave equation the damping being supported in a suitable subset of the domain under consideration so that the energy of solutions of the damped wave equation decays exponentially to zero as time goes to infinity the decay rate of the semi discrete systems turns out to depend on the mesh size h of the discretization and tends to zero as h goes to zero we prove that adding a suitable vanishing numerical viscosity term leads to a uniform with respect to the mesh size exponential decay of the energy of solutions this numerical viscosity term damps out the high frequency numerical spurious oscillations while the convergence of the scheme towards the original damped wave equation is kept we discuss this problem in 1d and 2d in the interval and the square respectively our method of proof relies on discrete multiplier techniques

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

subset selection in multiple linear regression models a hybrid of genetic and simulated annealing algorithms the question of variable selection in a multiple linear regression model is a major open research topic in statistics the subset selection problem in multiple linear regression deals with the selection of a minimal subset of input variables without loss of explanatory power in this paper we adapt the genetic and simulated annealing algorithms for variable selection in multiple linear regression the performance of this hybrid heuristic method is compared to those obtained by forward selection backward elimination and classical genetic algorithm search a comparative analysis on the literature data sets and simulation data shows that our hybrid heuristic method may suggest efficient alternative to traditional subset selection methods for the variable selection problem in multiple linear regression models

geometricity of genetic operators for real coded representation we investigate geometricity of operators for real coded genetic algorithms geometric operator is a representation independent generalization of the class of traditional mask based operators for binary strings it is defined as a function of the distance of the search space seen as a metric space although the real coded representation allows for a very familiar notion of distance namely the euclidean distance there are also other distances suiting it such as minkowski distances additionally topological transformations of the real space give rise to further notions of distance in this paper we study geometric crossover operators associated with minkowski spaces in a formal and general setting and show that some pre existing genetic operators for the real coded representation are geometric although geometric crossover operators defined in the plane are intuitive operators in higher dimensional spaces they are not trivial to understand and implement we derive formally algorithms to implement these geometric crossover operators in the generic n dimensional case we compare the performance of the presented operators with existing ones on test functions which are commonly used in the literature

general perturbative solution to wave scattering from a soft random cylindrical surface a perturbative solution to the problem of plane wave scattering from a soft randomly rough cylindrical surface is obtained by use of the rayleigh hypothesis and the assumption that coupled radiation modes can be present in the scattered wave the wave amplitudes of the cylindrical wave expansion of the scattered field are expressed as an asymptotic series in the root mean square of surface irregularities the end result of the analysis is a concise recursive formula for the coefficients of that series the solution is energy consistent up to fourth order in the smallness parameter specific information about the validity and applicability of the solution is given by use of the mean boundary condition error which is defined in this paper with a view to assessing the conformity of near field results with the boundary condition the numerical results show that the fourth order approximation is more accurate than the second order one but it may under certain conditions exhibit higher mean boundary condition error

on the benefits of laplace samples in solving a rare event problem using cross entropy method the convergence quality of the cross entropy ce optimizer relies critically on the mechanism meant for randomly generating data samples in agreement with the inference drawn in the earlier works the fast simulated annealing fsa and fast evolutionary programming fep since tracing a near global optimum embedded on a nonconvex search space can be viewed as a rare event problem a ce algorithm constructed using a long tailed distribution is intuitively attractive for effectively exploring the optimization landscape based on this supposition a set of ce algorithms employing the cauchy logistic and laplace distributions are experimentally validated in a wide range of optimization functions which are shifted rotated expanded and or composed characterized by convex unimodal discontinuous noisy and multimodal fitness landscapes the laplace distribution has been demonstrated to be more suitable for the ce optimization since the samples drawn have jump lengths long enough to elude local optima and short enough to preserve sufficient candidates in the global optimum neighborhood besides a theoretical analysis has been carried out to understand the following i benefits offered by the long tailed distributions towards evasion of local optima ii link between the variation in scale parameter estimate and the probability of producing candidate solutions arbitrarily close to the global optimum

real coded genetic algorithm with uniform random local search genetic algorithms are efficient global optimizers but they are weak in performing fine grained local searches in this paper the local search capability of genetic algorithm is improved by hybridizing real coded genetic algorithm with uniform random local search to form a hybrid real coded genetic algorithm termed rcgau the incorporated local technique is applied to all newly created offspring so that each offspring solution is given the opportunity to effectively search its local neighborhood for the best local optimum numerical experiments show that the performance of rcga is remarkably improved by the uniform random local search technique

a real coded genetic algorithm for solving integer and mixed integer optimization problems in this paper a real coded genetic algorithm named mi lxpm is proposed for solving integer and mixed integer constrained optimization problems the proposed algorithm is a suitably modified and extended version of the real coded genetic algorithm lxpm of deep and thakur k deep m thakur a new crossover operator for real coded genetic algorithms applied mathematics and computation 188 2007 895 912 k deep m thakur a new mutation operator for real coded genetic algorithms applied mathematics and computation 193 2007 211 230 the algorithm incorporates a special truncation procedure to handle integer restrictions on decision variables along with a parameter free penalty approach for handling constraints performance of the algorithm is tested on a set of twenty test problems selected from different sources in literature and compared with the performance of an earlier application of genetic algorithm and also with random search based algorithm rst2anu incorporating annealing concept the proposed mi lxpm outperforms both the algorithms in most of the cases which are considered

the convergence of galerkin approximation schemes for second order hyperbolic equations with dissipation in this paper we consider certain semidiscrete and fully discrete galerkin approximations to the solution of an initial boundary value problem for a second order hyperbolic equation with a dissipative term estimates are obtained in the energy and negative norms associated with the problem yielding in particular hland l2 error estimates the approximation to the initial data is taken in this case as the projection with respect to the energy inner product onto the approximating space we also obtain estimates for higher order time derivatives

approximation of the controls for the wave equation with a potential this article deals with the approximation of the boundary controls of a 1 d linear wave equation with a variable potential by using a finite difference space semi discrete scheme due to the high frequency numerical spurious oscillations the semi discrete model is not uniformly controllable with respect to the mesh size and the convergence of the approximate controls cannot be guaranteed in this paper we analyze how do the initial data to be controlled and their discretization affect the approximation of the controls under certain conditions on the potential we prove that the convergence of the scheme is ensured if the highest frequencies of the discrete initial data have been previously filtered out several filtration procedures are proposed and analyzed moreover we identify a class of regular continuous initial data which can be controlled uniformly without any special treatment

a hybrid genetic algorithm with the baldwin effect here we present a new hybrid genetic algorithm hga with the baldwin effect in the hga a local search is employed to change the fitness of individuals but the acquired improvements do not change the individual itself this local search step exploits the baldwin effect some numerical applications show that this algorithm can yield the global optimum more efficiently than commonly used hgas a theorem is presented that guarantees the convergence in probability of the new hga

exponential stabilization of well posed systems by colocated feedback we consider well posed linear systems whose state trajectories satisfy dot x ax bu where u is the input and a is an essentially skew adjoint and dissipative operator on the hilbert space x this means that the domains of a and a are equal and a a q where q geq 0 is bounded on x the control operator b is possibly unbounded but admissible and the observation operator of the system is b such a description fits many wave and beam equations with colocated sensors and actuators and it has been shown for many particular cases that the feedback u ka y v with ka 0 stabilizes the system strongly or even exponentially here y is the output of the system and v is the new input we show by means of a counterexample that if b is sufficiently unbounded then such a feedback may be unsuitable the closed loop semigroup may even grow exponentially our counterexample is a simple regular system with feedthrough operator zero however we prove that if the original system is exactly controllable and observable and if ka is sufficiently small then the closed loop system is exponentially stable

enhancing the performance of differential evolution using orthogonal design method differential evolution de is a simple and efficient global optimization algorithm it has been successfully applied to solve a wide range of real world optimization problems however de has been shown to have certain weaknesses especially if the global optimum should be located using a limited number of function evaluations nfes in this paper we incorporate the orthogonal design method into de to accelerate its convergence rate the orthogonal design method is not only to be used to generate the initial population but also to be applied to design the crossover operator in addition two models of de method are investigated moreover the self adaptive parameter control is employed to avoid tuning the parameters of de experiments have been conducted on 25 problems of diverse complexities and the results indicate that our approach is able to find the optimal or close to optimal solutions in all cases compared with other state of the art evolutionary algorithms eas our approach performs better or at least comparably in terms of the quality and stability of the final solutions

locally distributed control and damping for the conservative systems in this paper we note the equivalence between exact controllability and exponential stabilizability for an abstract conservative system with bounded control this enables us to establish a frequency domain characterization for the exact controllability uniform exponential decay property of second order elastic systems such as the wave equation and the petrovsky equation with locally distributed control damping a piecewise multiplier method for frequency domain is introduced for several classes of pdes on regions which are not necessarily smooth we obtain a sufficient condition for the subregion on which the application of control damping will yield the exact controllability uniform exponential decay property this result provides useful information for designing the location of controllers dampers for distributed systems with a law of conservation

backstepping observers for a class of parabolic pdes in this paper we design exponentially convergent observers for a class of parabolic partial integro differential equations p i des with only boundary sensing available the problem is posed as a problem of designing an invertible coordinate transformation of the observer error system into an exponentially stable target system observer gain output injection function is shown to satisfy a well posed hyperbolic pde that is closely related to the hyperbolic pde governing backstepping control gain for the state feedback problem for several physically relevant problems the observer gains are obtained in closed form the observer gains are then used for an output feedback design in both collocated and anti collocated setting of sensor and actuator the order of the resulting compensator can be substantially lowered without affecting stability explicit solutions of a closed loop system are found in particular cases

a nonstandard approach to a data assimilation problem and tychonov regularization revisited we consider evolution problems such as diffusion convection equations or the linearized navier stokes system or a weak coupling of them which we would like to predict on a time interval t 0 t 0 t but for which on one hand the initial value of the state variable is unknown on the other hand measurements of the solutions are known on a time interval 0 t 0 and for example on a subdomain in the space variable the classical approach in variational data assimilation is to look for the initial value at time 0 and this is known to be an ill posed problem which has to be regularized here we propose to look for the value of the state variable at time t 0 the end time of the measurements and we prove on some basic examples that this is a well posed problem we give a result of exact reconstruction of the value at t 0 which is based on global carleman inequalities and we give an approximation algorithm which uses classical optimal control auxiliary problems using the same mathematical arguments we also show why tychonov regularization for variational data assimilation works in practical situations corresponding to realistic applications