antiferromagnetic potts model in a magnetic field a finite size scaling study abstract the finite size scaling method is used to investigate the phase diagrams of the q state antiferromagnetic potts model in an external magnetic field on a square lattice critical lines where the system undergoes second order phase transitions between ordered and disordered phases are found which are in complete qualitative agreement with known results for q 3 also new unexpected features are found for q 4 where the transition vanishes in the negative field region while in the positive field region as q increases the critical line flattens out with increasing slopes both at the t 0 h h c point where h c is the critical field at zero temperature and at the t 0 h 0 point thermal exponents y t are also calculated for arbitrary q along the critical lines

a potts model with infinitely degenerate ground state a q component potts model with ferromagnetic and antiferromagnetic interactions in the two respective directions of a square lattice is considered an argument is given showing that an order phase can exist in this model even though the ground state is disordered and infinitely degenerate the authors use the migdal kadanoff transformation to obtain a closed form expression for its critical point they also carry out a monte carlo simulation of the model for q 3 the specific heat exhibits a broad maximum which does not sharpen appreciably as the lattice size is increased this suggests that the phase transition if it exists is of an unconventional type

an approximation theory of solutions to operator riccati equations for h infty control as in the finite dimensional case the appropriate state feedback for the infinite dimensional h infty disturbance attenuation problem may be calculated by solving a riccati equation this operator riccati equation can rarely be solved exactly we approximate the original infinite dimensional system by a sequence of finite dimensional systems and consider the corresponding finite dimensional disturbance attenuation problems we make the same assumptions required in approximations for the classical linear quadratic regulator problem and show that the sequence of solutions to the corresponding finite dimensional riccati equations converge strongly to the solution to the infinite dimensional riccati equation furthermore the corresponding finite dimensional feedback operators yield performance arbitrarily close to that obtained with the infinite dimensional solution

pareto optimal sensor locations for structural identification theoretical and computational issues arising in the selection of the optimal sensor configuration for parameter estimation in structural dynamics are addressed the objective is to optimally locate sensors in the structure such that the resulting measured data are most informative for estimating the parameters of a family of mathematical model classes used for structural modeling for a single model class the information entropy is used as the optimality criterion for selecting the best sensor configuration for multiple model classes the problem is formulated as a multi objective optimization problem of finding the pareto optimal sensor configurations that simultaneously minimize appropriately defined information entropy indices a heuristic algorithm is proposed for constructing effective pareto optimal sensor configurations that are superior in terms of computational efficiency and accuracy to the pareto sensor configurations predicted by evolutionary algorithms suitable for solving general multi objective optimisation problems the theoretical developments and the effectiveness of the proposed algorithms are illustrated for a 10 dof chain like spring mass model and a 32 dof truss structure

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

actuator and sensor placement in linear advection pde with building system application abstract we study the problem of actuator and sensor placement in a linear advection partial differential equation pde the problem is motivated by its application to actuator and sensor placement in building systems for the control and detection of a scalar quantity such as temperature and contaminants we propose a gramian based approach to the problem of actuator and sensor placement the special structure of the advection pde is exploited to provide an explicit formula for the controllability and observability gramian in the form of a multiplication operator the explicit formula for the gramian as a function of actuator and sensor location is used to provide test criteria for the suitability of a given sensor and actuator location furthermore the solution obtained using gramian based criteria is interpreted in terms of the flow of the advective vector field in particular the almost everywhere stability property of the advective vector field is shown to play a crucial role in deciding the location of actuators and sensors simulation results are performed to support the main results of this paper

sensor choice for minimum error variance estimation a kalman filter is optimal in that the variance of the error is minimized by the estimator it is shown here in an infinite dimensional context that the solution to an operator riccati equation minimizes the steady state error variance this extends a result previously known for lumped parameter systems to distributed parameter systems it is shown then that minimizing the trace of the riccati operator is a reasonable criterion for choosing sensor locations it is then shown that multiple inaccurate sensors that is those with large noise variance can provide as good an estimate as a single highly accurate but probably more expensive sensor optimal sensor location is then combined with estimator design a framework for calculation of the best sensor locations using approximations is established and sensor location as well as choice is investigated with three examples simulations indicate that the sensor locations do affect the quality of the estimation and that multiple low quality sensors can lead to better estimation than a single high quality sensor

critical behaviour in three state potts antiferromagnets on a bethe lattice abstract a rigorous method recently introduced for the solution of spin models on bethe lattices is used to solve the three state antiferromagnetic potts model in an external field and to find its phase diagram critical lines where the system undergoes first order or second order phase transitions are found which are in complete qualitative agreement with recent results by racz and vicsek also new unexpected ordered phases are found

brief decentralized h controller design a matrix inequality approach using a homotopy method this paper considers a decentralized h control problem for multi channel linear time invariant systems our interest is focused on dynamic output feedback the control problem is reduced to a feasibility problem of a bilinear matrix inequality bmi the objective of this paper is to propose an algorithm for solving the bmi by using the idea of the homotopy method where the controller s coefficient matrices are deformed from full matrices defined by a centralized h controller to block diagonal matrices of specified dimensions which describe a decentralized h controller when a feasible decentralized h control problem is considered it can be expected that there always exists a centralized h controller for which the algorithm converges and presents a desired solution to find such a suitable centralized h controller random search in a parametrized set of h controllers with a proper dimension is suggested the efficiency of the proposed algorithm is demonstrated by an example

assignment of complete structural properties of linear systems via sensor selection for x ax bu the problem of structural assignment via sensor selection is to find an output equation y cx du such that the resulting system a b c d has the pre specified structural properties such as the finite and infinite zero structures as well as the invertibility properties in this paper we establish a set of necessary and sufficient conditions under which a complete set of system structural properties can be assigned and an explicit algorithm for constructing the required matrix pair c d

phase diagrams of the q state potts model on bethe lattices abstract we use a rigorous recently developed method of solution of spin models on bethe lattices cayley trees it allows us to detect all the phases of the ferromagnetic and antiferromagnetic q state potts models in a field fpm and apm respectively the phase diagrams of the fpm are characterized by three critical lines of first order transitions in the apm the ordered phases which appear always for h 0 and under certain conditions for h 0 and or h

the number of runs in a string a run in a string is a nonextendable with the same minimal period periodic segment in a string the set of runs corresponds to the structure of internal periodicities in a string periodicities in strings were extensively studied and are important both in theory and practice combinatorics of words pattern matching computational biology let n be the maximal number of runs in a string of length n it has been shown that n o n the proof was very complicated and the constant coefficient in o n has not been given explicitly we demystify the proof of the linear upper bound for n and propose a new approach to the analysis of runs based on the properties of subperiods the periods of periodic parts of the runs we show that n n and there are at most o 67n runs with periods larger than 87 this supports the conjecture that the number of all runs is smaller than n we also give a completely new proof of the linear bound and discover several new interesting periodicity lemmas

closed form grammians and model reduction for flexible space structures the author derives analytical expressions for the grammians of a model given in modal coordinates for the dynamics of a flexible space structure fss these expressions are then used as the basis for a new algorithm to compute a dominant reduced order model for such a system in an efficient manner the resulting reduced order model is obtained directly rather than by truncating a balanced model of the entire system thus giving rise to significant efficiency gains for the typical fss case where the reduced order model is of very much lower order than the original system

repetitions in sturmian strings in this paper we apply a simple representation of sturmian strings which we call a reduction sequence to three algorithms the first algorithm accepts as input a given finite string x and determines in time whether or not x is sturmian the second algorithm is a modification of the first that in the case that x is sturmian outputs a reduction sequence for a superstring u of x that is a prefix of an infinite sturmian string the third algorithm uses the reduction sequence of u to compute all the repetitions in u in time thus extending a recent result for fibonacci strings the third algorithm is also based on a characterization of the repetitions in a sturmian string that describes them compactly in terms of runs finally for every integer r 4 we show how to construct an infinite sturmian string that contains maximal repetitions of exponents 2 3 r 1 but none of exponent r

on primary and secondary repetitions in words combinatorial properties of maximal repetitions runs in formal words are studied we classify all maximal repetitions in a word as primary and secondary where the set of all primary repetitions determines all the other repetitions in the word essential combinatorial properties of primary repetitions are established

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

the dual iteration for fixed order control this paper proposes a new heuristic algorithm for fixed order control problems using linear matrix inequalities the authors call the algorithm the dual iteration because it is based on the iteration of two design steps state feedback and filtering which are dual to each other extensive numerical experiments show that the algorithm has a decent performance

a spillover phenomenon in the optimal location of actuators in this paper we are interested in finding the optimal location and shape of the actuators in a stabilization problem namely we consider the one dimensional wave equation damped by an internal feedback supported on a subdomain omega of given length the criterion we want to optimize represents the rate of decay of the total energy of the system it theoretically involves all the eigenmodes of the operator from an engineering point of view it seems more realistic to consider only a finite number of modes say the n first ones in that context we are able to prove existence and uniqueness of an optimal domain omega n it is the better possible location for the actuators we characterize this optimal domain and we point out the following strange phenomenon at least for small lengths the optimal domain omega n which is the better one for the n first modes is actually the worse one for the n 1th mode this looks like the well known spillover phenomenon in control theory at last we will give some possible extension and open problems in higher dimension

spatially constrained fuzzy clustering based sensor placement for spatiotemporal fuzzy control system many industrial processes are spatiotemporal dynamic systems a three dimensional fuzzy logic controller 3 d flc has been recently developed to process the inherent capability of spatiotemporal dynamic systems sensor placement which is always crucial to the control of spatiotemporal dynamic systems is also critical to the design of the 3 d flc in this paper a new sensor placement strategy is developed its main feature is to position the sensor by utilizing the main characteristics of spatial distribution the key technique is to use a spatial constrained fuzzy c means algorithm to extract the characteristics of spatial distribution for an easy implementation a systematic sensor placement design scheme in four steps i e data collection dimension reduction data clustering and sensor locating is developed finally control of a catalytic packed bed reactor is taken as an application to demonstrate the effectiveness of the proposed sensor placement scheme

phase diagrams of the blume emery griffiths model real space renormalization group investigation and finite size scaling analysis abstract an approximate real space renormalization group scheme based on the migdal kadanoff recursion relations and the finite size scaling method are used to study the phase diagrams of the two dimensional spin 1 ising model with nearest neighbor interactions both bilinear and biquadratic and with a crystal field interaction contrary to previous studies we clarify the behavior of the model at low temperature including the region j k

h sub infinity control by state feedback and fast algorithms for the computation of optimal h sub infinity norms the suboptimality of some parameter for h sub infinity optimization by dynamic state feedback is characterized in terms of the solvability of riccati inequalities this is done without restricting the finite zero structure of the plant if there are no system zeros on the imaginary axis the h sub infinity problem can be treated in a complete and satisfactory way explicit characterizations optimum to be achieved are provided and a closed formula for the optimal value is derived in terms of the h sub infinity norm of some fixed transfer matrix if the optimum is not attained any sequence of controllers of bounded size which is constructed to approach the infimal norm must necessarily be high gain a globally and quadratically convergent algorithm to compute the optimal value is proposed this algorithm is generalized to the h sub infinity optimization problem by measurement feedback

h optimal actuator location in many control applications there is freedom to place the actuators the actuator location should be chosen to optimize certain performance objectives in this paper h performance with state feedback is considered that is both the controller and the actuator locations are chosen to minimize the effect of disturbances on the output a framework for calculating h optimal actuator locations is developed conditions for well posedness of the h optimal actuator location problem are presented many optimal actuator problems involve systems modelled by partial differential equations and conditions under which approximations yield reliable results are given a derivative free optimization algorithm to calculate h optimal actuator locations is described the results are illustrated using several examples

h control by state feedback an iterative algorithm and characterization of high gain occurrence we present an iterative algorithm to compute the achievable h norm by state feedbak for a standard regular problem and give a characterization when high gain feedback is necessary to approach the optimal value if there is no need for high gain components to approximate the optimal value we can reduce the problem to the computation of the h norm of a certain stable transfer matrix

some results on the number of periodic factors in words abstract the exponent of a word is the relation between its length and its minimal period a repetition subrepetition in a word is a factor of exponent not less than 2 less than 2 a gapped repeat in a word is a pair of identical factors with a positive gap between these factors in the paper a review of some recent results concerning the number of repetitions subrepetitions and gapped repeats in words of fixed length is presented

optimal sensor actuator placement for active vibration control using explicit solution of algebraic riccati equation abstract this paper deals with an optimal placement problem of sensors and actuators for active vibration control of flexible structures for undamped structures with collocated rate sensors and actuators two solutions of generalized algebraic riccati equations generalized control algebraic riccati equation gcare generalized filtering algebraic riccati equation gfare are obtained explicitly employing these explicit solutions we can obtain a stabilizing h controller based on the normalized coprime factorization approach without solving any algebraic riccati equations numerically generally in a optimal sensor actuator placement problem with a model based control law lqg or h the feedback controller needs to be obtained for all candidates of the optimal placement which may be derived with some numerical optimization techniques by solving algebraic riccati equations numerically therefore the amount of computation required to determine the optimal sensor actuator placement and the controller increases rapidly for large scale structures which have many pairs of sensor actuators the h controller in this paper can be obtained just by addition and multiplication of several matrices furthermore a closed loop property on h norm is automatically bounded for all candidates of the optimal placement hence we can formulate the optimal sensor actuator placement problem to optimize other closed loop properties norm of the closed loop system with less computational requirement than the model based method mentioned above the gradient of the h2norm of the closed loop system which is necessary for a descent based optimization technique is derived using this sensitivity formula we obtain the optimal placements of two pairs of sensors and actuators which minimize the h2norm of the closed loop system for a simply supported beam by the quasi newton method the simulation results show the effectiveness of the proposed design method

convex analysis and global optimization of joint actuator location and control problems it is shown that the optimal value of the continuous time linear quadratic problem regarded as a function of the system model and index parameters exhibits properties convexity concavity and monoticity specially suitable for optimization purposes based on this fact a procedure for the global solution determination of eventually nonconvex problems involving the above mentioned function is proposed such problems embody some known designs such as filtering under noise uncertainty or precision constraints and optimal actuator sensor location the last problem is deeply analyzed and two practical applications namely satellite attitude control and large flexible system control are included

linear quadratic optimal actuator location in control of vibrations diffusion and many other problems governed by partial differential equations there is freedom in the choice of actuator location the actuator location should be chosen to optimize performance objectives in this paper we consider linear quadratic performance two types of cost are considered the choice depends on whether the response to the worst initial condition is to be minimized or whether the initial condition is regarded as random in practice approximations are used in controller design and thus in selection of the actuator locations the optimal cost and location of the approximating sequence should converge to the exact optimal cost and location in this work conditions for this convergence are given in the case of linear quadratic control examples are provided to illustrate that convergence may fail when these conditions are not satisfied

operator theoretic framework for optimal placement of sensors and actuators for control of nonequilibrium dynamics abstract in this paper we present a novel operator theoretic framework for optimal placement of actuators and sensors in nonlinear systems the problem is motivated by its application to control of nonequilibrium dynamics in the form of temperature in building systems and control of oil spill in oceanographic flow the controlled evolution of a passive scalar field modeling the temperature distribution or density of oil dispersant is governed by a linear advection partial differential equation pde with spatially located actuators and sensors spatial locations of actuators and sensors are optimized to maximize the controllability and observability regions of the linear advection pde linear transfer perron frobenius and koopman operators associated with the advective velocity field are used to provide an analytical characterization for the controllable and observable spaces of the advection pde set oriented numerical methods are proposed for the finite dimensional approximation of the linear transfer operators the finite dimensional approximation is shown to introduce weaker notion of controllability and observability referred to as coarse controllability and observability the finite dimensional approximation is used to formulate the optimization problem for the optimal placement of sensors and actuators the optimal placement problem is a combinatorial optimization problem however the positivity property of the linear transfer operator is exploited to provide an exact solution to the optimal placement problem using greedy algorithm application of the framework is demonstrated for the placement of sensors in a building system for the detection of contaminants and for optimal release of dispersant location for control of contaminant in a double gyre velocity field simulation results reveal interesting connections between the optimal location of actuators and sensors maximizing the controllability and observability regions respectively and the coherent structures in the fluid flow

balanced actuator and sensor placement for flexible structures properties of flexible structures in modal and balanced coordinates are derived from these properties the root mean square law of the hankel singular values is obtained it says that the squares of the hankel singular values of a set of sensors and actuators is approximately a root mean square sum of the squares of the hankel singular values for each individual sensor and actuator this property allows us to evaluate each actuator and sensor in terms of the joint controllability and observability and to serve as a tool of the actuator and or sensor placement methodology

mechanical structure optimization in minimum time motion control of flexible bodies this paper considers the problem of minimum time motion control of a flexible body for which the dynamic properties can be optimized within a structural design this allows a matching of modal characteristics to a control task such that reductions in time of motion can be achieved compared with unoptimized designs the problem formulation is based on an elastic structure undergoing a motion task with specified boundary conditions and subject to limits on actuation forces a numerical method for calculating minimum time control input solutions based on an iterative construction of the reachable set is first considered a structural optimization approach is further developed based on continuity properties of the solution set these admitting a first order perturbation analysis from which an optimization of system design parameters can be achieved a selection of numerical case studies are presented involving single and multi mode structures possibilities for realization of the approach using variable stiffness deformable structures are discussed and results from a linear motion stage with tunable stiffness flexible armature presented that demonstrate the potential benefits

a characterization of the squares in a fibonacci string a finite fibonacci stringfn is defined as follows f0 b f1 a for every integer n 2 fn fn 1fn 2 for n 1 the length of fn is denoted by the infinite fibonacci stringf is the string which contains every fn n 1 as a prefix apart from their general theoretical importance fibonacci strings are often cited as worst case examples for algorithms which compute all the repetitions or all the abelian squares in a given string in this paper we provide a characterization of all the squares in f hence in every prefix fn this characterization naturally gives rise to a algorithm which specifies all the squares of fn in an appropriate encoding this encoding is made possible by the fact that the squares of fn occur consecutively in runs the number of which is by contrast the known general algorithms for the computation of the repetitions in an arbitrary string require time and produce outputs when applied to a fibonacci string fn

optimal sensor location for detecting changes in dynamical behavior we address the problem of optimal sensor location for monitoring the eigenstructure of a multivariable dynamical system the criterions which are optimized are the power of new tests designed for detecting and diagnosing changes in the eigencharacteristics of a system 3 12 the key points are the choice of the parameterization for computing the criterion and the comparison of designs with a different number of sensors the discussion of the numerical results for sensor location includes the analysis of the effect of the geometry of the unknown excitation

extended h 2 and h norm characterizations and controller parametrizations for discrete time systems this paper presents new synthesis procedures for discrete time linear systems it is based on a recently developed stability condition which contains as particular cases both the celebrated lyapunov theorem for precisely known systems and the quadratic stability condition for systems with uncertain parameters these new synthesis conditions have some nice properties a they can be expressed in terms of lmi linear matrix inequalities and b the optimization variables associated with the controller parameters are independent of the symmetric matrix that defines a quadratic lyapunov function used to test stability this second feature is important for several reasons first structural constraints as those appearing in the decentralized and static output feedback control design can be addressed less conservatively second parameter dependent lyapunov function can be considered with a very positive impact on the design of robust h 2 and h x control problems third the design of controller with mixed

linear output feedback controller design with joint selection of sensors and actuators addresses the problem of locating actuators and sensors for linear continuous time systems in several contexts open loop as well as closed loop problems are discussed both state and output feedback are considered in most cases global optimal solutions are attained by solving mixed boolean semidefinite or linear programs an algorithm which is able to find these global optima is provided a numerical example illustrates the results

space efficient search for maximal repetitions we study here a problem of finding all maximal repetitions in a string of length n we show that the problem can be solved in time o n log n in the presence of constant extra space and general unbounded alphabets subsequently we show that in the model with a constant size alphabet the problem can be solved in time o n with a help of o n extra space previously best known algorithms require linear additional space in both models

integrated design of structural and control systems with a homotopy like iterative method we consider an integrated design problem of structural and control systems it is well known that even the simplest formulation of this problem results in a kind of a bmi problem in this paper homotopy like iterative design method based on lmis is proposed to obtain an optimal plant and a controller simultaneously for a full order output feedback problem we can deal with a multiobjective problem e g control problem etc in the proposed design method we can also optimize structural design parameters appearing non linearly in the coefficient matrices of the plant state space form using the first order approximation of the non linear dependence in the proposed algorithm several design examples show that the proposed algorithm works quite effectively for various integrated design problems

repetitive perhaps but certainly not boring in this paper some of the work done on repetitions in strings is surveyed especially that of an algorithmic nature several open problems are described and conjectures formulated about some of them

critical temperature of an anisotropic two dimensional potts model the phase transition temperature tc of the q state potts model with ferromagnetic interactions jx and antiferromagnetic ones jy in the two respective directions of a 2d lattice is calculated by the high temperature series expansion htse of the appropriate staggered susceptibility as well a by the cluster variate approximation cva for q 3 the htse result in the range of mod jy mod jx or approximately 1 5 shows a good coincidence with the kosterlitz thouless type phase transition temperature calculated on the prescription by ostlund which is given by 1 16 pi exp 2 beta cjx coth beta cjy 2 beta 1 ktc the cva result shows similar behaviour of tc to that of the migdal kadanoff renormalisation group method obtained by kinzel et al but it is considered to be less reliable than the htse result

principal component analysis of flexible systems open loop case a generic class of flexible systems characterized by finitely many lightly damped harmonic oscillators is analyzed by means of the open loop principal component analysis that is singular value analysis and gramian balancing as the main result it is shown that as the damping ratio goes to zero the balanced state coordinates are decoupled and coincide with the modal coordinates further simple formulas expressing the asymptotic singular values as functions of the modal parameters are derived

how many runs can a string contain given a string x x 1 n a repetition of period p in x is a substring u r x i 1 i rp p u r 2 where neither u x i 1 i p nor x i 1 i r 1 p 1 is a repetition the maximum number of repetitions in any string x is well known to be q nlogn a run or maximal periodicity of period p in x is a substring u rt x i 1 i rp t of x where u r is a repetition t a proper prefix of u and no repetition of period p begins at position i of x or ends at position i rp t 1 in 2000 kolpakov and kucherov showed that the maximum number r n of runs in any string x 1 n is o n but their proof was nonconstructive and provided no specific constant of proportionality at the same time they presented experimental data to prompt the conjecture r n

optimal actuator and sensor placement in flexible structures using closed loop criteria abstract a closed loop optimal location selection method for actuators and sensors in flexible structures is developed the introduced technique simultaneously designs a computationally simple h controller and optimizes the location with a gradient based unconstrained minimization the h controller is a modified version of a normalized coprime controller and obtained by solving control and filter algrebraic riccati equations care and fare approximately different types of weights disturbance input performance output sensor noise inputs etc are incorporated to the generalized plant hence the approximate are solutions take into consideration the signal weightings in the system since an iterative gradient search algorithm is used the partial derivatives of the approximate ares with respect to the design parameters are taken developed method is detailed and illustrated by a euler bernoulli beam example

sensor and actuator placement for linear systems based on h_ 2 and h_ infty optimization sensor and actuator placement algorithms are developed for linear discrete time systems based on h 2 and h infty optimization for sensor placement we design an observer that minimizes the h 2 norm of the error dynamics and the number of sensors at the same time for actuator placement we design a state feedback controller that minimizes the h infty norm of the closed loop system and the number of actuators at the same time any other combination of actuator placement for state feedback design or sensor placement for observer design for continuous time or discrete time linear systems based on h 2 or h infty optimization can be derived from these results in both presented cases the number of sensors or actuators is formulated as the ell 0 norm of the observer or controller gain matrix this ell 0 norm is then relaxed to a weighted ell 1 norm in order to obtain an iterative convex optimization problem as an application example we use the sensor placement algorithm to place phase measurement units with maximal impact on the h 2 performance in a power grid

game theory approach for the integrated design of structures and controls the problem of design of actively controlled structures subject to constraints on the damping parameters of the closed loop system is formulated as a multiobjeetive optimization problem the structural weight and the controlled system energy are considered as objective functions for minimization with cross sectional areas of members as design variables a computational procedure is developed for solving the multiobjeetive optimization problem using cooperative game theory the feasibility of the procedure is demonstrated through the design of two truss structures

on nonconvergence of adjoint semigroups for control systems with delays it is shown that the adjoints of a spline based approximation scheme for delay equations do not converge strongly

closed form h infinity optimal control for a class of infinite dimensional systems h infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators diffusion equations are an important example in this class explicit formulas for the optimal state feedback controller as well as the optimal state estimator are given unlike traditional methods for h infinity synthesis no iteration is needed to obtain the optimal solution moreover the optimal performance for both the state feedback and state estimation problems are explicitly calculated this is shown to be useful for problems of h infinity optimal actuator and sensor location furthermore the results can be used in testing and bench marking of general purpose algorithms for h infinity synthesis the results also apply to finite dimensional systems

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

optimal actuator sensor location for active noise regulator and tracking control problems in this paper we investigate the problem of finding the optimal location of sensors and actuators to achieve reduction of the noise field in an acoustic cavity we offer two control strategies the first is based on linear quadratic tracking where the offending noise is tracked and the second considers the formulation of the harmonic control strategy as a periodic static output feedback control problem the first method which is based on full state information is suitable for optimal location of actuators while the second strategy can extend the results to finding optimal location of sensors as well as actuators for both methods we consider the optimization of an appropriate quadratic performance criterion with respect to the location of the actuators and or the sensors numerical examples are presented to compare the effectiveness of each control strategy and also the effect of optimal placement of actuators and sensors

technical communique new dilated lmi characterizations for continuous time multiobjective controller synthesis this paper provides new dilated linear matrix inequality lmi characterizations for continuous time controller synthesis the dilated lmis enable us to parametrize controllers without involving the lyapunov variables in the parametrizations taking advantage of this feature we can readily design multiobjective controllers with non common lyapunov variables whereas we are forced to employ a common one in the well known lyapunov shaping paradigm in particular it is shown that the proposed dilated lmi based approach to h 2 d stability synthesis encompasses the corresponding lyapunov shaping paradigm as a special case in this sense the results of this paper can be viewed as partial counterparts of those obtained in the discrete time setting

disturbance attenuation and h optimization a design method based on the algebraic riccati equation this note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system the problem under consideration involves attenuating the disturbances to a prespecified level the construction of the state feedback control law requires the solution of a certain algebraic riccati equation by applying the procedure with successively smaller values of the prespecifled disturbance level the result also provides an approach to the h infty optimization problem for the state feedback case

computing the positive stabilizing solution to algebraic riccati equations with an indefinite quadratic term via a recursive method an iterative algorithm to solve algebraic riccati equations with an indefinite quadratic term is proposed the global convergence and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given numerical examples are also provided to demonstrate the superior effectiveness of the proposed algorithm when compared with methods based on finding stable invariant subspaces of hamiltonian matrices a game theoretic interpretation of the algorithm is also provided