LPNN-based approach for LASSO problem via a sequence of regularized minimizations

In compressive sampling theory, the least absolute shrinkage and selection operator (LASSO) is a representative problem. Nevertheless, the non-differentiable constraint impedes the use of Lagrange programming neural networks (LPNNs). We present in this article the -LPNN model, a novel algorithm that tackles the LASSO minimization together with the underlying theory support. First, we design a sequence of smooth constrained optimization problems, by introducing a convenient differentiable approximation to the non-differentiable -norm constraint. Next, we prove that the optimal solutions of the regularized intermediate problems converge to the optimal sparse signal for the LASSO. Then, for every regularized problem from the sequence, the -LPNN dynamic model is derived, and the asymptotic stability of its equilibrium state is established as well. Finally, numerical simulations are carried out to compare the performance of the proposed -LPNN algorithm with both the LASSO-LPNN model and a standard digital method.     

Three-phase four-wire shunt active power filter based on the SOGI filter and Lyapunov function for DC bus control

The three-phase four-wire shunt active power filter (SAPF) was developed to suppress the harmonic currents generated by nonlinear loads, and for the compensation of unbalanced nonlinear load currents, reactive power, and the harmonic neutral current. In this work, we consider instantaneous reactive power theory (PQ theory) for reference current identification based on the following two algorithms: the classic low-pass filter (LPF) and the second-order generalized integrator (SOGI) filter. Furthermore, since an important process in SAPF control is the regulation of the DC bus voltage at the capacitor, a new controller based on the Lyapunov function is also proposed. A complete simulation of the resultant active filtering system confirms its validity, which uses the SOGI filter to extract the reference currents from the distorted line currents, compared with the traditional PQ theory based on LPF. In addition, the simulation performed also demonstrates the superiority of the proposed approach, for DC bus voltage control based on the Lyapunov function, compared with the traditional proportional-integral (PI) controller. Both novel approaches contribute towards an improvement in the overall performance of the system, which consists of a small rise and settling time, a very low or nonexistent overshoot, and the minimization of the total harmonic distortion (THD).     

Stabilization of uncertain boundary control systems

We consider a class of linear infinite-dimensional systems subject to boundary uncertainties, which are linear and time-invariant. Using a deterministic approach to the design of stabilizing feedback controls, uniform exponential stability of the zero state is achieved. Lyapunov techniques are combined with Datko or Ichikawa theory. Three illustrative examples are presented.     

基于一类T-模的模糊Hopfield网络的稳定性分析

本文建立了基于一类T-模的一种动态模糊神经网络-(∨,T)Hopfield网.文章首先证明了系统本身的稳定性及系统平衡态的Lyapunov稳定性,然后建立了吸引子的一个非平凡吸引域,使系统具有良好的容错性.最后,通过例子验证了得到的结论.     

Stability of Equilibria in a Four-dimensional Nonlinear Model of a Hydraulic Servomechanism

Starting from plysical laws a four-dimensional nonlinear model for mecano-hydraulic servomechanisms is deduced. The stability of its equilibria is analysed using a theorem of Lyapunov and Malkin to handle the critical case due to the presence of zero in the spectrum of the matrix of the linear part around equilibria. Stability diagrams are drawn and simulation results are presented through phase diagrams.     

Decentralized adaptive coordinated control of multiple robot arms without using a force sensor

This paper presents a distributed adaptive coordinated control method for multiple robot arms grasping a common object. The cases of rigid contact and rolling contact are analyzed. In the proposed controller, the dynamic parameters of both object and robot arms are estimated adaptively. The desired motions of the robot arms are generated by an estimated object reference model. The control method requires only the measurements of the positions and velocities of the object and robot arms, but not the measurements of forces and moments at contact points. The asymptotic convergence of trajectory is proven by the Lyapunov-like Lemma. Experiments involving two robot arms handling a common object are shown.     

Adaptive switching supervisory control of nonlinear systems with no prior knowledge of noise bounds

The problem of controlling nonlinear noisy systems affected by parametric uncertainties is approached via the introduction of a supervisor which, whenever needed, switches on, in feedback to the plant, a controller selected from a finite set of predesigned controllers. A Lyapunov-based falsification criterion allows one to ensure robust stability in the presence of uncertain constant parameters and exogenous bounded disturbances. Simulations are discussed in order to illustrate the merits of the proposed algorithms.     

Stochastic nonlinear stabilization — II: Inverse optimality

After considering the stabilization of a specific class of stochastic nonlinear systems in a companion paper, in this second part, we address the classical question of when is a stabilizing (in probability) controller optimal and show that for every system with a stochastic control Lyapunov function it is possible to construct a controller which is optimal with respect to a meaningful cost functional. Then we return to the problem from Part I and design an optimal backstepping controller whose cost functional includes penalty on control effort and which has an infinite gain margin.     

Stabilization of inter-area and/or oscillatory modes in large-scale power system by voltage impedance power system (VIPS) apparatus based on decentralized control scheme

New technologies such as power electronics have made it possible to change continuously the impedance of a power system not only to control power flow but also to enhance stability. A power system incorporating a variable impedance apparatus such as a variable series capacitor (VSrC) and high-speed phase shifter (HSPS) is called VIPS (Variable Impedance Power System) by the authors. This paper proposes a novel control method of VIPS apparatus such as VSrC and HSPS installed at an interconnecting point for stabilizing inter-area unstable and/or oscillatory modes. The proposed design method of the control system is a kind of hierarchical decentralized control method of a large-scale power system based on a Lyapunov function. Under the proposed control scheme, each subsystem can be stabilized independently by local controllers such as AVR, speed governor and PSS, and then the whole interconnected system can be stabilized by VIPS apparatus taking into account interactions between subsystems. The effectiveness and robustness of the VIPS apparatus control are shown by numerical examples with model systems including a large-scale power system.