Stability and stabilization of one class of three time-scale systems with delays

summary:A singularly perturbed linear time-invariant time delay controlled system is considered. The singular perturbations are subject to the presence of two small positive multipliers for some of the derivatives in the system. These multipliers (the parameters of singular perturbations) are of different orders of the smallness. The delay in the slow state variable is non-small (of order of $1$). The delays in the fast state variables are proportional to the corresponding parameters of singular perturbations. Three much simpler parameters-free subsystems are associated with the original system. It is established that the exponential stability of the unforced versions of these subsystems yields the exponential stability of the unforced version of the original system uniformly in the parameters of singular perturbations. It also is shown that the stabilization of the parameters-free subsystems by memory-free state-feedback controls yields the stabilization of the original system by a memory-free state-feedback control uniformly in the parameters of singular perturbations. Illustrative examples are presented

International Conference on Dynamic Control and Optimization - DCO 2021: book of abstracts

Sem resumo disponível.publishe

Робастная стабилизируемость и стабилизация трехтемповых линейных стационарных сингулярно возмущенных систем с запаздыванием

The objective of this study is to obtain the stabilizability conditions and a stabilizing composite state feedback control for the exponential stabilization of three-time-scale singularly perturbed linear time-invariant systems with multiple commensurate delays in the slow state variables and with two small parameters of perturbation (TSPLTISD). The stabilizability conditions and the stabilizing feedback do not depend on the small parameters and are valid for all of their sufficiently small values. The approach used in this work is the nondegenerate decoupling transformation that splits the TSPLTISD into three regularly dependent on the small parameters subsystems, which are lower in dimensions than the TSPLTISD. Further, the decoupled subsystems are approximated by three subsystems that do not depend on the small parameters. It is proven that the stabilizability of the approximating subsystems guarantees the robust (with respect to small parameters) stabilizability of the original TSPLTISD. Finally, we obtain a representation of a parameter free composite feedback control for the TSPLTISD, stabilizing it for all sufficiently small values of the parameters. A numerical example is given. Целью работы является получение условий стабилизируемости и построение композитной стабилизирующей обратной связи по состоянию для трехтемповых линейных стационарных сингулярно возмущенных систем с кратными соизмеримыми запаздываниями в медленных переменных состояния и с двумя малыми параметрами при части старших производных (ТСВЛССЗ). Условия стабилизируемости и стабилизирующая обратная связь не зависят от малых параметров и действительны для всех их достаточно малых значений. Применяемый в работе подход использует невырожденное преобразование, которое полностью расщепляет зависящую от двух малых параметров сингулярно возмущенную систему на три регулярно зависящие от параметров подсистемы меньших размерностей, чем исходная система, которые аппроксимируются подсистемами, не зависящими от малых параметров. Доказано, что стабилизируемость аппроксимирующих подсистем гарантирует робастную (по малым параметрам) стабилизируемость исходной ТСВЛССЗ. Получено представление не зависящего от параметра композитного управления с обратной связью для ТСВЛССЗ, стабилизирующего ее при всех достаточно малых значениях параметров. Приведен численный пример.

Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance

Issued as Progress report, and Final report, Project no. E-21-67

Book of Abstracts

USPCAPESFAPESPCNPqINCTMatICMC Summer Meeting on Differentail Equations.\ud São Carlos, Brasil. 3-7 february 2014

Dynamical problems and phase transitions

Issued as Financial status report, Technical reports [nos. 1-12], and Final report, Project B-06-68

A vision-based optical character recognition system for real-time identification of tractors in a port container terminal

Automation has been seen as a promising solution to increase the productivity of modern sea port container terminals. The potential of increase in throughput, work efficiency and reduction of labor cost have lured stick holders to strive for the introduction of automation in the overall terminal operation. A specific container handling process that is readily amenable to automation is the deployment and control of gantry cranes in the container yard of a container terminal where typical operations of truck identification, loading and unloading containers, and job management are primarily performed manually in a typical terminal. To facilitate the overall automation of the gantry crane operation, we devised an approach for the real-time identification of tractors through the recognition of the corresponding number plates that are located on top of the tractor cabin. With this crucial piece of information, remote or automated yard operations can then be performed. A machine vision-based system is introduced whereby these number plates are read and identified in real-time while the tractors are operating in the terminal. In this paper, we present the design and implementation of the system and highlight the major difficulties encountered including the recognition of character information printed on the number plates due to poor image integrity. Working solutions are proposed to address these problems which are incorporated in the overall identification system.postprin

Job shop scheduling with artificial immune systems

The job shop scheduling is complex due to the dynamic environment. When the information of the jobs and machines are pre-defined and no unexpected events occur, the job shop is static. However, the real scheduling environment is always dynamic due to the constantly changing information and different uncertainties. This study discusses this complex job shop scheduling environment, and applies the AIS theory and switching strategy that changes the sequencing approach to the dispatching approach by taking into account the system status to solve this problem. AIS is a biological inspired computational paradigm that simulates the mechanisms of the biological immune system. Therefore, AIS presents appealing features of immune system that make AIS unique from other evolutionary intelligent algorithm, such as self-learning, long-lasting memory, cross reactive response, discrimination of self from non-self, fault tolerance, and strong adaptability to the environment. These features of AIS are successfully used in this study to solve the job shop scheduling problem. When the job shop environment is static, sequencing approach based on the clonal selection theory and immune network theory of AIS is applied. This approach achieves great performance, especially for small size problems in terms of computation time. The feature of long-lasting memory is demonstrated to be able to accelerate the convergence rate of the algorithm and reduce the computation time. When some unexpected events occasionally arrive at the job shop and disrupt the static environment, an extended deterministic dendritic cell algorithm (DCA) based on the DCA theory of AIS is proposed to arrange the rescheduling process to balance the efficiency and stability of the system. When the disturbances continuously occur, such as the continuous jobs arrival, the sequencing approach is changed to the dispatching approach that involves the priority dispatching rules (PDRs). The immune network theory of AIS is applied to propose an idiotypic network model of PDRs to arrange the application of various dispatching rules. The experiments show that the proposed network model presents strong adaptability to the dynamic job shop scheduling environment.postprin