Optimal interval controller design for uncertain systems

Abstract

The interval controller design is a hot issue for uncertain systems, whereas how to design an optimal interval controller under the premise of ensuring system stability is a difficult problem that needs further study. This paper mainly aims at the single input single output uncertain system to propose an optimal interval controller based on the Kharitonov theorem and an interval optimization algorithm, which can guarantee the stability and optimization of a closed‐loop interval system. According to the Kharitonov theorem, the optimal interval controller design can be transformed into an optimal controller synthesis issue of multiple vertex objects. An interval particle swarm optimization (IPSO) algorithm is then used to optimize the quadratic performance index with interval variables for each vertex object to obtain the solution domains of the controller parameters, and the vertex method is utilized to prevent interval width expansion or divergence in the iteration. Finally, the intersections of the solution domains for all vertex objects are obtained as the optimal interval solution of interval controller parameters. In addition, the stability verification approach of the closed‐loop system and the empirical rule to select the interval particle width are given. Simulation results for typical examples demonstrate that the designed interval controller not only performs optimally but also can robustly stabilize the interval system.

Experimental study on robust non‐fragile control of DC‐DC buck converter

“…This method identifies the boundary region of controller parameters based on Kharitonov's theorem. The theorem provides a set of sufficient conditions for the stability of a polynomial system, given the ranges of variation of its uncertain parameters [19,20]. In the case of Kharitonov's theorem, instead of analyzing the stability of a single polynomial, we consider a family of polynomials, each corresponding to a specific range of variation of the uncertain parameters.…”