Non‐linear feedback optimal control law for minimum‐time injection problem using fuzzy system

To devise a new technique to synthesise optimal feedback control law for non‐linear dynamic systems through fuzzy logic.

The proposed methodology utilizes the open‐loop optimal control solutions (OCSs) of the non‐linear systems for the training of the fuzzy system in the process of developing closed‐loop fuzzy logic guidance (FLG). This is achieved through defining a set of non‐dimensionalised variables related to the system states.

FLG is capable of generating closed‐loop control law for the non‐linear problem investigated. Since the proposed fuzzy structure is independent of the system equations, the approach is potentially applicable to other non‐linear system. Introduction of the non‐dimensional variables in place of the regular states has effectively increased the fuzzy training performance and greatly reduced the number of fuzzy rule bases required to produce accurate solutions for other untrained scenarios.

There exist many complex non‐linear problems in guidance and control of aerospace vehicles. Determination of optimal control laws for such systems is usually a difficult task even in an open‐loop form and in a noise‐free off‐line environment. On the other hand, closed‐loop OCSs are highly desirable for their robust characteristics in actual operating environments, so are more suitable for online applications, but can seldom be realized for complex non‐linear systems. Even though a few researchers have worked in the area of non‐linear optimal control and application of fuzzy logic on such systems, non‐have dealt with closed‐loop optimal fuzzy controllers. This research proposes a new strategy for the determination of optimal feedback control laws for non‐linear systems, which can be utilized in many spacecraft mission applications.