Parametric control to quasi-linear systems based on dynamic compensator and multi-objective optimization

Abstract

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Parametric method to design dynamic compensator for descriptor high‐order quasi‐linear systems

“…where λ i ∈ ℂ − , i = 1, 2, …, n e , then Corollary 4 for Theorem 2 is provided with regard to Problem 2. Corollary 4: Let N(θ, y, s), D(θ, y, s) and N (θ, y, s), D (θ, y, s) be two pairs of polynomial matrices satisfying RCFs (21) and (24), respectively.…”

“…Our team has paid more attention to the quasi-linear system and obtained a series of research results, such as descriptor quasi-linear systems [19][20][21] and dynamic compensators with multi-objective optimisation [19,[22][23][24][25]. Notably, we also present an effective approach to design a static output feedback and a dynamic compensator for high-order quasi-linear systems (see [26,27]), which provides the basis to deal with the parametric design of a dynamic compensator for DHQ systems.…”

Output feedback predictive control for discrete quasilinear systems with application to spacecraft flying‐around

“…Proof Considering the lemma on eigenvector matrix in [26] obtains combined with A c ( θ , y ) in (), the generalized Sylvester equation is given as with then using the solution of generalized Sylvester equation in [35], V ( θ , y ) and W c ( θ , y ) are given in (), further, based on () and (), K ( θ , y ) can be obtained in () easily. This completes the proof.…”

“…Quasilinear systems, whose coefficient matrices include system outputs and time‐varying parameters, can maintain strong‐coupled and highly nonlinear characteristics but can be expressed in a linear form, which is regarded as the link and bridge between general nonlinear system and linear system [24]. So far, it has been widely used to be the mathematical model of some practical applications, such as spacecrafts rendezvous [25], attitude control of combined spacecrafts [26], circuits systems [27], chaos synchronization [28], and so on [29,30]. However, there is still a blank on control of discrete quasilinear systems, an interesting and valuable topic.…”

Controllability results for quasi‐linear systems: Standard and descriptor cases

“…Quasi-linear systems are commonly used for the modeling of spacecraft rendezvous [18], chaotic systems synchronization [19], spacecraft attitude control [20,21], circuit systems [22,23], and so on, which have a wide range of engineering applications. Meanwhile, quasi-linear systems maintain strong coupling and highly nonlinear characteristics but in a linear format, which can be regarded as the bridge and link between linear systems and nonlinear systems.…”