Finite codimension stability of invariant surfaces

In this paper, two technologies to design gain-scheduled controller are proposed for discretetime Linear Parameter Varying (LPV) systems with multiplicative noises. In the considered systems, the time-varying parameters are proposed to describe the uncertainties. And, the added multiplicative noise term is applied to describe the stochastic behaviors of the system. Furthermore, the gainscheduled design scheme is applied to deal with the stabilization problem of the LPV systems with multiplicative noises. Through the parameter-independent and parameter-dependent Lyapunov functions, the corresponding sufficient conditions are derived to discuss the stability and stabilization problems of the system. In order to apply the convex optimization algorithm, the derived sufficient conditions are converted into Linear Matrix Inequality (LMI) problems. Based on the proposed design technologies, gain-scheduled controllers are designed such that the considered system is asymptotically stable in the mean square. Finally, two numerical examples are applied to demonstrate the application and effectiveness of the proposed design technologies of this paper.

Interval exchange maps are related to geodesic flows on translation surfaces; they correspond to the first return maps of the vertical flow on a transverse segment. The Rauzy–Veech induction on the space of interval exchange maps provides a powerful tool to analyze the Teichmüller geodesic flow on the moduli space of Abelian differentials. Several major results have been proved using this renormalization. Danthony and Nogueira introduced in 1988 a natural generalization of interval exchange transformations, namely linear involutions. These maps are related to general measured foliations on surfaces (whether orientable or not). In this paper we are interested by such maps related to geodesic flow on (orientable) flat surfaces with ℤ/2ℤ linear holonomy. We relate geometry and dynamics of such maps to the combinatorics of generalized permutations. We study an analogue of the Rauzy–Veech induction and give an efficient combinatorial characterization of its attractors. We establish a natural bijection between the extended Rauzy classes of generalized permutations and connected components of the strata of meromorphic quadratic differentials with at most simple poles, which allows us, in particular, to classify the connected components of all exceptional strata.

The semi-global stabilization problem and output regulation problem of singular linear systems subject to input saturation are addressed. A reduced-order normal system is obtained by a standard coordinate transformation. It is further shown that the controller that solves the stabilization (output regulation) problem of the reduced-order normal systems also solves the stabilization (output regulation) problem of the original singular systems.

This paper addresses the stability problem of a biological system that describes the proliferation of sick cells in Acute Myeloid Leukemia (AML). AML therapies aim at eradicating malignant cells, reaching a biological status represented by the zero equilibrium point of the age-structured mathematical model describing pathological hematopoeisis. First, the AML stability problem is reformulated into a stability problem of a nonlinear cascaded system. Then based on a positivity property of the system, non quadratic Lyapunov candidates are constructed. Finally, necessary and stability conditions are obtained. These conditions complete and generalize previous results where the main contribution consists in providing necessary and sufficient conditions based on a general model that incorporates fast self renewal. This model is complex but more realistic from a practical pint of view. Further more, unlike previously published works, the proposed conditions do not depend on auxiliary parameters which are biologically ambiguous but depend only on the AML system which makes the results more biologically relevant for AML treatment.

In this manuscript, the stability and consensus problem of the leader-following multi-agent system is studied. The state information of the leader is only available to the dynamics of all the followers, while the communication among the agents occurs at sampling instant. The innovative part of this paper is to reach the consensus and attain the stability for prescribed MASs with interval time varying delay using impulsive control in the presence of leader. The interaction between the agent is illustrated by an undirected graph. A class of distributed impulsive protocol relying on sampling information is suggested to reach the leader following consensus. The consensus is critically relying on the sampling period, control gains. By performing the similar procedures, the consensus problem of multi-agent system is converted to stability problem of the error system. By utilizing the stability theory of impulsive systems, algebraic graph theory, sufficient conditions are derived to guarantee the leader-following consensus of the multi-agent system. Terminally, a numerical example is given to show an efficacy of this presented approach and the sureness of theoretical analysis.

A biologically inspired controller for sound and vibration applications

In the stabilization problem for systems with control and state constraints a domain of attraction is a set of initial states that can be driven to the origin by a feedback control without incurring constraints violations. If the problem is that of tracking a reference signal, that converges to a constant constraint-admissible value, a tracking domain of attraction is a set of initial states from which the reference signal can be asymptotically approached without constraints violation during the transient. Clearly, since the zero signal is an admissible reference signal, any tracking domain of attraction is a domain of attraction. We show that the opposite is also true. For constant reference signals we establish a connection between the convergence speed of the stabilization problem and tracking convergence which turns out to be independent of the reference signal. We also show that the tracking controller can be inferred from the stabilizing (possibly nonlinear) controller associated with the domain of attraction.

A biologically inspired control approach for reducing radiated sound power from distributed elastic systems has been experimentally verified for harmonic, narrowband excitation. The control paradigm approximates natural biological systems for initiating movement, hi that a small number of signals are sent from an advanced, centralized controller (analogous to the brain) and are then distributed by local rules and actions to multiple actuators (analogous to muscle fiber). The controller was applied to attenuate radiated sound power from a plate. Experimental investigations of two different local learning rules, the phase variation and optimal methods, were carried out. Performance of the various methods decreased radiated sound power from a clamped plate by up to 16 dB for harmonic off-resonance excitation and up to 22 dB for on-resonance excitation. In general the results have demonstrated that the biological control approach has the potential to control multimodal response in distributed elastic systems using an array of many actuators with a reduced-order main controller. Thus significant reductions in control system computational complexity have been realized by this approach. Nomenclature / = cost function M = number of microphones v = error sensor voltage y = slave actuator complex gains \JL = convergence parameter I. Introduction R ECENT work has demonstrated the potential of active control of distributed elastic systems using multiple, independent actuators and sensors. In work concerned with the control of sound radiation from vibrating panels, the importance of number of channels of control and optimization of the transducer position and shape has been demonstrated.1 However, these investigations were carried out for a fixed frequency, and it is apparent that for good control over a bandwidth of frequencies the control actuators and sensors need to be adaptive in shape. At first sight this problem could be solved using an overall transducer broken up into many individual small elements, each connected by an individual control channel. In this situation the control transducer would effectively reoptimize its configuration for different conditions by adaptively weighting each transducer segment. Meirovitch and Norris2 have demonstrated the advantage of such an approach by considering fully distributed control in reducing control spillover. The disadvantage of this approach is that, for systems with a high modal density, the number of actuators and sensors required becomes extremely large. A high number of control channels has a number of problems mainly associated with memory requirements and computational time in the hardware systems used to implement the control. In addition, collinearity of transducer transfer functions (i.e., the transducer transfer functions are not fully linear independent) causes stability problems in systems with a high number of transducers. A new approach of controlling distributed elastic systems is presented. The approach is inspired by the action of biological natural systems where a small number of main signals are transmitted from the brain to a large area of muscle tissue to activate many independent segments of muscle. The signals then stimulate local action that is governed by, for example, chemical interaction of locally

In this paper, a new phase plane analysis method is proposed to study the nonlinear phenomena of traffic flow. This method transforms the traditional traffic flow model into a new improved model through variable substitution to adapt to the phase plane analysis. According to the improved model, the corresponding relationship between traffic congestion and system instability can be seen on the phase plan, which can be used for the stability analysis of various traffic flow phenomena. Thus, the problem of traffic flow is transformed into the problem of system stability.

It is can identify three main classes of problems broadly characterizing stability of a dynamical systems, viz., (1) stability with respect to a part of the variables of the zero equilibrium position (Lyapunov-Rumyantsev stability problem), (2) stability of the partialzero equilibrium position, and (3) stability with respect to a part of the variables of the partialzero equilibrium position. In the problem of stability with respect to a part of the variables of the zero equilibrium position of systems of ordinary differential equations with continuous right-side assumes the domain of initial perturbations to be a sufficiently small neighborhood of the zero equilibrium position. Along with this statement, the case then initial perturbations can be large with respect to one part of non-controlled variables and arbitrary with respect to their other part is also considered. On the other hand, for stability problem of partial zero equilibrium positions of systems of ordinary differential equations also naturally assume that initial perturbations of variables that do not define the given equilibrium position can be large with respect to one part of the variables and arbitrary with respect to their other part. Contrary the assumptions that initial perturbations of this variables are either only arbitrary or only large the combined assumption made it possible an admissible trade-off between the meaning sense for notion of stability and the respective requirements on the Lyapunov functions. The article studies the problem of stability for nonlinear discrete-time systems: stability with respect to a part of the variables of partial equilibrium position. Initial perturbations of variables that do not define the given equilibrium position can be large (belonging to an arbitrary compact set) with respect to one part of the variables and arbitrary with respect to their other part. A conditions of stability of this type are obtained in the context of a discrete analog of the Lyapunov functions method, which generalize a number of existing results. Example is given. The problem of unification of process of studying stability problems of stationary and non-stationary nonlinear discrete-time systems is also discussed

Analyzing the research subjects and hot topics of power system reliability through the Web of Science from 1991 to 2015

This paper studies energy storage based output tracking and disturbance rejection problems for a simple interconnected power system suffered from a periodic load disturbance with unknown amplitude and frequency. By constructing a new exosystem, the problem is converted into output regulation problem of a composite system. Internal model theorem is introduced for the composite system, and output regulation problem is changed into stabilization problem of a new augmented system by imposing an appropriate transformation. An adaptive dynamical energy storage based controller can solve stabilization problem of the augmented system as well as output tracking and disturbance rejection problem for the original system. Finally, simulation results show the effectiveness of the proposed controller.

Of increasing importance in network design is the requirement to control power system transient stability following large disturbances. If series or shunt control devices are available within the network, then improvements to the transient properties of the network can generally be made (both from the perspective of preventing angular separation and improving damping). This paper uses non-linear control (dynamic programming) to examine the transient stability problem for single machine infinite bus systems. The developed approach explains the suitability of several existing approaches, as well as identifies some new ideas that may be applicable to the transient stability problem for multi-generator power systems.

In this paper, we study the global robust synchronization problem of the controlled Duffing system and the Van der Pol oscillator. By employing the internal model approach, we first show that the problem can be converted into a global robust stabilization problem of a time-varying nonlinear system in lower triangular form. Then we show that the global stabilization problem of the lower triangular system is solvable, thus leading to the solution of the global robust synchronization problem.

The paper considers the stabilization problem for systems with a single delay h in the feedback loop. The state-space parametrizations of all stabilizing regulators are derived. These parametrizations have simple structures and clear interpretations. In particular, it is shown that every stabilizing controller consists of a delayed state observer, an h time units ahead predictor and a stabilizing state feedback. Applications of the proposed parametrization to the H/sup 2/ control and robust stabilization are discussed.