Design method of controller based on semi-Markov system with limited controller number

Abstract

The invention discloses a design method of a controller based on a quantity-limited semi-Markov system. The controller design method comprises the following steps: S1, establishing a random hopping system; S2, according to the system established in the step S1, designing controllers with the number limited to be M, wherein M is larger than or equal to 1 and smaller than or equal to N; S3, constructing a corresponding Lyapunov function by utilizing the established system, and calculating to obtain a final control gain and an LMI solving result; and S4, proving that the designed number-limited controller is the minimum variance approximate value of the modal dependent controller. The method for designing the number-limited controller is based on the principle of the mapping relation betweenthe N subsystems and the M controllers and the stationary probability sequence, the sufficient LMI condition for designing the controllers is obtained through the Lyapunov function method. Therefore,the method is suitable for the situation that under the condition that the number of the controllers is limited, the controllers are designed to control the stability of the system according to a minimum variance approximate value of a modal dependent controller.

Description

technical field [0001] The invention relates to the technical field of controller design, in particular to a controller design method based on a semi-Markov system with a limited number of controllers. Background technique [0002] Markovian jumping systems have received a lot of attention in recent years. It is suitable for describing many physical systems whose structure changes suddenly, and is widely used in many fields. It is well known that a characteristic of Markov switching is that the dwell time of each mode follows an exponential distribution. Also, the rate or probability of its transition from one mode to another is usually constant and will have some limitations. Therefore, a semi-Markov process is often introduced. [0003] Most approaches to control synthesis of semi-Markovian process systems fall into two main categories. The first approach is called the modality-dependent approach, where the controller modality corresponds to the subsystem modality, and...

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Problems solved by technology

However, precise access to each subsystem with respect to switching signals is highly desirable and sometimes not

The second is about the design of mode-independent controllers. The number of controllers corresponding to the system synthesis problem is only one, and its switching signal is completely ignored, so sometimes the control results will be very conservative.

However, there will be many possible methods, their effects are not certain, and they cannot be tested one by one.

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