almost global stabilization of fully actuated rigid bodies this paper addresses the problem of stabilizing a fully actuated rigid body the problem is formulated by considering the natural configuration space for rigid bodies the special euclidean group se 3 the proposed solution consists of a landmark based controller for force and torque actuation that guarantees almost global asymptotic stability of the desired equilibrium point as such the equilibrium point is asymptotically stable and only a nowhere dense set of measure zero lies outside its region of attraction the controller uses velocity measurements and the position coordinates of a collection of landmarks fixed in the environment as an additional feature the control law is designed so as to verify prescribed bounds on the actuation

generic simplicity of the spectrum and stabilization for a plate equation in this work we prove the generic simplicity of the spectrum of the clamped plate equation in a bounded regular domain of mathbb r d that is given omega subset mathbb r d we show that there exists an arbitrarily small deformation of the domain u such that all the eigenvalues of the plate system in the deformed domain omega u are simple to prove this result we first prove a nonstandard unique continuation property for this system that also holds generically with respect to the perturbations of the domain both the proof of this generic uniqueness result and the generic simplicity of the spectrum use baire s lemma and shape differentiation finally we show an application of this unique continuation property to a result of generic stabilization for a plate system with one dissipative boundary condition

analysis of the energy based control for swinging up two pendulums this note studies the energy based control for swinging up two pendulums on a cart and it presents an original analysis of the convergence of the energy and the motion of the two pendulums for the two pendulums with the different natural frequencies irrespective of initial state of the two pendulums it is shown that the energy of each pendulum converges to either of two values and the motion of the two pendulums can be described by four invariant sets moreover the stability analysis of the motion of the two pendulums is performed via the concept of stability of an invariant set the results obtained in this note not only show theoretically the effectiveness of the energy based control for swinging up the two pendulums but also pave one way for analyzing and designing the energy based control for more complicated underactuated mechanical systems

brief almost global stabilization of the inverted pendulum via continuous state feedback continuous state feedback laws are presented for almost global stabilization of the planar inverted pendulum on a cart the synthesis is carried out exploiting energy shaping techniques and a suitable smooth switching between positive and negative feedback some of the employed ideas could be possibly generalized to the problem of stabilization of systems with multiple equilibrium points

existence of bounded solutions of a second order system with dissipation in this article we study the following second order system of ordinary differential equations with dissipationu cu dau khu pt u rn t r where c d and k are positive constants h rn rn is a locally lipschitz function and p r rn is a continuous and bounded function a is a n n matrix whose eigenvalues are positive under these conditions we prove that for some values of c d and k this system has a bounded solution which is exponentially asymptotically stable moreover if p t is almost periodic then this bounded solution is also almost periodic these results are applied to the spatial discretization of very well known second order partial differential equations

multicomponent acoustic distortion product otoacoustic emission phase in humans ii implications for distortion product otoacoustic emissions generation phase characteristics and latency of 2f1 f2 3f1 2f2 and 2f2 f1 acoustic distortion product otoacoustic emissions dpoaes recorded in normally hearing adults have been described in a companion paper moulin and kemp multicomponent acoustic distortion product otoacoustic emission phase in humans i general characteristics j acoust soc am 100 1617 1639 1996 phase versus frequency functions pff have been recorded using two methods depending whether f1 or f2 was swept in frequency defining respectively an f1 sweep and an f2 sweep method the present study compares 2f1 f2 3f1 2f2 4f1 3f2 and 2f2 f1 dpoaes phase characteristics and latencies obtained by these two methods for lower sideband dpoaes the f2 sweep gave consistently longer latencies than the f1 sweep method whereas no difference was obtained for the 2f2 f1 dpoae this suggests that the lower sideband dpoaes and the 2f2 f1 dpoae do not come from the same aspect of the traveling wave the longer delay obtained with an f2 sweep is suggested to be due to an additional delay added by the proximity of the peak of the f2 traveling wave the place fixed and the wave fixed models of dpoae generation are discussed and an intermediate model of dpoae generation is introduced to explain such additional delay and the existence of phase irregularities which were observed in the pff the ratio of the latencies obtained by the two sweep methods is frequency dependent and a relation to cochlear frequency selectivity is suggested finally analysis of the differences in latency of the different lower sideband dpoae components allowed an estimation of the return latency of dpoaes

energy control of a pendulum with quantized feedback the problem of controlling a nonlinear system to an invariant manifold using quantized state feedback is considered by the example of controlling the pendulum s energy a feedback control law based on the speed gradient algorithm is chosen the main result consisting in precisely characterizing allowed quantization error bounds and resulting energy deviation bounds is presented

swinging control of nonlinear oscillations the speed gradient method of control design used previously for problems of regulation and tracking is extended to oscillating systems with energy based objective functions the concept of swinging control is introduced meaning achievement of arbitrary large level of the objective function by arbitrary small control level the existence of swinging control for hamiltonian systems is established simulation results for pendulum swinging problem are demonstrated

almost periodic solutions to some semilinear non autonomous thermoelastic plate equations abstract the paper is concerned with the existence of almost periodic solutions to the so called semilinear thermoelastic plate systems for that the strategy consists of seeing these systems as a particular case of the semilinear parabolic evolution equations x t a t x t f t x t t r where a t for t r is a family of sectorial linear operators on a banach space x satisfying the so called acquistapace terreni conditions and f is a function defined on a real interpolation space x for 0 1 under some reasonable assumptions it will be shown that has a unique almost periodic solution we then make use of the previous result to obtain the existence and uniqueness of an almost periodic solution to the thermoelastic plate systems

existence stability and smoothness of a bounded solution for nonlinear time varying thermoelastic plate equations in this paper we study the existence stability and the smoothness of a bounded solution of the following nonlinear time varying thermoelastic plate equation with homogeneous dirichlet boundary conditions utt 2u f1 t u t 0 x t ut f2 t u t 0 x u u 0 t 0 x where 0 0 is a sufficiently regular bounded domain in rn n 1 and fe1 fe2 r l2 2 l2 define by fe t u x f t u x x x are continuous and locally lipschitz functions first we prove that the linear system f1 f2 0 generates an analytic strongly continuous semigroup which decays exponentially to zero second under some additional condition we prove that the nonlinear system has a bounded solution which is exponentially stable and for a large class of functions f1 f2 this bounded solution is almost periodic finally we use the analyticity of the semigroup generated by the linear system to prove the smoothness of the bounded solution

brief paper global stabilization of an inverted pendulum control strategy and experimental verification the problem of swinging up an inverted pendulum on a cart and controlling it around the upright position has traditionally been treated as two separate problems this paper proposes a control strategy that is globally asymptotically stable under actuator saturation and in addition locally exponentially stable the proposed methodology which performs swing up and control simultaneously uses elements from input output linearization energy control and singular perturbation theory experimental results on a laboratory scale setup are presented to illustrate the approach and its implementation

rate limited time optimal control of a planar pendulum abstract time optimal control problems often admit as solution bang bang controls but they present several drawbacks in real applications where additional degrees of regularity are desirable in this paper the rate limited time optimal swing up of an inverted pendulum is considered and necessary conditions that have to be satisfied by optimal trajectories in the presence of rate constraints are derived a comparison between this approach and the results from the standard time optimal problem is reported

ear canal acoustic distortion at 2f1 f2 from human ears relation to other emissions and perceived combination tones two aspects of the intermodulation distortion product at 2f1 f2 generated by normal human ears and measured acoustically in the ear canal were studied 1 its relation to tone evoked and spontaneous otoacoustic emissions and 2 its relation to the perceived combination tone at the same frequency with regard to 1 substantial differences among ears in the detectability of emissions were observed ears tended to exhibit all or none of the emission types that were sought within ears possessing emissions the magnitudes of tone evoked emissions and acoustic distortion showed a similar dependence on frequency with regard to 2 a three primary tone stimulus was employed to ask whether the ear canal acoustic distortion tone is canceled under the same stimulus conditions that produce perceptual cancellation simultaneous cancellation of perceptual and acoustic distortion was produced rarely results are interpreted qualitatively with a model in which primary tones produce distortion at their interaction

cochlear generation of intermodulation distortion revealed by dpoae frequency functions in normal and impaired ears distortion product otoacoustic emission dpoae frequency functions were measured in normal hearing and hearing impaired ears a fixed f2 swept f1 paradigm was used with f2 fixed at half octave intervals from 1 to 8 khz l1 was always 10 db greater than l2 and l2 was varied from 65 to 10 db spl in 5 db steps the responses were quantified by the frequency and amplitude of the peak response peak responses were closer to f2 in higher frequency regions and for lower intensity stimulation results from hearing impaired subjects suggest that audiometric thresholds at the distortion product frequency fdp in addition to hearing status at f2 can affect dpoae results results are discussed in terms of several manifestations of a second resonance model as well as a dual source model for the generation of dpoaes as measured in the ear canal of humans it appears that a dual source model accounts for the data better than second filter models

non local stabilization of a spherical inverted pendulum we design a non linear stabilizing control law for a four degree of freedom spherical inverted pendulum the pendulum is a slim cylindrical beam attached to a horizontal plane via a universal joint the joint is free to move in the plane under the influence of a planar force the upright position is an unstable equilibrium of the uncontrolled system because of gravity the objective is to design a controller so that it stabilizes the upright position starting from any position in the upper hemisphere with arbitrary velocity we achieve this by first transforming the original system to an appropriate upper triangular form and then designing a controller which incorporates a high gain design with the method of non linear forwarding the control law is evaluated through computer simulations

brief paper a family of smooth controllers for swinging up a pendulum the paper presents a new family of controllers for swinging up a pendulum the swinging up of the pendulum is derived from physical arguments based on two ideas shaping the hamiltonian for a system without damping and providing damping or energy pumping in relevant regions of the state space a family of simple smooth controllers without switches with nice properties is obtained the main result is that all solutions that do not start at a zero lebesgue measure set converge to the upright position for a wide range of the parameters in the control law thus the swing up and the stabilization problems are simultaneously solved with a single smooth law the properties of the solution can be modified by the parameters in the control law control signal saturation can also be taken into account using the hamiltonian approach

optimal regulator for the inverted pendulum via euler lagrange backward integration we present a time invariant nonlinear controller for the inverted pendulum based on optimal control which is defined for all pendulum angles the paper provides a case study in the brute force method of calculating the extremal field by solving the euler lagrange equations backward in time thus exploring the stable manifold of the hamiltonian flow the controller is only given numerically on an interpolation grid we use this controller for closed loop simulations corroborating considerable gain robustness

on the stability and stabilization of quaternion equilibria of rigid bodies we study attitude control of rigid bodies on quaternion coordinates under three mathematically different perspectives depending on how the system dynamics are assumed to evolve in the first case we suppose that one equilibrium point is chosen a priori and a continuous controller is used under the assumption that the rigid body always spins in the same direction in the second case we relax the assumption that the sense of rotation is constant finally a third scenario is considered in which hybrid switching control is used to choose the direction in which to spin that is both equilibria are continuously considered with regard to less energy consumption it is showed that each of three scenarios must be treated in a different theoretical setting a comparative study in simulations is also provided

sources of distortion product otoacoustic emissions revealed by suppression experiments and inverse fast fourier transforms in normal ears primary and secondary sources combine to produce the 2f1 f2 distortion product otoacoustic emission dpoae measured in the ear canals of humans dpoaes were obtained in nine normal hearing subjects using a fixed f2 paradigm in which f1 was varied the f2 was 2 or 4 khz and absolute and relative primary levels were varied data were obtained with and without a third tone f3 placed 15 6 hz below 2f1 f2 the level of f3 was varied in order to suppress the stimulus frequency otoacoustic emission sfoae coming from the 2f1 f2 place these data were converted from the complex frequency domain into an equivalent time representation using an inverse fast fourier transform ifft iffts of unsuppressed dpoae data were characterized by two or more peaks relative amplitudes of these peaks depended on overall primary level and on primary level differences the suppressor eliminated later peaks but early peaks remained relatively unaltered results are interpreted to mean that the dpoae measured in humans includes components from the f2 place intermodulation distortion and dp place in the form of a sfoae these findings build on previous work by providing evidence that multiple peaks in the ifft are due to a secondary source at the dp place

global set stabilisation of the spacecraft attitude using finite time control technique in this article we revisit the classical problem of attitude stabilisation for a rigid spacecraft with external disturbances a global set stabilisation method using finite time control technique is proposed in the absence of disturbances the states of the closed loop system will be stabilised in finite time to a set consisting of two equilibria in the presence of disturbances the states will be stabilised to a neighbourhood of this set by constructing a particular lyapunov function it is proved that the closed loop system satisfies global set stability the control method in this article is based on set control idea and thus is more natural and energy efficient numerical simulation results show the effectiveness of the method

stability and chaotic behavior of a pid controlled inverted pendulum subjected to harmonic base excitations by using the normal form theory abstract in this paper we investigate the stability and the onset of chaotic oscillations around the pointing up position for a simple inverted pendulum that is driven by a control torque and is harmonically excited in the vertical and horizontal directions the driven control torque is defined as a proportional plus integral plus derivative pid control of the deviation angle with respect to the pointing down equilibrium position the parameters of the pid controller are tuned by using the routh criterion to obtain a stable weak focus around the pointing up position whose stability is investigated by using the normal form theory the normal form theory is also used to deduce a simplified mathematical model that can be resolved analytically and compared with the numerical simulation of the complete mathematical model from the harmonic prescribed motions for the pendulum base necessary conditions for chaotic motion are deduced by means of the melnikov function when the pendulum is close to the unstable pointing up position the pid parameters are changed and the chaotic motion is destroyed which is achieved by employing very small control signals even in the presence of random noise the results of the analytical calculations are verified by full numerical simulations

boundary controllability of thermoelastic plates via the free boundary conditions controllability properties of a partial differential equation pde model describing a thermoelastic plate are studied the pde is composed of a kirchoff plate equation coupled to a heat equation on a bounded domain with the coupling taking place on the interior and boundary of the domain the coupling in this pde is parameterized by alpha 0 boundary control is exerted through the two free boundary conditions of the plate equation and through the robin boundary condition of the temperature these controls have the physical interpretation of inserted forces and moments and prescribed temperature respectively all of which act on the edges of the plate the main result here is that under such boundary control and with initial data in the basic space of well posedness one can simultaneously control the displacement of the plate exactly and the temperature approximately moreover the thermal control may be taken to be arbitrarily smooth in time and space and the thermal control region may be any nonempty subset of the boundary this controllability holds for arbitrary values of the coupling parameter alpha with the optimal controllability time in line with that seen for uncoupled kirchoff plates

a nonlinear small gain theorem for the analysis of control systems with saturation a nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation the theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear feedforward form this result in turn is applied to the control of 1 linear systems stable and unstable with inputs subject to magnitude and rate saturation and time delays 2 the cascade of globally asymptotically stable nonlinear systems with certain linear systems those that are stabilizable right invertible and such that all of their invariant zeros have nonpositive real part 3 the inverted pendulum on a cart and 4 the planar vertical takeoff and landing aircraft

approximate controllability of a semilinear heat equation in bbb r n we prove the approximate controllability of the semilinear heat equation in bbb r n we introduce the weighted sobolev spaces of escobedo and kavian and in that functional setting we adapt the technique introduced by fabre puel and zuazua for the problem in bounded domains that is we first prove the approximate controllability of the linear equation and by a fixed point method obtain the main result

asymptotic smooth stabilization of the inverted 3 d pendulum the 3 d pendulum consists of a rigid body supported at a fixed pivot with three rotational degrees of freedom it is acted on by gravity and it is fully actuated by control forces the 3 d pendulum has two disjoint equilibrium manifolds namely a hanging equilibrium manifold and an inverted equilibrium manifold the contribution of this paper is that two fundamental stabilization problems for the inverted 3 d pendulum are posed and solved the first problem asymptotic stabilization of a specified equilibrium in the inverted equilibrium manifold is solved using smooth and globally defined feedback of angular velocity and attitude of the 3 d pendulum the second problem asymptotic stabilization of the inverted equilibrium manifold is solved using smooth and globally defined feedback of angular velocity and a reduced attitude vector of the 3 d pendulum these control problems for the 3 d pendulum exemplify attitude stabilization problems on the configuration manifold so 3 in the presence of potential forces lyapunov analysis and nonlinear geometric methods are used to assess global closed loop properties yielding a characterization of the almost global domain of attraction for each case

time optimal swing up of the planar pendulum this paper presents qualitative results on the global structure of the time optimal trajectories of the planar pendulum on a cart this mechanical system is a benchmark to test nonlinear control methods and various papers addressed the problem of computing time optimal open loop controls relying on the theory of optimal synthesis we provide a discontinuous feedback giving optimal solutions for any initial data the approach is that of geometric control theory

case studies on the application of the stable manifold approach for nonlinear optimal control design this paper presents application results of a recently developed method for approximately solving the hamilton jacobi equation in nonlinear control theory the method is based on stable manifold theory and consists of a successive approximation algorithm which is suitable for computer calculations numerical approach for this algorithm is advantageous in that the computational complexity does not increase with respect to the accuracy of approximation and non analytic nonlinearities such as saturation can be handled first the stable manifold approach for approximately solving the hamilton jacobi equation is reviewed from the computational viewpoint and next the detailed applications are reported for the problems such as swing up and stabilization of a 2 dimensional inverted pendulum simulation stabilization of systems with input saturation simulation and a sub optimal servo system design for magnetic levitation system experiment

output feedback control for stabilization on se 3 this paper addresses the problem of stabilizing systems that evolve on se 3 the proposed solution consists of an output feedback controller that guarantees almost global asymptotic stability of the desired equilibrium point in the sense that the equilibrium point is stable and we have convergence for all initial conditions except for those in a nowhere dense set of measure zero the output vector is formed by the position coordinates of a collection of landmarks fixed in the environment the resulting closed loop system exhibits the following properties i the position and orientation subsystems are decoupled ii the position error is globally exponentially stable and iii the orientation error is almost globally exponentially stable results are also provided that allow one to select landmark configurations so as to control how the position and orientation of the rigid body converge to their final equilibrium values

evidence for the distortion product frequency place as a source of distortion product otoacoustic emission dpoae fine structure in humans ii fine structure for different shapes of cochlear hearing loss distortion product otoacoustic emissions dpoae were recorded from eight human subjects with mild to moderate cochlear hearing loss using a frequency spacing of 48 primary pairs per octave and at a level l1 l2 60 dbspl and with a fixed ratio f2 f1 subjects with different shapes of hearing thresholds were selected they included subjects with near normal hearing within only a limited frequency range subjects with a notch in the audiogram and subjects with a mild to moderate high frequency loss if the primaries were located in a region of normal or near normal hearing but dp frequencies were located in a region of raised thresholds the distortion product 2 f1 f2 was still observable but the dp fine structure disappeared if the dp frequencies fell into a region of normal thresholds fine structure was preserved as long as dpoae were generated even in cases of mild hearing loss in the region of the primaries these experimental results give further strong evidence that in addition to the initial s

global stabilization of spherical orientation by synergistic hybrid feedback with application to reduced attitude tracking for rigid bodies in this paper we propose a hybrid feedback based on a synergistic potential function that achieves global asymptotic stabilization of a desired orientation on the n sphere with a nominal robustness to measurement disturbances a task that is not possible by classical feedback be it smooth nonsmooth periodic or any combination thereof due to the topological structure of the sphere we extend this basic result to a tracking controller for the reduced attitude or pointing direction of a rigid body and provide a method to remove jumps in the controlled torque by backstepping the proposed hybrid feedback is compared with a similar smooth feedback in simulation where it is illustrated that the hybrid feedback overcomes performance limitations inherent to the smooth feedback we provide two examples of a synergistic potential function one defined on a general sphere and the other on the unit circle

almost periodic solutions of first and second order cauchy problems abstract almost periodicity of solutions of first and second order cauchy problems on the real line is proved under the assumption that the imaginary resp real spectrum of the underlying operator is countable related results have been obtained by ruess v and basit our proof uses a new idea it is based on a factorisation method which also gives a short proof of the vector valued version of loomis classical theorem saying that a bounded uniformly continuous function from r into a banach spacexwith countable spectrum is almost periodic ifc0 x our method can also be used for solutions on the half line this is done in a separate paper

finding the impedance of the organ of corti measurements of the nonlinear response of the basilar membrane to a pure tone are shown to have a simple form for moderate membrane velocities v x f vu vu x f vu x f f fc x where the response v is the velocity of the membrane at measurement position x vu is the umbo velocity f is the frequency of the stimulus and fc x is the local characteristic frequency the frequency dependence of the functions x f and x f is determined from the data and x f and ln x f are shown to be analytic functions in the lower half of the complex frequency plane with re x f a monotonically increasing function of f at fixed x the linear limit of basilar membrane motion is characterized by a transfer function t x f v1 1 estimated by extrapolating v x f vu vu to a small membrane velocity v1 t x f and ln t x f are shown to be analytic functions in the lower half of the complex frequency plane the inverse of the amplitude of the transfer function which has both a deep dip at f fc x