An artificial neural network is proposed as a function approximator for empirical modeling of a Lyapunov function for a nonlinear dynamic system that projects stable behavior as potentially observable in its state space. Theoretical framework for the methodology of designing the so-called Lyapunov neural network, which empirically models a Lyapunov function, is described. Algorithms for trainin...

This article investigates dynamical camera switching during visual servoing tasks using multicamera systems considering image-based and position-based Jacobian transpose control schemes. Stability is discussed using a common Lyapunov function assuming ideal target and camera models and multiple Lyapunov functions under parameter perturbations. It is shown that asymptotical stability cannot be a...

DONG, KE. Advanced Design Techniques in Linear Parameter Varying Control. (Under the direction of Associate Professor Fen Wu). To improve the analysis and control synthesis approach of linear fractional transformation (LFT) parameter-dependent systems, two types of non-quadratic Lyapunov function and switching control scheme are introduced and studied in this thesis. A gain-scheduled controller...

We introduce a new algorithm to check the local stability and compute the region of attraction of isolated equilibria of nonlinear systems with polynomial vector fields. First, we consider an arbitrary convex polytope that contains the equilibrium in its interior. Then, we decompose the polytope into several convex sub-polytopes with a common vertex at the equilibrium. Then, by using Handelman’...

By employing feedback control laws, the robust stochastic stability of distributed parameter large-scale control systems under random structural perturbations is investigated. The results are obtained by using vector Lyapunov-like functionals in the context of the block-comparison theorem, the theory of systems of differential inequalities, and decomposition-aggregation method. The complexity v...

This paper proposes an adaptive feedback controller for a class of chaotic systems. This controller can be used for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system. Based on Lyapunov approach, the adaptation law is determined to tune the controller gain vector in order to track a predetermined linearizing feedback control. To demonstrate the efficiency of ...

In this article, we consider the problem of estimating a scalar field using network mobile sensors which can measure value at their instantaneous location. The to be estimated is assumed represented by positive definite radial basis kernels and use techniques from adaptive control Lyapunov analysis prove stability proposed estimation algorithm. convergence parameter values true guaranteed plann...

We consider Lyapunov exponents of random iterates of monotone homogeneous maps. We assume that the images of some iterates are lines, with positive probability. Using this memory-loss property which holds generically for random products of matrices over the max-plus semiring, and in particular, for Tetris-like heaps of pieces models, we give a series expansion formula for the Lyapunov exponent,...

This paper studies the exponential stabilization problem for discrete-time switched linear systems based on a control-Lyapunov function approach. A number of versions of converse control-Lyapunov function theorems are proved and their connections to the switched LQR problem are derived. It is shown that the system is exponentially stabilizable if and only if there exists a finite integer N such...