Quadratic integrability of solutions based on a class of delayed systems

Some properties such as oscillation, stability, existence of periodic solutions and quadratic integrability of solutions based on a class of second order nonlinear delayed systems are analyzed by using the V-function, the Lyapunov functional or the Beuman-Bihari inequality, and some sufficient conditions based on those properties are given. Finally, the conclusions are applied to over-voltage models based on three-phase nonsynchronous closing of switches appearing in the power systems, the results in accord with the background physical meaning are obtained. And all the conditions of the conclusions are easy to validate, so the conclusions have definite theoretical meaning and are easy to apply in practice.

QUADRATIC INTEGRABILITY AND BOUNDEDNESS OF THE SOLUTIONS FOR SECOND ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS

In this paper, by means of auxiliary functions and inequalities, we obtain some sufficient conditions of second order nonhomogeneous delay differential equation belonging to the L.S. or L.S. ∩ L.C..

Truly optimal semi-active damping to control free vibration of a single degree of freedom system

This paper studies a single degree of freedom system under free vibration and controlled by a general semiactive damping.A general integral of squared error is considered as the performance index.A one-time switching damping controller is proposed and optimized.The pontryagin maximum principle is used to prove that no other form of semi-active damping can provide the better performance than the proposed one-time switching damping.

Robust Fuzzy Tracking Control for Nonlinear Networked Control Systems with Integral Quadratic Constraints

This paper investigates the robust tracking control problcm for a class of nonlinear networked control systems （NCSs） using the Takagi-Sugeno （T-S） fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints （IQCs） are satisfied while both time-varying network- induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities （LMIs） and parallel distributed compensation （PDC）. Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.

Linear Quadratic Integral Control for the Active Suspension of Vehicle

The quarter model of an active suspension is established in the form of controllable autoregressive moving average （CARMA） model. An accelerometer can be mounted on the wheel hub for measuring road disturbance; this signal is used to identify the CARMA model parameters by recursive forgetting factors least square method. The linear quadratic integral （LQI） control method for the active suspension is presented. The LQI control algorithm is fit for vehicle suspension control, for the control performance index can comprise multi controlled variables. The simulation results show that the vertical acceleration and suspension travel both are decreased with the LQI control in the low frequency band, and the suspension travel is increased with the LQI control in the middle or high frequency band. The suspension travel is very small in the middle or high frequency band, the suspension bottoming stop will not happen, so the vehicle ride quality can be improved apparently by the LQI control.

On n-universal quadratic forms over dyadic local fields

Let n≥2 be an integer. We give necessary and sufficient conditions for an integral quadratic form over dyadic local fields to be n-universal by using invariants from Beli's theory of bases of norm generators.Also, we provide a minimal set for testing n-universal quadratic forms over dyadic local fields, as an analogue of Bhargava and Hanke's 290-theorem(or Conway and Schneeberger's 15-theorem) on universal quadratic forms with integer coefficients.

On the Existence of an Optimal Control of Ship Automatic Steering Instruments

The existence of linear quadratic optimal control of ship automatic steering instruments is studied. Firstly, the sufficient conditions for the quadratic integrability of the solutions of linear second order time-variant differential equations are developed. Secondly, the optimal control form of the ship automatic steering instrument is obtained by using the dynamic programming method, which guarantees a minimal ship sway range, during long-distance navigation, by using as little energy as possible. Finally, based on the above mentioned sufficient conditions, the conditions for the realization of optimal control are obtained, which provides a foundation for choosing the weighted coefficients for optimal control in engineering.

STABILITY MARGIN OF SYSTEMS WITH MIXED UNCERTAINTIES UNDER THE IQC DESCRIPTIONS

Stability perturbation bounds problem for systems with mixed uncertainties is discussed. It is supposed that the linear part in the forward loop is of parametric uncertainties described by interval perturbation mode, and that the nonlinear part in the feedback loop is characterized by an integral quadratic constraint (IQC). The definition of stability margin under the interval perturbation mode is given by using the Minkowski functional. The infinite stability checking problem of the mixed uncertain system can be converted to finite or one dimensional stability checking for different structures of the IQC multipliers based on the concepts of biconvex and convex-concave junctions and their properties. The result is illustrated to be efficient through an example.

Missile autopilot design based on robust LPV control

This paper proposes an effective algorithm to work out the linear parameter-varying (LPV) framework autopilot for the air defense missile so as to simultaneously guarantee the closed-loop system properties globally and locally, which evidently reduces the number of unknown variables and hence increases the computational efficiency. The notion of 'robust quadratic stability' is inducted to meet the global properties, including the robust stability and robust performance, while the regional pole placement scheme together with the adoption of a model matching structure is involved to satisfy the dynamic performance, including limiting the 'fast poles'. In order to reduce the conservatism, the full block multiplier is employed to depict the properties, with all specifications generalized in integral quadratic constraint frame and finally transformed into linear matrix inequalities for tractable solutions through convex optimization. Simulation results validate the performance of the designed robust LPV autopilot and the proposed framework control method integrating with the full block multiplier approach and the regional pole placement scheme, and demonstrate the efficiency of the algorithm. An efficient algorithm for the air defense missile is proposed to satisfy the required global stability and local dynamical properties by a varying controller according to the flight conditions, and shows sufficient promise in the computational efficiency and the real-time performance of the missile-borne computer system.

Unfolding of a Quadratic Integrable System with a Homoclinic Loop

In this paper, we make a complete study of the unfolding of a quadratic integrable system with a homoclinic loop. Making a Poincare transformation and using some new techniques to estimate the number of zeros of Abelian integrals, we obtain the complete bifurcation diagram and all phase portraits of systems corresponding to different regions in the parameter space. In particular, we prove that two is the maximal number of limit cycles bifurcating from the system under quadratic non- conservative perturbations.

On Superintegrable Systems with a Cubic Integral of Motion

We present a variety of superintegrable systems in polar coordinates possessing a cubic and a quadratic integral of motion, where Noether integrals of kinetic energy are used to build the integrals. In addition, the associated polynomial Poisson algebras with their algebraic dependence relations are exhibited.

Robustness analysis and distributed control of a networked system with time-varying delays

This paper is concerned with the robustness analysis and distributed output feedback control of a networked system with uncertain time-varying communication delays.This system consists of a collection of linear time-invariant subsystems that are spatially interconnected via an arbitrary directed network.Using a dissipation inequality that incorporates dynamic hard lQCs(integral quadratic constraints)for the delay uncertainties,we derive some sufficient robustness conditions in the form of coupled linear matrix inequalities,in which the couplld parts reflect the interconnection structure of the system.We then provide a procedure to construct a distributed controller to ensure the robust stability of the closed-loop system and to achieve a prescribed lzgain performance.The effectiveness of the proposed approach is demonstrated by some numerical examples.

Stable reinforcement learning with recurrent neural networks

In this paper,we present a technique for ensuring the stability of a large class of adaptively controlled systems.We combine IQC models of both the controlled system and the controller with a method of filtering control parameter updates to ensure stable behavior of the controlled system under adaptation of the controller.We present a specific application to a system that uses recurrent neural networks adapted via reinforcement learning techniques.The work presented extends earlier works on stable reinforcement learning with neural networks.Specifically,we apply an improved IQC analysis for RNNs with time-varying weights and evaluate the approach on more complex control system.

Realization of Numbers As the Degrees of Maps between Manifolds

We determine the set of degrees between some classes of oriented closed （n - 1）-connected 2n-manifolds by using the arithmetic theory of quadratic forms.