Incremental Control to Reduce Model Dependency of Classical Nonlinear Control

Incremental control was proposed to reduce the model dependency of classical nonlinear control algorithms. Despite classical nonlinear controllers such as backstepping (BKS) controllers, incremental control systems, such as incremental backstepping (IBKS) controllers, utilize state derivatives and control input measurements instead of model information. In this chapter, we present the design of an incremental controller, and its closed-loop characteristics are provided. Remarkably, in the absence of uncertainties in the model and the measurements, the closed-loop transfer functions with IBKS and BKS are shown to be the same. To display the features of this controller, IBKS is applied to design the controller for a 6-degrees-of-freedom (DoF) unmanned aerial vehicle (UAV). Then, its performance is compared to that of a BKS controller to show that the model dependency is reduced by utilizing the state derivative and control input measurements. A closed-loop analysis with IBKS is conducted for three different cases. In the first test case, which involves model uncertainties and ideal measurements, unlike BKS, the closed-loop stability and performance of IBKS are not affected if the control system is fast enough. In the second test case, wherein both model uncertainties and measurements are biased, a steady-state error is experienced, but the system’s stability is unaltered. In the third test case, which involves model uncertainties and measurement delays, the closed-loop system’s stability is guaranteed by IBKS only if the delays on the state derivatives and the control input measurements satisfy a certain relationship which is dependent on the model uncertainty in the control effectiveness information.