Robust Generalized Incremental Predictive Control: An Approach for Bounded Uncertain Systems

This paper proposes a robust control method known as robust generalized incremental predictive control (RGIPC) for uncertain systems characterized by bounded uncertainties in both the system and input matrices. Conventional control strategies, such as H[Formula: see text] and traditional predictive controllers, face considerable challenges in maintaining a satisfactory balance between performance and robustness under such demanding conditions. To address these challenges, the newly framework integrates structured uncertainties into the optimization cost function, improving robustness in practical applications. This approach converts complex differential optimization equations into algebraic forms over a finite horizon, simplifying the derivation of optimal control signals. The RGIPC can be applied to control design by defining the design bounds. The proposed method comprises a two-step process: first, determining the appropriate design boundaries, and second, analytically computing the robust predictive control signal within the defined bounds during finite-horizon optimization. To thoroughly evaluate the proposed method, two benchmark systems are examined: an inverted pendulum, representing unstable and nonminimum phase dynamics, and a nonlinear multiple-input multiple-output (MIMO) flying object system exhibiting highly statically unstable dynamics with cross-coupling effects. Comparative analysis with H[Formula: see text] and generalized incremental predictive control (GIPC) methods confirms the superior performance of the proposed framework across all evaluation metrics. The obtained results demonstrate substantial enhancements in multiple key areas: Reduced overshoot, improved disturbance rejection, strengthened robustness against model uncertainties, enhanced noise attenuation capabilities, and more efficient control signals.