saari s homographic conjecture of the three body problem saari s homographic conjecture which extends a classical statement proposed by donald saari in 1970 claims that solutions of the newtonian n body problem with constant configurational measure are homographic in other words if the mutual distances satisfy a certain relationship the configuration of the particle system may change size and position but not shape we prove this conjecture for large sets of initial conditions in three body problems given by homogeneous potentials including the newtonian one some of our results are true for n 3

design of fuzzy control systems with guaranteed stability abstract this paper addresses the analysis and design of fuzzy control systems the fuzzy systems are represented by a family of local state space models with aggregation the controller is designed by considering each local state feedback controller and a compensating controller the compensating controller is based on the well known variable structure control theory it is shown that this controller guarantees global stability of the closed loop fuzzy system the issues of a state observer for the fuzzy system is also addressed a numerical example and an example of nonlinear system control are given for demonstration of the performance of the method

robust stabilization of nonlinear multiple time delay large scale systems via decentralized fuzzy control to overcome the effect of modeling errors between nonlinear multiple time delay subsystems and takagi sugeno t s fuzzy models with multiple time delays a robustness design of fuzzy control is proposed in this work in terms of lyapunov s direct method a delay dependent stability criterion is hence derived to guarantee the asymptotic stability of nonlinear multiple time delay large scale systems based on this criterion and the decentralized control scheme a set of model based fuzzy controllers is then synthesized via the technique of parallel distributed compensation pdc to stabilize the nonlinear multiple time delay large scale system finally a numerical example with simulations is given to demonstrate the concepts discussed throughout this work

criteria for asymptotic stability of linear time delay systems several sufficient conditions which guarantee stability of linear time delay systems are derived each of these results is expressed by a succinct scalar inequality and corresponds to a certain extent to the tradeoff between simplicity and sharpness

polygonal homographic orbits of the curved n body problem in the 2 dimensional n body problem n 3 in spaces of constant curvature 6 0 we study polygonal homographic solutions we first provide necessary and sufficient conditions for the existence of these orbits and then consider the case of regular polygons we further use this criterion to show that for any n 3 the regular ngon is a polygonal homographic orbit if and only if all masses are equal then we prove the existence of relative equilibria of non equal masses on the sphere of curvature 0 for n 3 in the case of scalene triangles such triangular relative equilibria occur only along fixed geodesics and are generated from fixed points of the sphere finally through a classification of the isosceles case we prove that not any three masses can form a triangular relative equilibrium

sparse antenna array optimization with the cross entropy method the interest in sparse antenna arrays is growing mainly due to cost concerns array size limitations etc formally it can be shown that their design can be expressed as a constrained multidimensional nonlinear optimization problem generally through lack of convex property such a multiextrema problem is very tricky to solve by usual deterministic optimization methods in this article a recent stochastic approach called cross entropy method is applied to the continuous constrained design problem the method is able to construct a random sequence of solutions which converges probabilistically to the optimal or the near optimal solution roughly speaking it performs adaptive changes to probability density functions according to the kullback leibler cross entropy the approach efficiency is illustrated in the design of a sparse antenna array with various requirements

fuzzy control design for the trajectory tracking on uncertain nonlinear systems based on the concept of sliding mode control smc the paper designs fuzzy logic controls to achieve the prespecified trajectory tracking for an uncertain nonlinear system the prespecified trajectory is composed of several nonisoclinal segments in the phase plane and is regarded as the piecewise sliding surface first let the uncertain system be approximated by a linguistic fuzzy rule base then two fuzzy logic controllers are designed to achieve the hitting motion and preserve the system s state traveling on the prespecified trajectory the main advantage of this control design is that the trial and error of the conventional fuzzy control design disappears a practical example is given to illustrate the applicability of the algorithm

phase space structure and regularization of manev type problems phase space structure and regularization of manev type problems florin diacu a vasile mioc b cristina stoica c a department of mathematics and statistics university of victoria victoria canada v8w 3p4 b astronomical institute of the romanian academy astronomical observatory cluj napoca str cire silor 19 3400 cluj napoca romania c institute for gravitation and space sciences laboratory for gravitation str mendeleev 21 25 bucharest romania

delay dependent decentralized h_ infty filtering for discrete time nonlinear interconnected systems with time varying delay based on the t s fuzzy model this paper is concerned with the problem of delay dependent h filter design for a class of discrete time nonlinear interconnected system with time varying delays via the takagi sugeno t s fuzzy model the t s fuzzy model consists of n time delay t s fuzzy subsystems and a decentralized h filter is designed for each subsystem based on the delay dependent piecewise lyapunov krasovskii functional ddplkf and with an improved free weighting matrix technique the delay dependent stability and a prescribed h performance index are guaranteed for the overall filtering error system a sufficient condition for the existence of such a filter is established by using linear matrix inequalities lmis that are numerically feasible two numerical examples are given to demonstrate the effectiveness and advantage of the proposed approach

adaptive fuzzy identification and control for a class of nonlinear pure feedback mimo systems with unknown dead zones the adaptive fuzzy identification and control problems are considered for a class of multi input multi output nonlinear systems with unknown functions and unknown dead zone inputs the main characteristics of the considered systems are that 1 they are composed of n subsystems and each subsystem is in nested lower triangular form 2 dead zone inputs are in nonsymmetric nonlinear form and 3 dead zone inputs appear nonlinearly in the systems and their parameters are not required to be known the controller design for this class of systems is a difficult and complicated task because of the existences of unknown functions the couplings among the nested subsystems and the dead zone inputs in the controller design the fuzzy logic systems are employed to approximate the unknown functions and the differential mean value theorem is used to separate dead zone inputs to compensate for dead zone inputs the compensative terms are designed in the controllers the stability of the closed loop system is proved via the lyapunov stability theorem a simulation example is provided to validate the feasibility of the approach

the flow of the n body problem near a simultaneous binary collision singularity and integrals of motion on the collision manifold we study the flow for the n body problem near a simultaneous binarycollision singularity we blow up the singularity to an invariant collision manifold we show the existence of integrals of motion on the collision manifold we integrate the flow on the collision manifold explicitly in terms of elementary functions we give a complete description of the flow near the singularity

saari s conjecture for the collinear n body problem in 1970 don saari conjectured that the only solutions of the newtonian n body problem that have constant moment of inertia are the relative equilibria we prove this conjecture in the collinear case for any potential that involves only the mutual distances furthermore in the case of homogeneous potentials we show that the only collinear and non zero angular momentum solutions are homographic motions with central configurations

star pentagon and many stable choreographic solutions of the newtonian 4 body problem abstract in this paper we give a rigorous proof of the existence of infinitely many simple choreographic solutions in the classical newtonian 4 body problem these orbits are discovered by a variational method with structural prescribed boundary conditions spbc this method provides an initial path that is obtained by minimizing the lagrangian action functional over the spbc we prove that the initial path can be extended to a periodic or quasi periodic solution with computer assistance a family of choreographic orbits of this type is shown to be linearly stable among the many linearly stable simple choreographic orbits the most extraordinary one is the stable star pentagon choreographic solution we also prove the existence of infinitely many double choreographic periodic solutions infinitely many non choreographic periodic solutions and uncountably many quasi periodic solutions each type of periodic solutions has many stable solutions and possibly infinitely many stable solutions our results with spbc largely complement the current results by minimizing the action on a loop space

constrained least squares optimization in conformal array antenna synthesis the least mean square error of the constrained least squares optimization method is studied the phases of non zero goal values and the phases of non zero constraint values can be selected by a fast iteration for optimum fit to the goal function amplitude this kind of modified least squares optimization method opens up a fast and robust synthesis method for large conformal antenna arrays constraints can be written also for the element excitation amplitudes and a phase synthesis with predefined amplitudes can be done iterative weight correction technique is used for accurate sidelobe control synthesis examples of two dimensional elliptical and large three dimensional conformal antenna arrays are presented

on the c8 3 regularisation of simultaneous binary collisions in the collinear 4 body problem abstract a conjecture on the nature of the simultaneous binary collision is explored in the collinear 4 body problem it is known that any attempt to remove the singularity via block regularisation will result in a regularised flow that is no more than c 8 3 differentiable with respect to initial conditions through a blow up of the singularity this loss of differentiability is investigated and a new proof of the c 8 3 regularity is provided in the process it is revealed that the collision manifold consists of two manifolds of normally hyperbolic saddle singularities which are connected by a manifold of heteroclinics by utilising recent work on transitions near such objects and their normal forms an asymptotic series of the transition past the singularity is explicitly computed it becomes remarkably apparent that the finite differentiability at 8 3 is due to the inability to construct a set of integrals local to the simultaneous binary collision the finite differentiability is shown to be independent of the value of the masses

an index theory for asymptotic motions under singular potentials abstract we develop an index theory for parabolic and collision solutions to the classical n body problem and we prove sufficient conditions for the finiteness of the spectral index valid in a large class of trajectories ending with a total collapse or expanding with vanishing limiting velocities both problems suffer from a lack of compactness and can be brought in a similar form of a lagrangian system on the half time line by a regularising change of coordinates which preserve the lagrangian structure we then introduce a maslov type index which is suitable to capture the asymptotic nature of these trajectories as half clinic orbits by taking into account the underlying hamiltonian structure we define the appropriate notion of geometric index for this class of solutions and we develop the relative index theory

robust h sub spl infin disturbance attenuation for a class of uncertain discrete time fuzzy systems the paper is concerned with robust stabilization and h sub spl infin control of a class of uncertain discrete time fuzzy systems the class of uncertain systems is described by state space takagi sugeno ts fuzzy models with linear nominal parts and norm bounded parameter uncertainties in the state and output equations first a sufficient condition on robust stability of the fuzzy models is proposed then h sub spl infin disturbance attenuation performance of the fuzzy models is analyzed some sufficient conditions are derived on robust h sub spl infin disturbance attenuation in which both robust stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainties a numerical example shows the use of the results on the stabilization and h sub spl infin disturbance attenuation of a class of discrete time nonlinear systems via fuzzy switch

adaptive fuzzy control via observer design for uncertain nonlinear systems with unmodeled dynamics in this paper the problems of stability and tracking control for a class of large scale nonlinear systems with unmodeled dynamics are addressed by designing the decentralized adaptive fuzzy output feedback approach because the dynamic surface control technique is introduced the designed controllers can avoid the issue of explosion of complexity which comes from the traditional backstepping design procedure that deals with large scale nonlinear systems with unmodeled dynamics in addition a reduced order observer is designed to estimate those immeasurable states based on the lyapunov stability method it is proven that all the signals in the closed loop system are bounded and the system outputs track the reference signals to a small neighborhood of the origin by choosing the design parameters appropriately the simulation examples are given to verify the effectiveness of the proposed techniques

a joint optimization approach for the synthesis of large 4 d heterogeneous antenna arrays due to the inherent nonlinearity in the synthesis of large four dimensional 4 d heterogeneous arrays conventional pattern synthesis techniques are no longer suitable in this paper an effective joint optimization approach based on the combination of convex programming cp and differential evolution de algorithm is proposed by designing suitable time sequences of a 4 d heterogeneous array with uniform static amplitude excitations the original synthesis problem is simplified into two independent small problems which can be easily solved in two steps respectively in the first step the approach takes definite advantages from the convexity of the problem with respect to the static phase excitations and the switch on duration times these optimization variables become known and are fixed in the second step then the de algorithm is used to optimize the switch on time instants owing to the efficiency of the cp only 2 3 of the optimization variables need be solved in the first step while even fewer number of optimization variables are solved in the second step consequently the joint optimization of cp and de algorithm significantly improves the overall synthesis efficiency two numerical examples are presented to demonstrate the effectiveness of the proposed approach

homoclinic orbits and oscillation for the planar three body problem sitnikov proved the existence of oscillation and capture for a special motion of the restricted three body problem m 0 141 alekseev made a systematic study of this situation 11 he also proved the same result for all nonzero masses see section 5 below for a discussion of this case a good exposition of this example following lectures of conley is contained in 9 using the stable manifold result for a degenerately hyperbolic closed orbit of mcgehee 81 easton and mcgehee proposed a planar three body example with negative energy which could possibly exhibit similar oscillation and capture 3 while sitnikov s example has two degrees of freedom this planar example after all the integrals and symmetries are removed has three degrees of freedom they studied a model example which completely decouples when the third body is near infinity and proved oscillation and capture exist for this model example their work left the following three steps undone 1 show the parabolic orbits form a submanifold for the real equations 2 show the a parabolic orbits and w parabolic orbits are transverse in a strong sense see the definition of a hyperbolic homoclinic orbit defined below and 3 show that symbolic dynamics can be used to show oscillation and capture exist using only the fact that the binary asymptotically decouples and not that it completely decouples when the third body is near infinity for negative energy h as the third particle goes to infinity parabolically the asymptotic motion of q r2 rl is that of a two body problem with energy h after regularization the set of all two body motions with energy h 0 is the hopf flow on the three sphere s3 let ivs s3 resp wu s be the set of w parabolic orbits resp w parabolic orbits easton has now shown that ws s3 and wl s3 are lipschitz manifolds 2 this paper proves they are real analytic manifolds and cm at infinity at s

a fuzzy approach for robust reference tracking control design of nonlinear distributed parameter time delayed systems and its application this paper addresses the robust reference tracking control problem for nonlinear distributed parameter systems ndpss with time delays external disturbances and measurement noises the ndps is measured at several sensor locations for output feedback tracking control a fuzzy spatial state space model derived via finite difference approach is introduced to represent the nonlinear distributed parameter time delayed system thus we use a fuzzy interpolation method with several local linear systems to approximate the nonlinear system and employ the finite difference method to approximate the partial differential operators in fuzzy spatial state space model based on this model a robust fuzzy observer based reference tracking controller is proposed to control the ndps to track a desired reference trajectory first a 2 d tracking performance in a spatiotemporal domain is proposed for robust tracking design of nonlinear distributed parameter time delayed systems then an equivalent 1 d reference tracking design is developed to simplify the design procedure and the linear matrix inequality lmi technique is applied to solve the control gains and observer gains for the robust tracking design problem via a systematic control design procedure finally a tracking control design example for the nervous system is given to confirm the proposed reference tracking control scheme of nonlinear distributed parameter time delayed systems

h spl infin decentralized fuzzy model reference tracking control design for nonlinear interconnected systems in general due to the interactions among subsystems it is difficult to design an h sub spl infin decentralized controller for nonlinear interconnected systems the model reference tracking control problem of nonlinear interconnected systems is studied via h sub spl infin decentralized fuzzy control method first the nonlinear interconnected system is represented by an equivalent takagi sugeno type fuzzy model a state feedback decentralized fuzzy control scheme is developed to override the external disturbances such that the h spl infin model reference tracking performance is achieved furthermore the stability of the nonlinear interconnected systems is also guaranteed if states are not all available a decentralized fuzzy observer is proposed to estimate the states of each subsystem for decentralized control consequently a fuzzy observer based state feedback decentralized fuzzy controller is proposed to solve the h sub spl infin tracking control design problem for nonlinear interconnected systems the problem of h sub spl infin decentralized fuzzy tracking control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem evp the evp can be solved very efficiently using convex optimization techniques finally simulation examples are given to illustrate the tracking performance of the proposed methods

triple collision in the quasi homogeneous collinear three body problem abstract we generalize and improve the result of f diacu j differential equations 128 1996 58 77 concerning the dynamics of three points particles moving on the line under the influence of a quasihomogeneous potential w u v where u and v are homogeneous functions of degree a and b respectively for b 2 we found a set of positive measure of collision orbits that do not tend to form asymptotically a central configuration

central configurations and homographic solutions for the quasihomogeneous n body problem for the n body problem given by quasihomogeneous force functions of the form c1 ra c2 rb c1 c2 real and 0 a b we prove that the simultaneous and extraneous central configurations are the only types of central configurations then we focus on attractive attractive force functions c1 and c2 positive and analyze the connection between central configurations and homographic solutions namely we extend the classical lagrange s theorem a solution is homographicif and only if the bodies form equivalent central configurations for all times to attractive attractive quasihomogeneous problems and give sufficient conditions for the construction of homographic solutions

on the anisotropic manev problem we consider the manev potential given by the sum between the inverse and the inverse square of the distance in an anisotropic space i e such that the force acts differently in each direction using mcgehee coordinates we blow up the collision singularity paste a collision manifold to the phase space study the flow on and near the collision manifold and find a positive measure set of collision orbits besides frontal homothetic frontal nonhomothetic and spiraling collisions and ejections we put into the evidence the surprising class of oscillatory collision and ejection orbits using the infinity manifold we further tackle capture and escape solutions in the zero energy case by finding the connection orbits between equilibria and or cycles at impact and at infinity we describe a large class of capture collision and ejection escape solutions

central configurations and total collisions for quasihomogeneous n body problems abstract we consider n body problems given by potentials of the form r a r b with a b constants 0 a b to analyze the dynamics of the problem we first prove some properties related to central configurations including a generalization of moulton s theorem then we obtain several qualitative properties for collision and near collision orbits in the manev type case a 1 at the end we point out some new relationships between central configurations relative equilibria and homothetic solutions

a continuum of periodic solutions to the planar four body problem with two pairs of equal masses abstract in this paper we apply the variational method with structural prescribed boundary conditions spbc to prove the existence of periodic and quasi periodic solutions for the planar four body problem with two pairs of equal masses m 1 m 3 and m 2 m 4 a path q t on 0 t satisfies the spbc if the boundaries q 0 a and q t b where a and b are two structural configuration spaces in r 2 4 and they depend on a rotation angle 0 2 and the mass ratio m 2 m 1 r we show that there is a region 0 2 r such that there exists at least one local minimizer of the lagrangian action functional on the path space satisfying the spbc q t h 1 0 t r 2 4 q 0 a q t b for any the corresponding minimizing path of the minimizer can be extended to a non homographic periodic solution if is commensurable with or a quasi periodic solution if is not commensurable with in the variational method with the spbc we only impose constraints on the boundary and we do not impose any symmetry constraint on solutions instead we prove that our solutions that are extended from the initial minimizing paths possess certain symmetries the periodic solutions can be further classified as simple choreographic solutions double choreographic solutions and non choreographic solutions among the many stable simple choreographic orbits the most extraordinary one is the stable star pentagon choreographic solution when 4 5 1 remarkably the unequal mass variants of the stable star pentagon are just as stable as the equal mass choreographies

multiobjective tracking control design of t s fuzzy systems in this study a multiobjective fuzzy control design method is introduced for nonlinear dynamic systems to guarantee the optimal h 2 and h reference tracking performance simultaneously first the takagi and sugeno t s fuzzy model is used to represent the nonlinear dynamic system then based on the t s fuzzy model multiobjective h 2 h tracking control design problem is formulated as a multiobjective problem mop to minimize the h 2 tracking error and h disturbance attenuation level for the fuzzy system at the same time since it is not easy to solve this mop directly an indirect method is proposed for the multiobjective h 2 h tracking control design finally in order to achieve the simultaneous optimization of the mop linear matrix inequality lmi based multiobjective evolution algorithm lmi based moea is developed based on non dominating sorting scheme to efficiently search the set of pareto optimal solutions for the mop from which designer can select one design according to his own preference further the multiobjective h 2 h fuzzy control design problem based on the weighted sum method is also solved as an alternative choice finally a simulation example of a robotic system is given to illustrate the design procedure and to confirm the robust and optimal tracking performance of the proposed method

output feedback robust h sup spl infin control of uncertain fuzzy dynamic systems with time varying delay this paper presents an output feedback robust h sup spl infin control problem for a class of uncertain fuzzy dynamic systems with time varying delayed state the takagi sugeno fuzzy model is employed to represent an uncertain nonlinear systems with time varying delayed state using a single quadratic lyapunov function the globally exponential stability and disturbance attenuation of the closed loop fuzzy control system are discussed sufficient conditions for the existence of robust h sup spl infin controllers are given in terms of matrix inequalities constructive algorithm for design of robust h sup spl infin controller is also developed the resulting controller is nonlinear and automatically tuned based on fuzzy operation

comet and hill type periodic orbits in restricted n 1 body problems abstract we consider the planar restricted n 1 body problem where the interaction potential between the particle and the primaries is taken to be a finite sum of terms of the form distance with 0 the primaries are assumed to be in a relative equilibrium that is they form a uniformly rotating rigid configuration we show two results first if the infinitesimal particle is far from the primaries and the long range dominant term r of the potential is such that 0 and 2 then there exist two one parameter families of large nearly circular periodic solutions these solutions called comet solutions are elliptic and kam stable for 2 and unstable for 2 second if the infinitesimal particle is close to one of the primaries and the short range dominant term r of the potential near that primary is such that 0 and 2 then there exist two one parameter families of nearly circular periodic solutions called hill solutions that encircle the nearby primary for 2 these orbits are unstable the methodology applied involves appropriate symplectic scalings poincare s continuation method and averaging theory the kam stability of the comet periodic orbits is decided by verifying arnol d s non degeneracy conditions

on the singularities of the curved n body problem we study singularities of the n body problem in spaces of constant curvature and generalize certain results due to painleve weierstrass and sundman for positive curvature some of our proofs use the correspondence between total collision solutions of the original system and their orthogonal projection a property that offers a new method of approaching the problem in this par ticular case

h_ infty fuzzy control synthesis for a large scale system with a reduced number of lmis this paper introduces an h infty fuzzy control synthesis method for a nonlinear large scale system with a reduced number of linear matrix inequalities lmis it is well known that a nonlinear large scale system can be transformed to a takagi sugeno t s fuzzy system by using sector nonlinearity or local approximation in fuzzy partition spaces methods next in order to achieve the fuzzy control design for this t s fuzzy system we solve the stabilization conditions that are represented by the lmis however if the number of lmis is large the control design process may become very complicated in this study based on the lyapunov method and s procedure several theorems are proposed for the synthesis of parallel distributed compensation pdc type fuzzy control such that the nonlinear large scale system achieves h infty control performance and the number of lmis to be solved is reduced explicitly as a result the control design process will become much easier furthermore if the modeling error between the nonlinear system and t s fuzzy system exists the robust h infty control performance and the number reduction of lmis are also achieved by the proposed theorem several examples are presented in this paper to show the number reduction effect of lmis and the effectiveness of the proposed controller synthesis

robust filter for nonlinear stochastic partial differential systems in sensor signal processing fuzzy approach this study addresses a robust h filter design problem for nonlinear stochastic partial differential systems nspdss with random external disturbance and measurement noise in the spatiotemporal domain for nspdss a robust h filter design through a set of sensor measurements needs to solve a complex second order hamilton jacobi integral inequality hjii in order to simplify the design procedure a fuzzy stochastic partial differential system based on a fuzzy interpolation approach is proposed to approximate the nspds then a fuzzy stochastic spatial state space model is developed to represent the fuzzy stochastic partial differential system via the semidiscretization finite difference scheme and the kronecker product based on this model a robust h filter design is proposed to achieve the robust state estimation via solving linear matrix inequalities lmis instead of a second order hjii the proposed robust fuzzy h filter efficiently attenuates the effect of spatiotemporal external disturbances and measurement noise on the state estimation of nspdss from the area energy point of view finally a robust h state estimation example of heat transfer system is given to illustrate the design procedure and to confirm the h filtering performance of the proposed robust filter design method

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

decentralized adaptive output feedback control for a class of nonlinear large scale systems with unknown time varying delayed interactions in this paper the authors investigate a decentralized adaptive output feedback controller design for large scale nonlinear systems with input saturations and time delayed interconnections unmatched in control inputs the interaction terms with unknown time varying delays are bounded by unknown nonlinear bounding functions including all states of subsystems this point is a main contribution of this paper compared with previous output feedback control approaches which assume that the time delayed bounding functions only depend on measurable output variables the bounding functions are compensated by using appropriate lyapunov krasovskii functionals and the function approximation technique based on neural networks the observer dynamic surface design technique is employed to design the proposed memoryless local controller for each subsystem in addition we prove that all signals in the closed loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin finally an example is provided to illustrate the effectiveness of the proposed control system

homographic solutions of the curved 3 body problem abstract in the 2 dimensional curved 3 body problem we prove the existence of lagrangian and eulerian homographic orbits and provide their complete classification in the case of equal masses we also show that the only non homothetic hyperbolic eulerian solutions are the hyperbolic eulerian relative equilibria a result that proves their instability

decentralized sampled data h fuzzy filter for nonlinear large scale systems this paper presents a decentralized sampled data h fuzzy filter design method for nonlinear large scale systems which are represented by a takagi sugeno t s fuzzy model based on the t s fuzzy model the error system between the nonlinear large scale system and the filter is obtained the discretization process of the error system is accomplished with the exact discrete time approach to eliminate the exact approximate mismatch by using the discrete time lyapunov sense the sufficient condition of the asymptotic stability for the error system is given and a prescribed level of the h norm is ensured to guarantee the h fuzzy filter performance finally numerical examples are given to show the effectiveness of the proposed methods

delay dependent robust and reliable h fuzzy hyperbolic decentralized control for uncertain nonlinear interconnected systems this paper develops the delay dependent robust and reliable h fuzzy hyperbolic control for nonlinear large scale interconnected systems with parameter uncertainties firstly the modeling method of fuzzy hyperbolic model fhm is given for the general large scale interconnected systems the main advantages of using fhm over t s fuzzy model are that neither premise structure identification nor completeness design of premise variables space is needed therefore the required computational effort is less than that of using t s fuzzy model especially when a lot of fuzzy rules are needed to model complex nonlinear systems then according to the lyapunov direct method and the decentralized control theory of large scale interconnected systems linear matrix inequality lmi based conditions with some free weighting matrices are derived which guarantee the closed loop interconnected systems to be robustly stable with the h performance even in the presence of some possible actuator failures moreover precise failure parameters of actuators are not required and the only requirements are the lower and upper bounds of failure parameters the restriction that the derivative of the time varying delay is smaller than one is removed therefore the results obtained are less conservative three simulation examples are provided to show the effectiveness of the proposed approach

analysis and design of fuzzy controller and fuzzy observer this paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the takagi sugeno t s fuzzy model the main contribution of the paper is the development of the separation property that is the fuzzy controller and the fuzzy observer can be independently designed a numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

robust stability analysis and fuzzy scheduling control for nonlinear systems subject to actuator saturation takagi sugeno ts fuzzy models can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output submodels in this paper the ts fuzzy modeling approach is utilized to carry out the stability analysis and control design for nonlinear systems with actuator saturation the ts fuzzy representation of a nonlinear system subject to actuator saturation is presented in our ts fuzzy representation the modeling error is also captured by norm bounded uncertainties a set invariance condition for the system in the ts fuzzy representation is first established based on this set invariance condition the problem of estimating the domain of attraction of a ts fuzzy system under a constant state feedback law is formulated and solved as a linear matrix inequality lmi optimization problem by viewing the state feedback gain as an extra free parameter in the lmi optimization problem we arrive at a method for designing state feedback gain that maximizes the domain of attraction a fuzzy scheduling control design method is also introduced to further enlarge the domain of attraction an inverted pendulum is used to show the effectiveness of the proposed fuzzy controller

fast iterative method of power synthesis for antenna arrays a fast and simple method of power synthesis for antenna arrays of arbitrary geometry is presented the method adopts an auxiliary function having the desired amplitude pattern and a generic phase pattern and determines in closed form the array pattern approximating the auxiliary function in both amplitude and phase a cost function involving the auxiliary function and the approximating pattern is minimized by modifying the phase pattern of the auxiliary function using a simple and fast iterative technique once the optimal phase pattern has been found the array pattern approximating the corresponding auxiliary function is the synthesized pattern the proposed method allows to satisfy stringent requirements on the amplitude pattern including multibeam synthesis and radiation suppression within large angular regions numerical results show the effectiveness of the algorithm and are compared to those obtained using other existing methods in order to achieve a more significant comparison such methods have been properly modified to improve their performances such comparison shows that the presented algorithm allows a significant reduction of cpu time with respect to the other considered methods as well as a weaker dependence on the starting point finally the presented method is extended in such a way as to reduce the dynamic range ratio drr of the array excitations

decentralized h fuzzy filter for nonlinear large scale sampled data systems with uncertain interconnections abstract this paper proposes a decentralized h fuzzy filter technique for nonlinear large scale interconnected systems that are based on the takagi sugeno fuzzy model the large scale system has unknown interconnection terms that are assumed to satisfy the quadratic bounds an error system between the nonlinear large scale system and the decentralized filter is constructed by using the fuzzy lyapunov technique sufficient conditions are proposed for both showing asymptotic stability and guaranteeing h fuzzy filter performance these sufficient conditions are derived in terms of linear matrix inequalities finally simulation examples are given to demonstrate the effectiveness of the proposed technique

a novel approach to h_ bm infty decentralized fuzzy observer based fuzzy control design for nonlinear interconnected systems in general due to the interactions among subsystems it is difficult to design an h infin decentralized output feedback controller for nonlinear interconnected systems this study introduces h infin decentralized fuzzy observer based fuzzy control design where the premise variables depend on the state variables estimated by a fuzzy observer for nonlinear interconnected systems via t s fuzzy models the fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables depend on the state variables only a novel decoupled method is proposed in this study to transform the non linear matrix inequality non lmi conditions into some lmi forms by the proposed decoupled method the problem of h infin decentralized fuzzy observer based fuzzy control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem evp with five prespecified scalars for each subsystem in general it is a difficult task to solve the evp with five prespecified scalars fortunately this special evp can be easily solved by using a genetic algorithm and an lmi based optimization method finally a simulation example is given to illustrate the design procedure and robust performance of the proposed methods

central configurations with many small masses abstract by using the method of analytical continuation we find the exact numbers of central configurations for some open sets of n positive masses for any choice of n it turns out that the numbers increase dramatically as n increases e g for some open set of 18 positive masses some 2 08766 1020 classes of distinctive central configurations are found in the mean time we obtained some results about the hausdorff measure for the set of n positive masses where degenerate central configuration arises

polygonal rotopulsators of the curved n body problem we revisit polygonal positive elliptic rotopulsator solutions and polygonal negative elliptic rotopulsator solutions of the n body problem in h3 and s3 and prove the existence of these solutions and prove that the masses of these rotopulsators have to be equal if the rotopulsators are of nonconstant size and show that the number of negative elliptic relative equilibria of this type is finite as is the number of positive elliptic relative equilibria if an upper bound on the size of the relative equilibrium is imposed additionally we prove that a class of negative hyperbolic rotopulsators is in fact a subclass of the class of polygonal negative elliptic rotopulsators

robust optimal reference tracking design method for stochastic synthetic biology systems t s fuzzy approach at present the development in the nascent field of synthetic gene networks is still difficult most newly created gene networks are nonfunctioning due to intrinsic parameter fluctuations uncertain interactions with unknown molecules and external disturbances of intra and extracellular environments on the host cell how to design a completely new gene network that is to track some desired behaviors under these intrinsic and extrinsic disturbances on the host cell is the most important topic in synthetic biology in this study the intrinsic parameter fluctuations uncertain interactions with unknown molecules and environmental disturbances are modeled into the nonlinear stochastic systems of synthetic gene networks in vivo four design specifications are introduced to guarantee the stochastic synthetic gene network which can achieve robust optimal tracking of a desired reference model in spite of these intrinsic and extrinsic disturbances on the host cell however the robust optimal reference tracking design problem of nonlinear synthetic gene networks is still hard to solve in order to simplify the design procedure of the robust optimal nonlinear stochastic tracking design for synthetic gene networks the takagi sugeno t s fuzzy method is introduced to solve the nonlinear stochastic minimum error tracking design problem hence the robust optimal reference tracking design problem under four design specifications can be solved by the linear matrix inequality lmi constrained optimization method using convex optimization techniques further a simple design procedure is developed for synthetic gene networks to meet the four design specifications to achieve robust optimal reference tracking finally an eigenvalue shifted design method is also proposed as an expedient scheme to improve the stochastic optimal tracking design method of synthetic gene oscillators

lagrange pizzetti theorem for the quasihomogeneous n body problem we consider the n body problem given by quasihomogeneous force functions of the form c1 r a c2 r b c1 c2 a b positive constants and a b and address the fundamentals of homographic solutions generalizing techniques of the classical n body problem we prove that if the homographic solution is not flat then it is homothetic if the homographic solution is flat then it is planar using them we prove an analogue of the lagrange pizzetti theorem for quasihomogeneous potentials

the global flow of the manev problem the manev problem a two body problem given by a potential of the form a r b r2 where r is the distance between particles and a b are positive constants comprises several important physical models having its roots in research done by isaac newton we provide its analytic solution then completely describe its global flow using mcgehee coordinates and topological methods and offer the physical interpretation of all solutions we prove that if the energy constant is negative the orbits are generically precessional ellipses except for a zero measure set of initial data for which they are ellipses for zero energy the orbits are precessional parabolas and for positive energy they are precessional hyperbolas in all these cases the set of initial data leading to collisions has positive measure

finiteness of polygonal relative equilibria for generalised quasi homogeneous n body problems and n body problems in spaces of constant curvature we prove for generalisations of quasi homogeneous n body problems with centre of mass zero and n body problems in spaces of negative constant gaussian curvature that if the masses and rotation are fixed there exists for every order of the masses at most one equivalence class of relative equilibria for which the point masses lie on a circle as well as that there exists for every order of the masses at most one equivalence class of relative equilibria for which all but one of the point masses lie on a circle and rotate around the remaining point mass the method of proof is a generalised version of a proof by j m cors g r hall and g e roberts on the uniqueness of co circular central configurations for power law potentials

fuzzy model based control of complex plants in the field of fuzzy modeling the takagi sugeno fuzzy model has been used to approximate accurately the dynamics of complex plants the paper addresses two control design problems associated with state space realizations of such fuzzy models first we treat the stability robustness of fuzzy model based controllers against modeling uncertainty second we develop observer based control schemes and further investigate the behavior of estimated state feedback in both cases we provide sufficient conditions that guarantee stability of the closed loop the results are demonstrated on the fuzzy model of a gas furnace process

robustness design of nonlinear dynamic systems via fuzzy linear control this study introduces a fuzzy linear control design method for nonlinear systems with optimal h sup spl infin robustness performance first the takagi and sugeno fuzzy linear model 1985 is employed to approximate a nonlinear system next based on the fuzzy linear model a fuzzy controller is developed to stabilize the nonlinear system and at the same time the effect of external disturbance on control performance is attenuated to a minimum level thus based on the fuzzy linear model h sup spl infin performance design can be achieved in nonlinear control systems in the proposed fuzzy linear control method the fuzzy linear model provides rough control to approximate the nonlinear control system while the h sup spl infin scheme provides precise control to achieve the optimal robustness performance linear matrix inequality lmi techniques are employed to solve this robust fuzzy control problem in the case that state variables are unavailable a fuzzy observer based h sup spl infin control is also proposed to achieve a robust optimization design for nonlinear systems a simulation example is given to illustrate the performance of the proposed design method

parabolic orbits in the planar three body problem it is not known whether there exist oscillatory and capture orbits in the planar 3 body problem sitnikov 6 proved such orbits exist for the restricted 3 body problem alekseev i extended this work and related it to the existence of homoclinic orbits mcgehee and easton 3 studied a model problem closely related to the planar 3 body problem and proved the existence of oscillatory and capture orbits near certain orbits biasymptotic to an invariant 3 sphere the goal of this paper is to construct an invariant 3 sphere at infinity in the planar 3 body problem and to prove that the stable and unstable manifolds of this sphere are lipschitz manifolds to complete the study of oscillatory and capture orbits one must investigate the way in which the stable and unstable manifolds of the 3 sphere intersect each other this is a difficult question which is not treated here however using methods of melnikov and using one of the masses as a perturbation parameter such an investigation might be possible the stable manifold theorem which is proven here is not standard since the invariant 3 sphere is not hyperbolic geometric methods of mcgehee 4 are extended and applied to obtain the theorem a special case of the system of equations that we study has the form j x dy lx e x y l f 4 dy l x e x y l 0 1 4

n body spatial parabolic orbits asymptotic to collinear central configurations an orbit for the newtonian n body problem is called parabolic when all the mutual distances between particles approach infinity while the velocities tend to zero as time t goes to infinity the asymptotic growth rate for these mutual distances turns out to be constant multiples of t raised to the 2 3 power or to the power 2 p 1 for the inverse p central force law 1 p 3 111 indeed when the position vectors are scaled by dividing by t213 or by the square root of the moment of inertia then the scaled position vectors tend to the set of central configurations a central configuration is formed whenever for all the particles a fixed constant multiple of the mass times the position vector is equal to the corresponding force vector it turns out that central configurations can be identified with the critical point set of a certain function then the configurations are classified as being either degenerate or nondegenerate to correspond with the classification of the critical point of this function should the central configuration be nondegenerate as is known to be the case for collinear central configurations the equilateral triangle configuration for the three body problem and the equilateral tetrahedron configuration for the four body problem then the limiting configuration of a given motion must be unique for a discussion of central configurations see 15 chap 5 8 121 this uniqueness follows by combining two facts first the nondegeneracy implies that the orbit of the central configuration by the w 3 action must be isolated in the set of all central configurations the so 3 action on configuration space is rotation about the center of mass of the system secondly there can be no rotation of the limiting configuration in the sense of motion along the so 3 action on configuration space see 71 for the planar three body problem and 13 for the general case the lack of

near collision dynamics for particle systems with quasihomogeneous potentials abstract we study collision and ejection orbits of 3 particle systems having the potential w u v where u and v are homogeneous functions of degree a and b respectively with 1 a b we show that for b 2 collision and ejection orbits tend to form asymptotically a central configuration for the case b 2 which corresponds to maneff s gravitational law we find a set of collision and ejection orbits reaching the triple collision manifold without asymptotic phase this set contains an uncountable union of manifolds and has positive measure within the set of all rectilinear solutions

a profit maximizing solid transportation model under a rough interval approach this study attempts to establish an innovative solid transportation problem that intends to maximize profit under the rough interval approximation methodology two transportation problems were constructed in this regard with interval coefficients corresponding to the upper approximations and the lower approximations of the rough intervals under study furthermore from the contingent solid transportation problems four different classical solid transportation problems were derived which were subsequently solved on the lingo iteration platform the concepts of completely satisfactory solution and rather satisfactory solution surely optimal range possibly optimal range and rough optimal range have been discussed with a perspective to its relevance to real world practical problems the rough chance constrained programming and the expected value operator for rough interval have been applied to solve the problem under study the distinct advantages of the proposed method over those existing have been outlined numerical examples have also been provided to illustrate the solution procedure and the methodologies adopted

phase synthesis of conformal array antennas a new phase synthesis method for planar and conformal arrays is presented the method is based on approximate linearized equations for small phase changes in the excitations which can be determined by the least squares method and used iteratively to obtain the final solutions for the excitation phases several different kinds of contoured beams can be used in the same array by using only phase shifters in the elements as demonstrated in the calculated synthesis examples

sparsening conformal arrays through a versatile bcs based method sparsening conformal arrangements is carried out through a versatile multi task bayesian compressive sensing mt bcs strategy the problem formulated in a probabilistic fashion as a pattern matching synthesis is that of determining the sparsest excitation set locations and weights fitting a reference pattern subject to user defined geometrical constraints results from a set of representative numerical experiments are presented to illustrate the key features of the proposed approach as well as to assess also through comparisons its potentials in terms of matching accuracy element saving and computational costs

on the noise enhancing ability of stochastic hodgkin huxley neuron systems recently noise has been shown to be useful in enhancing neuron sensitivity by stochastic resonance in this study in order to measure the noise enhancing factor nef a nonlinear stochastic model is introduced for the hodgkin huxley hh neuron system with synaptic noise input stimulation and channel noises in the sodium and potassium channels the enhancing factor of the hh neuron system is measured from the point of view of the noise exploiting level of nonlinear stochastic h signal processing since the nonlinear stochastic enhancing measure problem of hh neuron systems requires a solution for the difficulty presented by the hamilton jacobi inequality hji a fuzzy interpolation of locally linearized systems is employed to simplify the nonlinear noise enhancing problems by solving only a set of linear matrix inequalities the nef of the hh neuron system is found to be related to the locations of eigenvalues of linearized hh neuron systems and can be estimated through the h signal processing method based on a stochastic fuzzy linearized hh neuron system we found that channel noises are enhanced by the active eigenvalues of ionic channels while synaptic noises are attenuated by the passive eigenvalues of synaptic process

analysis and synthesis of nonlinear time delay systems via fuzzy control approach takagi sugeno ts fuzzy models 1985 1992 can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output i o submodels in this paper the ts fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete time nonlinear systems with time delay the ts fuzzy models with time delay are presented and the stability conditions are derived using lyapunov krasovskii approach we also present a stabilization approach for nonlinear time delay systems through fuzzy state feedback and fuzzy observer based controller sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities an illustrative example based on the cstr model is given to design a fuzzy controller

on the stability of tetrahedral relative equilibria in the positively curved 4 body problem abstract we consider the motion of point masses given by a natural extension of newtonian gravitation to spaces of constant positive curvature in which the gravitational attraction between the bodies acts along geodesics we aim to explore the spectral stability of tetrahedral orbits of the corresponding 4 body problem in the 2 dimensional case a situation that can be reduced to studying the motion of the bodies on the unit sphere we first perform some extensive and highly precise numerical experiments to find the likely regions of stability and instability relative to the values of the masses and to the latitude of the position of the three equal masses then we support the numerical evidence with rigorous analytic proofs in the vicinity of some limit cases in which certain masses are either very large or negligible or the latitude is close to zero

the existence of oscillatory and superhyperbolic motion in newtonian systems we establish the existence of solutions for the collinear newtonian four body problem where the maximum spacing between particles exceeds any given function of time as t as an example there exist solutions where the maximum spacing separates faster than any constant multiple of time also it is shown that the three and four body problems admit oscillatory solutions

formation of symmetric structures in the dynamics of repelling particles we consider hamiltonian systems corresponding to the motions of a system of n repelling particles evolving in space under the action deriving from a very long range potential energy the asymptotic behavior of the system is analysed for the cases u ln r and only special asymptotic shapes are reached which may present quite interesting symmetries and correspond to the critical points of a gradient system the relationships between the original hamiltonian and the asymptotic gradient system are discussed

existence of a lower bound for the distance between point masses of relative equilibria for generalised quasi homogeneous n body problems and the curved n body problem we prove that if for relative equilibrium solutions of a generalisation of quasi homogeneous n body problems the masses and rotation are given then the minimum distance between the point masses of such a relative equilibrium has a universal lower bound that is not equal to zero we furthermore prove that the set of such relative equilibria is compact and prove related results for n body problems in spaces of constant gaussian curvature

the existence of noncollision singularities in newtonian systems in this paper we solve a long standing problem in celestial mechanics proposed by painleve and poincare in the last century the problem which concerns the nature of the singularities in the n body problem asks whether there exists a noncollision singularity in the newtonian n body problem here we give an affirmative answer to this problem by proving the existence of noncollision singularities in the 5 body problem we consider n point masses moving in a euclidean space w3 let the mass of the ith particle be mi 0 let its position be qj e r3 and let 4i e 3 be its velocity according to newton s law

an intrinsic approach in the curved n body problem the negative curvature case abstract we consider the motion of n point particles of positive masses that interact gravitationally on the 2 dimensional hyperbolic sphere which has negative constant gaussian curvature using the stereographic projection we derive the equations of motion of this curved n body problem in the poincare disk where we study the elliptic relative equilibria then we obtain the equations of motion in the poincare upper half plane in order to analyze the hyperbolic and parabolic relative equilibria using techniques of riemannian geometry we characterize each of the above classes of periodic orbits for n 2 and n 3 we recover some previously known results and find new qualitative results about relative equilibria that were not apparent in an extrinsic setting

development of a systematic methodology of fuzzy logic modeling this paper proposes a systematic methodology of fuzzy logic modeling for complex system modeling it has a unified parameterized reasoning formulation an improved fuzzy clustering algorithm and an efficient strategy of selecting significant system inputs and their membership functions the reasoning mechanism introduces 4 parameters whose variation provides a continuous range of inference operation as a result we are no longer restricted to standard extremes in any step of reasoning the fuzzy model itself can then adjust the reasoning process by optimizing the inference parameters based on input output data the fuzzy rules are generated through fuzzy c means fcm clustering major bottlenecks are addressed and analytical solutions are suggested we also address the classification process to extend the derived fuzzy partition to the entire output space in order to select suitable input variables among a finite number of candidates unlike traditional approaches we suggest a new strategy through which dominant input parameters are assigned in one step and no iteration process is required furthermore a clustering technique called fuzzy fine clustering is introduced to assign the input membership functions in order to evaluate the proposed methodology two examples a nonlinear function and a gas furnace dynamic procedure are investigated in detail the significant improvement of the model is concluded compared to other fuzzy modeling approaches

stability in a rhomboidal 5 body problem with generalized central forces we consider a system of five mass points r1 r2 r3 and r4 with masses m1 m2 m and m3 m4 m moving about a single massive body r0 with mass m0 at its center which is assumed to be the origin of the coordinates system we assume that the central body r0 makes a generalized force on the four mass points and that such a force is generated by a manev s type potential i e characterized by a potential of the form 1r er2 on the other hand is assumed that the attraction between the bodies r1 r2 r3 and r4 is of the newtonian type this model represents several cases for instance when the central body is a spheroid or a radiating source first we prove the existence of three different relative rhomboidal solutions and its central configuration is as follows 1 the rhombus is a square and all primaries have equal masses 2 the rhombus is not a square but all masses are equal and 3 the rhombus is not a square and the pairs of primaries have different masses the first two cases present two pa

on the manifolds of total collapse orbits and of completely parabolic orbits for the n body problem abstract in this paper we show for most choices of masses in the coplanar n body problem and for certain masses in the three dimensional n body problem that the set of initial conditions leading to complete collapse forms a smooth submanifold in phase space where the dimension depends upon properties of the limiting configuration a similar statement holds for completely parabolic motion by a proper scaling these two motions become dual to each other in the sense that one forms the unstable set while the other forms the stable set of a particular set of points in the new phase space most of the paper is devoted to solving the painleve wintner problem which asserts that these types of orbits cannot enter in an infinite spin

bifurcations of the lagrangian orbits from the classical to the curved 3 body problem we consider the 3 body problem of celestial mechanics in euclidean elliptic and hyperbolic spaces and study how the lagrangian equilateral relative equilibria bifurcate when the gaussian curvature varies we thus prove the existence of new classes of orbits in particular we find some families of isosceles triangles which occur in elliptic space

pattern synthesis of conformal array antenna in the presence of platform using differential evolution algorithm a synthesis method based on differential evolution algorithm is proposed for conformal antenna arrays in the presence of platform with the desired phase weights determined by the scan angle and array geometry the amplitude weights of elements are optimized by differential evolution algorithm to drive down the side lobes both the effect of platform on radiation pattern of conformal array and the mutual coupling between the elements are taken into account by calculating the antenna array and platform simultaneously using the method of moment application of adaptive integral method reduces the storage and computation time needed by the method of moments

simple stability criteria for single and composite linear systems with time delays easy ways to test the stability of systems involving time delays have been sought in this paper several stability conditions with an extremely simple form are provided first some criteria for single linear systems with time delays are presented then these results are extended to the composite linear systems with time delays which exist in each subsystem and in the interconnections between subsystems among these criteria those which are expressed by scalar inequalities also permit us to assess the transient behaviour of systems

adaptive fuzzy control for a class of nonlinear discrete time systems with backlash an adaptive fuzzy controller design is studied for uncertain nonlinear systems in this paper the considered systems are of the discrete time form in a triangular structure and include the backlash and the external disturbance by using the prediction function of future states the systems are transformed into an n step ahead predictor the fuzzy logic systems flss are used to approximate the unknown functions unknown backlash and backlash inversion respectively a discrete time tuning algorithm is developed to estimate the optimal fuzzy parameters compared with the previous works for the discrete time systems with backlash the main contributions of the paper are that 1 the rigorous restriction for the functional estimation error is removed and 2 the external disturbance is bounded but the bound is not required to be known a novel controller and the adaptation laws are constructed by using the discrete taylor series expansion and the difference lyapunov analysis and thus those limitations in the previous works are overcome it is proven that all the signals in the closed loop system are bounded and that the system output can be to follow the reference signal to a bounded compact set a simulation example is provided to illustrate the effectiveness of the proposed approach

pattern synthesis for arbitrary arrays using an adaptive array method this paper presents a new pattern synthesis algorithm for arbitrary arrays based on adaptive array theory with this algorithm the designer can efficiently control both mainlobe shaping and sidelobe levels the element weights optimize a weighted l sub 2 norm between desired and achieved patterns the values of the weighting function in the l sub 2 norm interpreted as imaginary jammers as in olen and compton s 1990 method are iterated to minimize exceedance of the desired sidelobe levels and minimize the absolute difference between desired and achieved mainlobe patterns the sidelobe control can be achieved by iteration only on sidelobe peaks in comparison to olen and compton s method the new algorithm provides a great improvement in mainlobe shaping control example simulations including both nonuniform linear and planar arrays are shown to illustrate the effectiveness of this algorithm

array pattern synthesis with excitation control via norm minimization simple and efficient procedures are presented to synthesize antenna array patterns focused or shaped beams while controlling the excitations this synthesis problem is of great practical interest as it makes active arrays more attractive by reducing their complexity cost and weight with a proper regularization of the array pattern synthesis solution the excitations can be optimized in order to design uniform amplitude sparse arrays arrays whose excitations have a low dynamic range ratio or a smooth amplitude variation more specifically the synthesis procedures are composed of the minimization of a norm mixed ell 1 ell infty norm total variation norm or a combination of the ell 1 and ell infty norms associated with radiation pattern constraints various representative array synthesis problems are considered examples including the coupling between antennas and a comparison with a deterministic approach confirm both the usefulness and effectiveness of the proposed procedures

central configurations with a quasihomogeneous potential function for the classical n body problem if the masses are paced at rest in the configuration that is central then the masses will tend to the origin and result in a simultaneous collision a winter the analytical foundations of celestial mechanics 1st ed princeton university press princeton 1941 however if the potential is quasihomogeneous in nature that is the potential is of the form u v w where w i jamimjrij and v i jbmimjrij then we will dramatically get different results this paper determines the orbits that will result when the potential function is quasihomogeneous it also shows when there existences a relative equilibrium solution for the regular n gon configuration this is one half of perko s theorem for a homogeneous potential finally we show the existence of a central configuration which is not central for either w or v this configuration is the placement of two mutual equal pairs of masses placed at the vertices of a square this shows that the reverse implication of perk