Pareto-based guaranteed cost control of discrete-time uncertain stochastic systems

Abstract

The Pareto-based guaranteed cost control (GCC) of discrete-time uncertain stochastic systems in the infinite horizon is studied. Firstly, the convexity of the weighted sum objective function is proved. Based on this convexity, we demonstrate the relationship between Pareto optimality and minimization of the weighted sum objective function. This relationship confirms that the Pareto-based GCC strategy can be obtained by optimizing the weighted sum objective function. Secondly, to address the Pareto-based GCC issue for discrete-time uncertain stochastic systems, we derive the generalized algebraic Riccati inequality (GARI) specific to these systems. Thirdly, the necessary condition for a Pareto-based guaranteed cost controller is derived using the Karush–Kuhn–Tucker (KKT) condition. Lastly, we introduce a method based on linear matrix inequality (LMI) to determine the Pareto-based GCC strategy. This method reduces computational complexity and establishes the sufficient conditions for a Pareto-based guaranteed cost controller. To validate our findings, we provide a example implemented in MATLAB, confirming the accuracy of the proposed approach.

Keywords

• Pareto game
• KKT conditions
• Linear matrix inequality
• Guaranteed cost control
• Discrete-time uncertain stochastic systems