Control Performance Orientated Region Stabilization and <i>H</i> _∞ Control of Discrete Stochastic Systems: A Data-Driven Approach

A data-driven <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control method with dynamic performance constraints is proposed for the problem of region stabilization control in the case of unknown system matrix. By establishing a system characterization model based on measured data, the generalized pole configuration theory is ingeniously combined with the data-driven control framework. Firstly, the real-time data generated from the system operation is used to construct a data-driven dynamic characterization. A generalized pole constraint-based regional constraints condition is established to accurately regulate the state convergence rate and damping response characteristics while ensuring the stability of the closed-loop system. The classical <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control framework is further integrated to construct a novel data-driven <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance criterion to achieve the synergistic optimization of dynamic performance constraints and disturbance suppression capability. The method gets rid of the dependence on the a priori model of the system and solves the co-optimization problem of unknown system dynamic performance regulation and robustness enhancement under a unified framework. Numerical simulations and power system control case validations show that the integrated control performance of uncertain complex systems is significantly improved.