Robust decentralized adaptive stabilization for a class of interconnected systems

The robust decentralized adaptive output-feedback stabilization for a class of interconnected systems with static and dynamic interconnections by using the MT-filters and backstepping design method is studied. By introducing a new filtered transformation, the adaptive laws were derived for measurement. Under the assumption of the nonlinear growth conditions imposed on the nonlinear interconnections and by constructing the error system and using a new proof method, the global stability of the closed-loop system was effectively analyzed, and the exponential convergence of all the signals except for parameter estimates were guaranteed.

Adaptive stabilization of uncertain nonholonomic systems by output feedback

The adaptive output feedback control strategy is presented for a class of nonholonomic systems in chained form with nonlinearity uncertainties. A new observer and a filter are introduced for the states and parameter estimation. The proposed control strategies guarantee the convergence of the closed-loop system. The simulation example demonstrates the efficiency of the proposed method.

Comparing dynamical systems concepts and techniques for biomechanical analysis

Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predominately nonlinear.For this reason,nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature.These analysis techniques have provided new insights into how systems(1) maintain pattern stability,(2) transition into new states,and(3) are governed by short-and long-term(fractal) correlational processes at different spatio-temporal scales.These different aspects of system dynamics are typically investigated using concepts related to variability,stability,complexity,and adaptability.The purpose of this paper is to compare and contrast these different concepts and demonstrate that,although related,these terms represent fundamentally different aspects of system dynamics.In particular,we argue that variability should not uniformly be equated with stability or complexity of movement.In addition,current dynamic stability measures based on nonlinear analysis methods(such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics,but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored.Finally,systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.

Genotype-environment interaction in Cordia trichotoma(Vell.)Arráb.Ex Steud.progenies in two different soil conditions

Investment in silvicultural techniques is noticeably lacking,especially in breeding programs for non-conventional wood species.Studying genotype×environment interaction(G×E)is essential to the development of breeding programs.Thus,this study aimed to estimate genetic diversity of and the effects of G×E interaction on two progeny tests of Cordia trichotoma,including the estimation of genetic gain and genetic diversity after selection.For the experiment,30 progenies of C.trichotoma were tested at two sites with differing soil textures.Diameter at breast height(1.30 m above soil surface,dbh-cm),total height,diameter at 30 cm from the soil,first branch height,and survival were all monitored for four years.Statistical deviance,best linear unbiased estimator,and harmonic mean of relative performance of genetic values(MHPRVG)were all calculated to predict breeding values,estimate genetic parameters,and analyze deviance.All quantified traits varied significantly among progenies by soil type,with greatest variation recorded for genetic variability.Heritability of the progenies led to predictions of genetic gain,ranging from 7.73 to 15.45%,for dbh at four years of age.The calculated decrease in genetic diversity after selection showed that this parameter should be monitored in subsequent breeding cycles.G×E was low for all tests.The best-performing progenies proved most stable and best adapted to the different environmental conditions tested.

Adaptive Output-Feedback Stabilization for PDE-ODE Cascaded Systems with Unknown Control Coefficient and Spatially Varying Parameter

This paper investigates the adaptive stabilization for a class of uncertain PDE-ODE cascaded systems. Remarkably, the PDE subsystem allows unknown control coefficient and spatially varying parameter, and only its one boundary value is measurable. This renders the system in question more general and practical, and the control problem more challenging. To solve the problem,an invertible transformation is first introduced to change the system into an observer canonical form,from which a couple of filters are constructed to estimate the unmeasurable states. Then, by adaptive technique and infinite-dimensional backstepping method, an adaptive controller is constructed which guarantees that all states of the resulting closed-loop system are bounded while the original system states converging to zero. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed method.

STATE-FEEDBACK ADAPTIVE STABILIZING CONTROL DESIGN FOR A CLASS OF HIGH-ORDER NONLINEAR SYSTEMS WITH UNKNOWN CONTROL COEFFICIENTS

In this paper, a new approach is successfully addressed to design the state-feedback adaptive stabilizing control law for a class of high-order nonlinear systems in triangular form and with unknown and nonidentical control coefficients, whose stabilizing control has been investigated recently under the knowledge that the lower bounds of the control coefficients are exactly known. In the present paper, without any knowledge of the lower bounds of the control coefficients, based on the adaptive technique and appropriately choosing design parameters, we give the recursive design procedure of the stabilizing control law by utilizing the approach of adding a power integrator together with tuning functions. The state-feedback adaptive control law designed not only preserves the equilibrium at the origin, but also guarantees the global asymptotic stability of the closed-loop states and the uniform boundedness of all the other closed-loop signals.

Adaptive control for a class of nonlinear systems with time-varying delays in state and input

This paper is concerned with the adaptive stabilization problem of uncertain input delayed systems.A solution to this problem is given for a class of uncertain nonlinear systems with time-varying delays in both state and input.An adaptive asymptotically stabilizing controller,which can guarantee the stability of the closed-loop system and the convergence of the original system state,is designed by means of the Lyapunov-Krasovskii functional stability theory combined with linear matrix inequalities (LMIs) and nonlinear adaptive techniques.Some numerical examples are presented to demonstrate the effectiveness of the derived controller.

Adaptive Stabilization for ODE Systems Coupled with Parabolic PDES

This paper is concerned with the adaptive stabilization for ODE systems coupled with parabolic PDEs. The presence of the uncertainties/unknonws and the coupling between the subsystems makes the system under investigation essentially different from those of the existing literature,and hence induces more technique obstacles in control design. Motivated by the related literature, an invertible infinite-dimensional backstepping transformation with appropriate kernel functions is first introduced to change the original system into a new one, from which the control design becomes much convenient. It is worthwhile pointing out that, since the kernel equations for which the kernel functions satisfy are coupled rather than cascaded, the desirable kernel functions are more difficult to derive than those of the closely related literature. Then, by Lyapunov method and a dynamics compensated technique, an adaptive stabilizing controller is successfully constructed, which guarantees that all the closed-loop system states are bounded while the original system states converging to zero. Finally, a simulation example is provided to validate the proposed method.

STABILIZATION FOR A CLASS OF LARGE-SCALE STOCHASTIC NONLINEAR SYSTEMS WITH DECENTRALIZED CONTROLLER DESIGN

In this paper, a state feedback adaptive stabilization for a class of large-scale stochastic nonlinear systems is designed with Lyapunov and Backstepping method. In the systems there are uncertain terms, whose bounds are governed by a set of unknown parameters. The designed controllers would make the close-loop systems asymptotically stable and adaptive for the unknown parameters. As an application, a second order example is delivered to illustrate the approach.

Design method and verification of a hybrid prosthetic mechanism with energy-damper clutchable device for transfemoral amputees

Transfemoral amputees(TAs)have difficulty in mobility during walking,such as restricted movement of lower extremity and body instability,yet few transfemoral prostheses have explored human-like multiple motion characteristics by simple structures to fit the kinesiology,biomechanics,and stability of human lower extremity.In this work,the configurations of transfemoral prosthetic mechanism are synthesized in terms of human lower-extremity kinesiology.A hybrid transfemoral prosthetic(HTP)mechanism with multigait functions is proposed to recover the gait functions of TAs.The kinematic and mechanical performances of the designed parallel mechanism are analyzed to verify their feasibility in transfemoral prosthetic mechanism.Inspired by motion-energy coupling relationship of the knee,a wearable energy-damper clutched device that can provide energy in knee stance flexion to facilitate the leg off from the ground and can impede the leg’s swing velocity for the next stance phase is proposed.Its co-operation with the springs in the prismatic pairs enables the prosthetic mechanism to have the energy recycling ability under the gait rhythm of the knee joint.Results demonstrate that the designed HTP mechanism can replace the motion functions of the knee and ankle to realize its multimode gait and effectively decrease the peak power of actuators from 94.74 to 137.05 W while maintaining a good mechanical adaptive stability.

An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation

In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation, is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional.For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.