Adaptive suboptimal H_∞ control for time-varying systems with uncertainty, unknown parameters and disturbance

The design of optimal (Formula presented.) control becomes significantly more challenging in the presence of time-varying parameters, uncertainties and external disturbances. Existing solution methods under such conditions are often characterised by high computational complexity, infeasibility and inefficiency. This study introduces a new control strategy called adaptive suboptimal (Formula presented.) control (ASHC), which includes a suboptimal (Formula presented.) controller and a model reference adaptive control, offering a more efficient and practical alternative to conventional methods. The suboptimal (Formula presented.) controller component eliminates disturbances by solving the Riccati equation online, even with unknown parameters, while the adaptive control component compensates for time-varying parameters and parametric uncertainties. In fact, by leveraging the advantages of both adaptive and robust controllers, the proposed method achieves superior performance in handling uncertainties and disturbances compared to classical methods. To validate its performance, the ASHC was applied to a servomechanism and a spring-mass-damper system. Comparative analysis with methods such as PID, adaptive, robust and fractional-order sliding mode PID control reveals the superior capability of the proposed controller in compensating for system uncertainties and external disturbances.