Abstract
This paper presents a novel approach to automatic design of a robust optimal controller for interval plants with Genetic Programming based on Kharitonov Theorem (KT), which provides a theoretical foundation in the design of robust controller for interval plants. The structure and parameters of the robust optimal controller for interval plants are optimized by Genetic Programming and the Generalized KT related stability criteria are integrated into the solution to guarantee the stability of the closed-loop system. Consequently, the evolved controller not only minimizes time-weighted absolute error (ITAE) of the closed-loop system, but also stabilizes the whole interval plant family robustly. Finally, the simulations on a benchmark problem show that the proposed method can effectively generate a robust optimal controller for interval plants.
Highlights
During the last few decades, significant progresses have been made in the realm of robust stability and control for parameter uncertain systems.1-6 The Kharitonov Theorem has been one of the most popular approaches to investigate stability of interval systems via four vortex polynomials with real-valued min-max bounds.7 Based on Kharitonov Theorem, both Edge Theorems and Box Theorems suggest that the set of transfer functions generated by changing the perturbed coefficients in the parameter ranges correspond to a box in parameter space and are referred to “interval plants”.8,9 the stability criterion of the entire family of infinite interval plants can be simplified to only check the stability with limited number of systems
The objective of this study is to develop a novel robust optimal controller synthesis approach for interval plants in terms of Genetic Programming (GP) associated with Kharitonov Theorem
A novel solution has been developed to automatically evolve a discrete robust optimal controller for interval plant family by integrating rigorous mathematical stability criteria into GP evolution, which is formulated as an optimization of time domain index on the worst cases revealed by Kharitonov Theorem
Summary
During the last few decades, significant progresses have been made in the realm of robust stability and control for parameter uncertain systems. The Kharitonov Theorem has been one of the most popular approaches to investigate stability of interval systems via four vortex polynomials with real-valued min-max bounds. Based on Kharitonov Theorem, both Edge Theorems and Box Theorems suggest that the set of transfer functions generated by changing the perturbed coefficients in the parameter ranges correspond to a box in parameter space and are referred to “interval plants”.8,9 the stability criterion of the entire family of infinite interval plants can be simplified to only check the stability with limited number of systems. It should be emphasized that one of the major disadvantages preventing the GP applications in control engineering is the lack of mathematical foundation in stability, reliability and robustness under system parameter uncertainties.. It should be emphasized that one of the major disadvantages preventing the GP applications in control engineering is the lack of mathematical foundation in stability, reliability and robustness under system parameter uncertainties.20 All those issues are vitally critical when designing a robust controller with desired performances subject to the relevant constraints. The Generalized Kharitonov Theorem is integrated into the heuristic genetic programming method to guarantee that the evolved controller can strictly stabilize entire family of the interval plants and minimize the worst case Integral of Time-weighted Absolute Error (ITAE) in the mean time, which has never been studied before.
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