problems on time varying port controlled hamiltonian systems geometric structure and dissipative realization to apply time varying port controlled hamiltonian pch systems to practical control designs two basic problems should be dealt with one is how to provide such time varying systems a geometric structure to guarantee the completeness of representations in mathematics and the other is how to express the practical system under consideration as a time varying pch system which is called the dissipative hamiltonian realization problem the paper investigates the two basic problems a suitable geometric structure for time varying pch systems is proposed first then the dissipative realization problem of time varying nonlinear systems is investigated and serval new methods and sufficient conditions are presented for the realization

applications of cumulants to array processing iv direction finding in coherent signals case for pt iii see ibid vol 45 no 9 p 2253 64 1997 we present a subspace based direction finding method for coherent signal environments using an antenna array our method which uses fourth order statistics is capable of resolving more signals than a comparable second order statistics based subspace method and is applicable to a larger class of arrays the maximum number of signals resolvable with our method may exceed the number of sensors in the array only a uniform linear subarray is needed the rest of the array may have arbitrary and unknown response and does not require calibration on the other hand the comparable second order statistics based method is limited to uniform linear arrays only no search procedure is needed in our method simulation experiments supporting our conclusions are provided

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

interconnection and damping assignment passivity based control of port controlled hamiltonian systems passivity based control pbc is a well established technique that has shown to be very powerful to design robust controllers for physical systems described by euler lagrange el equations of motion for regulation problems of mechanical systems which can be stabilized shaping only the potential energy pbc preserves the el structure and furthermore assigns a closed loop energy function equal to the difference between the energy of the system and the energy supplied by the controller thus we say that stabilization is achieved via energy balancing unfortunately these nice properties of el pbc are lost when used in other applications which require shaping of the total energy for instance in electrical or electromechanical systems or even some underactuated mechanical devices our main objective in this paper is to develop a new pbc theory which extends to a broader class of systems the aforementioned energy balancing stabilization mechanism and the structure invariance towards this end we depart from the el description of the systems and consider instead port controlled hamiltonian models which result from the network modelling of energy conserving lumped parameter physical systems with independent storage elements and strictly contain the class of el models

stabilization of hamiltonian systems with nonholonomic constraints based on time varying generalized canonical transformations this paper is concerned with the stabilization of nonholonomic systems in port controlled hamiltonian formulae based on time varying generalized canonical transformations a special class of time varying generalized canonical transformations are introduced which modify the kinetic energy of the original system without changing the generalized hamiltonian structure with passivity utilizing these transformations time varying asymptotically stabilizing controllers for the nonholonomic hamiltonian systems are derived since the proposed method is a natural generalization of passivity based control for conventional holonomic systems it is expected that the tools developed for conventional systems will be applicable to nonholonomic systems based on the proposed method

on the 2 decomposition numbers of steinberg s triality groups d43 q q odd abstract we compute the 2 modular decomposition numbers of steinberg s triality groups d 4 3 q where q is a power of an odd prime except for two decomposition numbers in the steinberg character and classify all absolutely irreducible representations of d 4 3 q in non defining characteristic up to a certain degree

on decomposition matrices for graded algebras abstract we study the relations between the decomposition matrix of a module over a graded algebra and the decomposition matrix of its restriction to the grading subalgebra we show that under appropriate hypotheses if one of the decomposition matrices is stable unitriangular then so is the other a particular case is when one of them is square unitriangular then both are using these results we describe the decomposition matrices of the hecke algebras of the complex reflection groups g de e n with respect to the ones of the ariki koike algebras or the decomposition matrices of q schur algebras of type dn with respect to the ones of q schur algebras of type bn

brief paper canonical transformations used to derive robot control laws from a port controlled hamiltonian system perspective this paper addresses the problem of deriving control laws for robot manipulators in the framework of port controlled hamiltonian systems via canonical transformations and passivity based control the control design is focused on the presentation of a new energy shaping methodology for tracking control based on the introduction of virtual non homogeneous fields where a desired energy is defined to compensate for the actual energy of the robot manipulator while a virtual field forces the system to track a general reference trajectory this requires use of the legendre fenchel transformation and allows for the derivation standard control laws in the robotics field such as pd control with gravity compensation or pd with precompensation finally the passivity of the input output mapping of the non autonomous hamiltonian system is analyzed in detail resulting in new lyapunov candidate functions having their roots in physics

iterative learning control of hamiltonian systems i o based optimal control approach in this note a novel iterative learning control scheme for a class of hamiltonian control systems is proposed which is applicable to electromechanical systems the proposed method has the following distinguished features this method does not require either the precise knowledge of the model of the target system or the time derivatives of the output signals despite the lack of information the tracking error monotonously decreases in l sub 2 sense and further perfect tracking is achieved when it is applied to mechanical systems the self adjoint related properties of hamiltonian systems proven in this note play the key role in this learning control those properties are also useful for general optimal control furthermore experiments of a robot manipulator demonstrate the effectiveness of the proposed method

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

on the inductive alperin mckay and alperin weight conjecture for groups with abelian sylow subgroups abstract we study the inductive alperin mckay conjecture the inductive isaacs navarro refinement and the inductive blockwise alperin weight conjecture for groups of lie type in the generic case of abelian sylow l subgroups we also show that the alternating groups the suzuki groups and the ree groups satisfy the inductive condition necessary for spath s reduction of the blockwise alperin weight conjecture to the case of simple groups

quantum weyl reciprocity and tilting modules quantum weyl reciprocity relates the representation theory of hecke algebras of type a with that of q schur algebras this paper establishes that weyl reciprocity holds integrally i e over the ring q q 1 of laurent polynomials and that it behaves well under base change a key ingredient in our approach involves the theory of tilting modules for q schur algebras new results obtained in that direction include an explicit determination of the ringel dual algebra of a q schur algebra in all cases in particular in the most interesting situation the ringel dual identifies with a natural quotient algebra of the hecke algebra

on the decomposition numbers of the finite general linear groups ii let g gl q q a prime power and let r be an odd prime not dividing q let s be a semisimple element of g of order prime to r and assume that r divides qdeg x 1 for all elementary divisors a of s relating representations of certain hecke algebras over symmetric groups with those of g we derive a full classification of all modular irreducible modules in the r block bh of g with semisimple part s the decomposition matrix d of bs may be partly described in terms of the decomposition matrices of the symmetric groups corresponding to the hecke algebras above moreover d is lower unitriangular this applies in particular to all r blocks of g if r divides q 1 thus in this case the r decomposition matrix of g is lower unitriangular introduction the modular representation theory of finite groups of lie type defined over a field of characteristic p is naturally divided into the cases of equal characteristic r p and unequal characteristic r p this paper begins the study of decomposition numbers in the unequal characteristic case of the finite general linear groups when r 2 let g be the full linear group of degree n over gf q and 2 r be a prime not dividing q let s c g be semisimple and consider the geometric conjugacy class s g of irreducible characters corresponding to the g conjugacy class of s using basic properties of the deligne lusztig operators introduced in 7 we will determine a parabolic subgroup p ps of g and a cuspidal irreducible character of x of p such that s g is just the set of constituents of xg the induced character let r r k be an r modular system for g and m a kp module affording x then end kg m is called the hecke algebra of m compare 5 and has been calculated in a more general context by r b howlett and g i lehrer in 12 it turns out that end kg m k w the hecke algebra of w where w wj denotes the weyl group of cg s the centralizer of s in g compare 1 2 4 13 in particular k w has a basis tw iw c w such that the structure constants of the multiplication are all contained in r c k so let r w be the r order in k w generated by wtiw ew and r w r r r w choosing a special rp lattice s in m and using the classification of the r blocks of rg given by p fong and b srinivasan in received by the editors july 25 1983 and in revised form october 18 1983 may 23 1984 and september 1 1984 1980 mathematics subject classification primary 20c20 secondary 20g40 this work was supported by the deutsche forschungsgemeinschaft 1985 american mathematical society 0002 9947 85 1 00 25 per page

a support vector machine music algorithm this paper introduces a new support vector machine svm formulation for the direction of arrival doa estimation problem we establish a theoretical relationship between the minimum variance distortionless response mvdr and the multiple signal characterization music methods this leads naturally to the derivation of an svm music algorithm which combines the benefits of subspace methods with those of svm spatially smoothed versions and a recursive form of the algorithms exhibit good performance against coherent signals we test the method s performance in scenarios with noncoherent and coherent signals and in small sample size situations obtaining an improved performance in comparison with existing standard approaches

relaxing the conditions for parameter estimation based observers of nonlinear systems via signal injection parameter estimation based observers are a new kind of state reconstruction methods where the state observation task is translated into an on line parameter estimation problem a key step for its application is the transformation of the system dynamics into a particular cascade form which involves the solution of a partial differential equation that moreover should satisfy some injective requirement in this note we use a recently proposed technique of signal injection to generate new outputs and simplify these tasks in this way we make this observer applicable to a wider class of nonlinear systems even with indistinguishable states the application of the proposed approach is illustrated with the design of a novel sensorless controller for magnetic levitation systems

doa estimation by exploiting the symmetric configuration of uniform linear array a new direction of arrival doa estimation method is proposed for uniform linear array in this paper when both uncorrelated and coherent sources are present the uncorrelated and coherent sources are estimated at two different stages the uncorrelated sources are first estimated using conventional subspace methods and then they are eliminated by exploiting the symmetric configuration of the array finally the remaining coherent sources are estimated by reconstructing a non toeplitz matrix the number of sources resolved by our method can exceed the number of array elements simulation results demonstrate the effectiveness and efficiency of our proposed method

approximate dissipative hamiltonian realization and construction of local lyapunov functions the key in applying energy based control approach is to be able to express the system under consideration as a dissipative hamiltonian system i e to obtain dissipative hamiltonian realization dhr for the system in general the precise dhr form is hard to obtain for nonlinear dynamic systems when a precise dhr does not exist for a dynamic system or such a precise realization is difficulty to obtain it is necessary to consider its approximate realization this paper investigates approximate dhr and construction of local lyapunov functions for time invariant nonlinear systems it is shown that every nonlinear affine system has an approximate dhr if linearization of the system is controllable based on the diagonal normal form of nonlinear dynamic systems a new algorithm is established for the approximate dhr finally we present the concept of kth degree approximate lyapunov function and provide a method to construct such a lyapunov function example studies show that the methodology presented in this paper is very effective

doa estimation for mixed signals in the presence of mutual coupling in this paper a new direction of arrival doa estimation method is proposed in the presence of unknown mutual coupling the impinging signals are a mixture of signals in different correlation degrees which are uncorrelated partially correlated or coherent with each other the method proceeds in three steps the noncoherent uncorrelated or partially correlated signals are firstly estimated with unknown mutual coupling then these estimates are utilized to get the mutual coupling coefficients finally by eliminating the contributions of the noncoherent signals and compensating the mutual coupling effect only coherent signals remain to be estimated this method is simple but effective and does not need iterative processing simulation results demonstrate the effectiveness and performance of the proposed method

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

forward backward spatial smoothing techniques for coherent signal identification a spatial smoothing scheme is further investigated in the context of coherent signal classification it is shown that by making use of a set of forward and complex conjugated backward subarrays simultaneously it is always possible to estimate any k directions of arrival using at most 3k 2 sensor elements this is achieved by creating a smoothed array output covariance matrix that is structurally identical to a covariance matrix in some noncoherent situation by incorporating eigenstructure based techniques on this smoothed covariance matrix it then becomes possible to correctly identify all directions of arrival irrespective of their correlation

sectional rank and cohomology abstract donovan s conjecture implies a bound on the dimensions of cohomology groups in terms of the size of a sylow p subgroup and we give a proof of a stronger bound in terms of sectional p rank for dim h 1 g v we also prove a reduction theorem for higher cohomology

average sinr calculation of a persymmetric sample matrix inversion beamformer based on the bartlett s decomposition of a wishart random matrix we study the normalized output signal to interference plus noise ratio sinr of a sample matrix inversion smi beamformer with exploiting a priori information on persymmetric structures in the received signal the persymmetric structure exists when a system is equipped with a symmetrically spaced linear array or symmetrically spaced pulse trains in the matched case we obtain an exact expression for the expectation of the normalized output sinr i e average sinr loss of the persymmetric smi beamformer considering the mismatch in the signal steering vector we derive an approximate expression for the average sinr loss of the persymmetric smi beamformer in a non homogeneous environment where the test and training data have different covariance matrices these theoretical results are all verified by using monte carlo techniques simulation results reveal that the exploitation of the persymmetric structure is equivalent to doubling the amount of training data and thus the sinr loss of the persymmetric smi beamformer can be significantly reduced in particular the persymmetric smi beamformer can work in the case of limited training data where the traditional beamformers cannot work

on an intrinsic formulation of time variant port hamiltonian systems in this contribution we present an intrinsic description of time variant port hamiltonian systems as they appear in modeling and control theory this formulation is based on the splitting of the state bundle and the use of appropriate covariant derivatives which guarantees that the structure of the equations is invariant with respect to time variant coordinate transformations in particular we will interpret our covariant system representation in the context of control theoretic problems typical examples are time variant error systems related to trajectory tracking problems which allow for a hamiltonian formulation furthermore we will analyze the concept of collocation and the balancing interaction of power flows in an intrinsic fashion

decomposition matrices for low rank unitary groups we study the decomposition matrices of the unipotent blocks of finite special unitary groups sun q for unitary primes larger than n up to few unknown entries we give a complete solution for n 2 10 we also prove a general result for two column partitions when divides q 1 this is achieved using projective modules coming from the adic cohomology of deligne lusztig varieties

passivity based control of a class of hamiltonian systems with nonholonomic constraints this paper is concerned with state and output feedback stabilization of a class of port hamiltonian systems with nonholonomic constraints first we study canonical forms for port hamiltonian systems with nonholonomic constraints second we give a new state feedback stabilization method by using non smooth hamiltonian functions via generalized canonical transformations third we propose a dynamic output feedback stabilization method without measuring the velocity based on the corresponding state feedback result numerical examples demonstrate the effectiveness of the proposed method

simultaneous stabilization of a set of nonlinear port controlled hamiltonian systems this paper investigates simultaneous stabilization of a set of nonlinear port controlled hamiltonian pch systems and proposes a number of results on the design of simultaneous stabilization controllers for the pch systems firstly the case of two pch systems is studied using the dissipative hamiltonian structural properties the two systems are combined to generate an augmented pch system with which some results on the control design are then obtained for the case that there exist parametric uncertainties in the two systems hamiltonian structures an adaptive simultaneous stabilization controller is proposed when there are external disturbances and parametric uncertainties in the two systems two simultaneous stabilization controllers are designed for the systems one is a robust controller and the other is a robust adaptive one secondly the case of more than two pch systems is investigated and a new result is proposed for the simultaneous stabilization of the systems finally two illustrative examples are studied by using the results proposed in this paper simulations show that the simultaneous stabilization controllers obtained in this paper work very well

performance analysis for finite sample mvdr beamformer with forward backward processing the employment of forward backward fb processing to both batch and adaptive beamformers provides a superior performance than the forward only fo algorithm based on the finite sample minimum variance distortionless response mvdr beamformer a set of closed form expressions for the variance of the weight vector the output signal to interference plus noise ratio sinr and the mean square error mse is derived for both fb and fo algorithms as shown in our analysis all errors of the fb algorithm are only approximately half of the fo case

dynamic extension is unnecessary for stabilization via interconnection and damping assignment passivity based control interconnection and damping assignment passivity based control ida pbc is a technique that regulates the behavior of nonlinear systems assigning a desired port hamiltonian structure to the closed loop this basic idea introduced seven years ago has turned out to be very successful and has provided solutions to a wide variety of physical problems although ida pbc is originally formulated as a static state feedback technique a natural question that arises is whether it is possible to extend the realm of applicability of the method by considering dynamic controllers more precisely is the set of plants that is stabilizable with static state feedback ida pbc smaller than the one stabilizable with dynamic ida pbc the main contribution of this paper is to prove that the answer to this question is unfortunately negative

on the modular composition factors of the steinberg representation abstract let g be a finite group of lie type and st k be the steinberg representation of g defined over a field k we are interested in the case where k has prime characteristic l and st k is reducible tinberg has shown that the socle of st k is always simple we give a new proof of this result in terms of the hecke algebra of g with respect to a borel subgroup and show how to identify the simple socle of st k among the principal series representations of g furthermore we determine the composition length of st k when g gl n q or g is a finite classical group and l is a so called linear prime

exponential stabilization of port hamiltonian boundary control systems via energy shaping this article is concerned with the exponential stabilization of a class of linear boundary control systems bcss in port hamiltonian form through energy shaping starting from a first feedback loop that is in charge of modifying the hamiltonian function of the plant a second control loop that guarantees exponential convergence to the equilibrium is designed in this way a major limitation of standard energy shaping plus damping injection control laws applied to linear port hamiltonian bcss namely the fact that only asymptotic convergence is assured has been removed

on donovan s conjecture abstract this article contains reduction theorems for some weaker variants of donovan s conjecture which supposes that for every finite group d of prime order p there are only finitely many morita equivalence classes of p blocks of finite groups having defect groups isomorphic to d i when restricting the conjecture to the case of abelian defect groups it can be reduced to only considering p blocks of a class of groups that are close to being direct products of simple groups ii when restricting the conjecture to the case of principal blocks of finite groups having an abelian sylow p subgroup it can be reduced to only considering p blocks of simple groups a weaker version of donovan s conjecture would suppose that there are only finitely many cartan matrices of p blocks of finite groups with defect group isomorphic to a given one iii this conjecture can be reduced to only considering p blocks of quasisimple groups with centers having orders prime to p

source association doa and fading coefficients estimation for multipath signals this paper addresses the source association sa direction of arrival doa and fading coefficients fcs estimation problem in multipath environment first we establish a rank reduction property for a multipath signal model with the existence of multiple groups of coherent signals subsequently based on this property effective algorithms for sa doa and fcs estimation have been developed the proposed doa and fcs estimation methods exploit the multipath structure information to achieve improved accuracy the new doa estimation methods work well even in the case that the doas of the multipath signals associated with different sources are nearly overlapped meanwhile the new methods are applicable to arbitrary array geometry while without decreasing the effective array aperture then the stochastic cramer rao bound on doa and fcs estimation of multipath model mcrb exploiting the multipath structure information is derived in closed form numerical simulations have been provided to demonstrate the effectiveness of the proposed methods

two dimensional direction estimation for a mixture of noncoherent and coherent signals this paper deals with the two dimensional 2 d direction of arrival doa estimation of a mixture of noncoherent including uncorrelated and partially correlated and coherent i e fully correlated narrowband signals impinging on a planar sensor array composed of two parallel uniform linear arrays ulas an oblique projection based approach for 2 d direction estimation opade is proposed by using some cross correlations between the received array data in the proposed opade the oblique projection is utilized to isolate the coherent signals from the noncoherent ones and the effect of additive noise is alleviated while the computationally intensive eigendecomposition is avoided and the estimated elevation and azimuth angles are paired automatically further an iterative alternating scheme is presented to improve the estimation accuracy of the oblique projector and hence that of the doas of coherent signals the cramer rao lower bound crb for the mixture of noncoherent and coherent signals is also derived explicitly where the prior knowledge of the signal correlation is incorporated into the 2 d doa estimation of noncoherent signals finally the effectiveness of the opade and the theoretical analysis are substantiated through numerical examples

shaping the energy of mechanical systems without solving partial differential equations control of underactuated mechanical systems via energy shaping is a well established robust design technique unfortunately its application is often stymied by the need to solve partial differential equations pdes in this technical note a new fully constructive procedure to shape the energy for a class of mechanical systems that obviates the solution of pdes is proposed the control law consists of a first stage of partial feedback linearization followed by a simple proportional plus integral controller acting on two new passive outputs the class of systems for which the procedure is applicable is identified imposing some directly verifiable conditions on the systems inertia matrix and its potential energy function it is shown that these conditions are satisfied by three benchmark examples

trajectory tracking control of port controlled hamiltonian systems via generalized canonical transformations this paper addresses trajectory tracking control of port controlled hamiltonian systems via generalized canonical transformations and passivity based control the main strategy adopted in this paper is to construct an error system which describes the dynamics of the tracking error by a passive port controlled hamiltonian system after obtaining the error system tracking control of the original system can be achieved by stabilizing the error system via passivity based approach first a fundamental framework is provided for constructing the error system via generalized canonical transformations then a concrete design procedure is derived for a class of electro mechanical systems furthermore the proposed method is applied to a magnetic levitation system and laboratory experiments demonstrate its effectiveness

repetitive control of hamiltonian systems based on variational symmetry this paper is concerned with repetitive control of hamiltonian systems which is based on iterative learning control utilizing the variational symmetry of those systems variational symmetry allows us to obtain an algorithm to solve a certain class of optimal control problems in a repetitive control framework therefore the proposed method can deal with not only trajectory tracking control problems but also optimal trajectory generation problems never before considered in a repetitive control framework a convergence analysis of this algorithm is also discussed furthermore some numerical simulations demonstrate the effectiveness of the proposed method

bounded stabilisation of stochastic port hamiltonian systems this paper proposes a stochastic bounded stabilisation method for a class of stochastic port hamiltonian systems both full actuated and underactuated mechanical systems in the presence of noise are considered in this class the proposed method gives conditions for the controller gain and design parameters under which the state remains bounded in probability the bounded region and achieving probability are both assignable and a stochastic lyapunov function is explicitly provided based on a hamiltonian structure although many conventional stabilisation methods assume that the noise vanishes at the origin the proposed method is applicable to systems under persistent disturbances

control by interconnection and standard passivity based control of port hamiltonian systems the dynamics of many physical processes can be suitably described by port hamiltonian ph models where the importance of the energy function the interconnection pattern and the dissipation of the system is underscored to regulate the behavior of ph systems it is natural to adopt a passivity based control pbc perspective where the control objectives are achieved shaping the energy function and adding dissipation in this paper we consider the pbc techniques of control by interconnection cbi and standard pbc in cbi the controller is another ph system connected to the plant through a power preserving interconnection to add up their energy functions while in standard pbc energy shaping is achieved via static state feedback in spite of the conceptual appeal of formulating the control problem as the interaction of dynamical systems the current version of cbi imposes a severe restriction on the plant dissipation structure that stymies its practical application on the other hand standard pbc which is usually derived from a uninspiring and non intuitive ldquopassive output generationrdquo viewpoint is one of the most successful controller design techniques the main objectives of this paper are 1 to extend the cbi method to make it more widely applicable in particular to overcome the aforementioned dissipation obstacle 2 to show that various popular variants of standard pbc can be derived proceeding from a unified perspective 3 to establish the connections between cbi and standard pbc proving that the latter is obtained restricting the former to a suitable subset providing a nice geometric interpretation to standard pbc and comparing the size of the set of ph plants for which they are applicable

power based control canonical coordinate transformations integral and adaptive control power based modeling was originally developed in the early sixties to describe a large class of nonlinear electrical rlc networks in a special gradient form recently this idea has been extended for modeling and control of a larger class of physical systems in this paper first coordinate transformations are introduced for systems described in this framework such that the physical structure is preserved such a transformation can provide new insights for both analysis and control design second power based integral and adaptive control schemes are presented advantages of these schemes are shown by their application on standard mechanical systems

robust integral control of port hamiltonian systems the case of non passive outputs with unmatched disturbances regulation of passive outputs of nonlinear systems can be easily achieved with an integral control ic in many applications however the signal of interest is not a passive output and ensuring its regulation remains an open problem also ic of passive systems rejects constant input disturbances but no similar property can be ensured if the disturbance is not matched in this paper we address the aforementioned problems and propose a procedure to design robust ics for port hamiltonian models that characterize the behavior of a large class of physical systems necessary and sufficient conditions for the solvability of the problem in terms of some rank and controllability properties of the linearized system are provided for a class of fully actuated mechanical systems a globally asymptotically stabilizing solution is given simulations of the classical pendulum system illustrate the good performance of the scheme

an equivariant bijection between irreducible brauer characters and weights for sp 2n q abstract the longstanding alperin weight conjecture and its blockwise version have been reduced to simple groups recently by navarro tiep spath and koshitani thus to prove this conjecture it suffices to verify the corresponding inductive condition for all finite simple groups the first is to establish an equivariant bijection between irreducible brauer characters and weights for the universal covering groups of simple groups assume q is a power of some odd prime p we first prove the blockwise alperin weight conjecture for sp 2 n q and odd non defining characteristics if the decomposition matrix of sp 2 n q is unitriangular with respect to an aut sp 2 n q stable basic set this assumption holds for linear primes we can establish an equivariant bijection between the irreducible brauer characters and weights

the weighted fusion category algebra and the q schur algebra for gl 2 q abstract we show that the weighted fusion category algebra of the principal 2 block b 0 of gl 2 q is the quotient of the q schur algebra s 2 q by its socle for q an odd prime power as a consequence we get a canonical bijection between the set of isomorphism classes of simple k gl 2 q b 0 modules and the set of conjugacy classes of b 0 weights in this case

estimation of fading coefficients in the presence of multipath propagation in order to get the information about multipath propagation this communication presents two estimation methods for slowly varying fading coefficients with known numbers of the far field sources and multipaths from each far field source the fading coefficients in multipath propagation can be well estimated the methods not only have low complexity but also have high performance and the fading coefficients can be resolved directly without a searching procedure afterwards we make an extension to further improve the estimation accuracy of both direction of arrival doa and fading coefficients after obtaining their estimations the cramer rao bound crb for this problem is also deduced simulation results demonstrate the effectiveness and efficiency of the proposed methods

total energy shaping control of mechanical systems simplifying the matching equations via coordinate changes total energy shaping is a controller design methodology that achieves asymptotic stabilization of mechanical systems endowing the closed loop system with a lagrangian or hamiltonian structure with a desired energy function that qualifies as lyapunov function for the desired equilibrium the success of the method relies on the possibility of solving two pdes which identify the kinetic and potential energy functions that can be assigned to the closed loop particularly troublesome is the partial differential equation pde associated to the kinetic energy which is nonlinear and inhomogeneous and the solution that defines the desired inertia matrix must be positive definite in this note we prove that we can eliminate or simplify the forcing term in this pde by modifying the target dynamics and introducing a change of coordinates in the original system furthermore it is shown that in the particular case of transformation to the lagrangian coordinates the possibility of simplifying the pdes is determined by the interaction between the coriolis and centrifugal forces and the actuation structure the examples of pendulum on a cart and furuta s pendulum are used to illustrate the results

equivariance and extendibility in finite reductive groups with connected center we show that several character correspondences for finite reductive groups g are equivariant with respect to group automorphisms under the additional assumption that the linear algebraic group associated to g has connected center the correspondences we consider are the so called jordan decomposition of characters introduced by lusztig and the generalized harish chandra theory of unipotent characters due to broue malle michel in addition we consider a correspondence giving character extensions due to the second author in order to verify the inductive mckay condition from isaacs malle navarro for the non abelian finite simple groups of lie types 3 mathsf d 4 mathsf e 8 mathsf f 4 2 mathsf f 4 and mathsf g 2

structure preserving adaptive control of port hamiltonian systems in this technical note an adaptive control scheme is presented for general port hamiltonian systems adaptive control is used to compensate for control errors that are caused by unknown or uncertain parameter values of a system the adaptive control is also combined with canonical transformation theory for port hamiltonian systems this allows for the adaptive control to be applied on a large class of systems and for being included in the port hamiltonian framework

asymptotic stabilization via control by interconnection of port hamiltonian systems we study the asymptotic properties of control by interconnection a passivity based controller design methodology for stabilization of port hamiltonian systems it is well known that the method in its basic form imposes some unnatural controller initialization to yield asymptotic stability of the desired equilibrium we propose two different ways to overcome this restriction one based on adaptation ideas and the other one adding an extra damping injection to the controller the analysis and design principles are illustrated through an academic example

stabilization of oscillations through backstepping in high dimensional systems this note introduces a method for obtaining stable and robust self sustained oscillations in a class of single input nonlinear systems of dimension n spl ges 2 the oscillations are associated to a limit cycle that is produced in a second order subsystem by means of an appropriate feedback law then the controller is extended to the full system by a backstepping procedure it is shown that the closed loop system turns out to be generalized hamiltonian and that the limit cycle can be thought as born in a hopf bifurcation after moving a parameter

canonical transformation and stabilization of generalized hamiltonian systems abstract this paper introduces generalized canonical transformations for generalized hamiltonian systems which convert a generalized hamiltonian system into another one and preserve the generalized hamiltonian structure of the original as in classical mechanics it is expected that canonical transformations will provide new insights and fundamental tools for both analysis and synthesis of those systems firstly the class of generalized canonical transformations and some of their properties are indicated secondly it is shown how to stabilize the generalized hamiltonian systems using canonical transformations in addition some examples illustrate how such transformations are utilized for control systems design

brief generalized hamiltonian realization of time invariant nonlinear systems a key step in applying the hamiltonian function method is to express the system under consideration into a generalized hamiltonian system with dissipation which yields the so called generalized hamiltonian realization ghr in this paper we investigate the problem of ghr several new methods and the corresponding sufficient conditions are presented a major result is that if the jacobian matrix of a time invariant nonlinear system is nonsingular the system has a ghr whose structure matrix and hamiltonian function are given in simple forms then the orthogonal decomposition method and a sufficient condition for the feedback dissipative realization are proposed

sensor array processing based on subspace fitting algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem the methods considered are the deterministic maximum likelihood method ml esprit and a recently proposed multidimensional signal subspace method these methods are formulated in a subspace fitting based framework which provides insight into their algebraic and asymptotic relations it is shown that by introducing a specific weighting matrix the multidimensional signal subspace method can achieve the same asymptotic properties as the ml method the asymptotic distribution of the estimation error is derived for a general subspace weighting and the weighting that provides minimum variance estimates is identified the resulting optimal technique is termed the weighted subspace fitting wsf method numerical examples indicate that the asymptotic variance of the wsf estimates coincides with the cramer rao bound the performance improvement compared to the other techniques is found to be most prominent for highly correlated signals

on the matching equations of energy shaping controllers for mechanical systems total energy shaping is a controller design methodology that achieves asymptotic stabilisation of mechanical systems endowing the closed loop system with a lagrangian or hamiltonian structure with a desired energy function the success of the method relies on the possibility of solving two partial differential equations pdes which identify the kinetic and potential energy functions that can be assigned to the closed loop particularly troublesome is the pde associated to the kinetic energy ke which is quasi linear and non homogeneous and the solution that defines the desired inertia matrix must be positive definite this task is simplified by the inclusion of gyroscopic forces in the target dynamics which translates into the presence of a free skew symmetric matrix in the ke matching equation that reduces the number of pdes to be solved recently it has been claimed that considering a more general form for the target dynamic forces that relax the skew symmetry condition further reduces the number

modular irreducibility of cuspidal unipotent characters we prove a long standing conjecture of geck which predicts that cuspidal unipotent characters remain irreducible after ell reduction to this end we construct a progenerator for the category of representations of a finite reductive group coming from generalised gelfand graev representations this is achieved by showing that cuspidal representations appear in the head of generalised gelfand graev representations attached to cuspidal unipotent classes as defined and studied in geck and malle j lond math soc 2 53 63 78 1996

on feedback equivalence to port controlled hamiltonian systems in the last few years port controlled hamiltonian pch systems have emerged as an interesting class of nonlinear models suitable for a large number of physical applications in this paper we study the question of feedback equivalence of nonlinear systems to pch systems more precisely we give conditions under which a general nonlinear system can be transformed into a pch system via static state feedback we consider the two extreme cases where the target pch system is completely a priori fixed or completely free as well as the case where it is only partially predetermined when the energy function is free a set of partial differential equations needs to be solved on the other hand if it is fixed we have to deal with a set of algebraic equations in the former case we give some verifiable necessary and sufficient conditions for solvability as a by product of our analysis we obtain some stabilization results for nonlinear systems

transient stabilization of multimachine power systems with nontrivial transfer conductances we provide a solution to the long standing problem of transient stabilization of multimachine power systems with nonnegligible transfer conductances more specifically we consider the full 3n dimensional model of the n generator system with lossy transmission lines and loads and prove the existence of a nonlinear static state feedback law for the generator excitation field that ensures asymptotic stability of the operating point with a well defined estimate of the domain of attraction provided by a bona fide lyapunov function to design the control law we apply the recently introduced interconnection and damping assignment passivity based control methodology that endows the closed loop system with a port controlled hamiltonian structure with desired total energy function the latter consists of terms akin to kinetic and potential energies thus has a clear physical interpretation our derivations underscore the deleterious effects of resistive elements which as is well known hamper the assignment of simple gradient energy functions and compel us to include nonstandard cross terms a key step in the construction is the modification of the energy transfer between the electrical and the mechanical parts of the system which is obtained via the introduction of state modulated interconnections that play the role of multipliers in classical passivity theory

maximum likelihood methods for direction of arrival estimation five methods of direction of arrival doa estimation which can be derived from the maximum likelihood ml principle are considered the ml method mlm results from the application of the ml principle to the statistics of the observed raw data the standard multiple signal classification music procedure called music 1 is obtained as a brute force approximation of the mlm an improved music procedure named music 2 is obtained by applying the ml principle to the statistics of certain linear combinations of the sample noise space eigenvectors a procedure which compromises between the good performance of the mlm and the computational simplicity of music is a method of direction estimation mode 1 which is derived as a large sample realization of the mlm a fifth method called mode 2 is obtained by using the ml principle on the statistics of certain linear combinations of the sample eigenvectors mode 2 is computationally less demanding than the mlm it is of the same complexity as mode 1 and statistically more efficient a numerical comparison of these five doa estimation methods is presented it confirms the analytic results on their theoretical performance levels

on the inductive blockwise alperin weight condition for classical groups abstract recently there has been substantial progress on the alperin weight conjecture as a step to establish the alperin weight conjecture for all finite groups we prove the inductive blockwise alperin weight condition for simple groups of classical type under some additional assumption

control via interconnection and damping assignment of linear time invariant systems a tutorial interconnection and damping assignment is a controller design methodology that regulates the behaviour of dynamical systems assigning a desired port hamiltonian structure to the closed loop a key step for the application of the method is the solution of the so called matching equation that in the case of nonlinear systems is a partial differential equation it has recently been shown that for linear systems the problem boils down to the solution of a linear matrix inequality that moreover is feasible if and only if the system is stabilisable making the method universally applicable it has also been shown that if we narrow the class of assignable structures e g to mechanical instead of the larger port hamiltonian the problem is still translated to a linear matrix inequality but now stabilisability is not sufficient to ensure its feasibility it is additionally required that the uncontrolled modes are simple and lie on the j axis which is consistent with the considered scenario of mechanical

scopes reduction and morita equivalence classes of blocks in finite classical groups ii abstract we extend our work of j algebra 230 2000 378 423 on unipotent blocks of classical groups to blocks of orthogonal groups containing characters labelled by degenerate symbols we also show that for classical groups in the linear prime case there are only finitely many morita types of unipotent blocks with a given defect group