Limited and short time control method of double-random-jumping system

Abstract

The invention discloses a limited and short time control method of a double-random-jumping system, and relates to multiple-probability description of a multiple-random-jumping system and transient state performance control of a random system within a limited and short period. Firstly, the probability random distribution feature of the double-random-jumping system is described through a Gaussian probability-density function; secondly, by broadening the condition that a system Lyapunov energy function strictly and gradually decreases at a sampling moment, a novel limited and short time stability definition in each mode in a double-random-jumping process is made; thirdly, for an energy bounded disturbance design controller of the system, the process track of a closed-loop system is made to move within a certain range of a balance point in a limited mode, and therefore the requirement for gradual stability is abandoned. According to the limited and short time control method of the double-random-jumping system, for a short-time work system required by actual production requirements, the double-random-jumping phenomenon is taken into account, the requirements for a system energy function are broadened, and an idea is provided for lowering the conservativeness of a common gradual and stable project from the aspect of time.

Description

technical field [0001] The invention relates to a finite time control method of a random jump system, especially a finite short time control method for a double random jump process. The method can be used in biochemical systems, network systems, robot systems, communication systems, economic systems, aerospace and other fields. Background technique [0002] For a long time, control theory has focused on the stability characteristics of the system in the infinite time domain, but in engineering systems, the transient characteristics may be more important. On the one hand, a progressively stable system does not mean good transition characteristics, and sometimes even violent shocks, which cannot meet the requirements of industrial production; on the other hand, many practical systems, such as biochemical systems, economic systems, robot systems, etc. In addition to the asymptotic stability of the system in the infinite time domain, people are more interested in whether it can...

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Problems solved by technology

On the one hand, a progressively stable system does not mean good transition characteristics, and sometimes even violent shocks, which cannot meet the requirements of industrial production; on the other hand, many practical systems, such as biochemical systems, economic systems, robot systems, etc. In addition to focusing on its asymptotic stability in the infinite time domain, people are often more interested in whether it can meet the transient requirements in a finite short time

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