Monitoring function based extremum seeking control for uncertain relative degrees with light source seeking experiments

Abstract

In this paper, we consider the problem of seeking a light source with a cart-track linear positioning servomechanism. The cart does not have the capability of sensing its position/velocity or the position of the source but is capable of sensing the light signal generated by a light bulb. The light field created by the light source decays away from the position of the light bulb but the servo does not have the knowledge of the functional form of this field. We employ an extremum seeking control strategy based on monitoring functions recently proposed by the authors. First, we briefly introduce the theoretical results of the monitoring function based extremum seeking controller for one-dimensional (1D) optimization. The class of systems previously considered was restricted to the relative degree one case. Here, as a theoretical contribution, generalization is achieved to include more general dynamics with arbitrary and uncertain relative degrees. In lieu of using differentiators to compensate the relative degree, a time-scaling procedure is developed. Then, we present the design for a light-seeking servomechanism and obtain experimental results of such a mounted device performing localizing and tracking of the level-sets of the light source.

Energy Management Considering Unknown Dynamics Based on Extremum Seeking Control and Particle Swarm Optimization

“…Consequently, the fitness value can be calculated by the PSO algorithm. Then, the price is updated by the PSO algorithm based on (17) and (18). The PSO algorithm and the ESC algorithm are repeated until the price and the power consumption converge or the maximum number of iterations is reached.…”

“…For example, gradient-based algorithms are used in [5], [6], and [10]- [12], numerical algorithms are considered in [13] and [14], and bioinspired algorithms are applied in [15] and [16]. It is noted that unknown dynamics exist in the operation of some typical appliances, such as the heating, ventilation, and air conditioning (HVAC) system [17] and the lighting system [18]. In this case, the gradientbased algorithms cannot be used, and the numerical algorithms and bioinspired algorithms are not suitable for the dynamic system.…”

Controle Extremal para Mapeamentos Dinâmicos Multivariáveis usando Função de Monitoração e Busca Cíclica

“…O escalonamento temporal reduz a ordem do sistema dinâmico estável e permite a análise e projeto de controladores por busca extremal, independentemente da ordem ou grau relativo do modelo e o conhecimento exato de seus parâmetros (Oliveira et al, 2014).…”

Controle Multivariável para Busca Extremal Cíclica Usando Modos Deslizantes e Função de Chaveamento Periódica

“…O método mais conhecido baseiase em sinais de excitação periódica ou dithers (Krstić and Wang, 2000). Outra abordagem trata do controle extremal utilizando funções de monitoração e modos deslizantes (Aminde et al, 2013;Oliveira et al, 2014), onde a função de monitoraçãoé usada para suprir a falta de conhecimento da direção de controle.…”