Abstract
In this paper, the controller based on sliding mode observer (SMO) is studied for a singular biological economic model with stage structure and uncertain parameters. First, a biological economic system is established by the singular system with uncertain parameters for the invasion of alien species. And SMO is designed by use of control inputs and measurement outputs. Then, the integral sliding surface is constructed for the error system and the SMO system. Second, by constructing an augmented system, it is ensured that the system is regular, free of impulse, and stable by use of the linear matrix inequality technique and Lyapunov stability theory. Third, a sliding mode control (SMC) law is designed to guarantee the considered system reaching the sliding mode surface. Finally, the effectiveness of the proposed method is illustrated by a simulation example.
Highlights
With the increasing research of modern control theory and the penetration into other disciplines such as aviation, energy, network, environmental protection, etc., a more generalized dynamic system has been discovered
SLIDING MODE OBSERVER DESIGN This paper mainly studies the population density of alien species
Two novel integral sliding surfaces are constructed for the error system and the sliding mode observer (SMO) system
Summary
With the increasing research of modern control theory and the penetration into other disciplines such as aviation, energy, network, environmental protection, etc., a more generalized dynamic system has been discovered. We all know that in reality, the state of the system is usually not easy to obtain To solve this problem, we construct observers [28]–[30] by considering control inputs and measurement outputs. The emergence of state observers solves many of its problems and provides a broader space for the development of sliding mode control systems, such as replicating disturbances to achieve complete compensation for disturbances. We apply the observer theory to the problem of alien species to obtain the population density of alien species. This is the main contribution of this paper. A. SLIDING MODE OBSERVER DESIGN This paper mainly studies the population density of alien species. According to the proving process of Theorem 1, (34) is obtained LMI
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