Adaptive backstepping control for an engine cooling system with guaranteed parameter convergence under mismatched parameter uncertainties

This paper proposes a novel adaptive backstepping control for a special class of nonlinear systems with both matched and mismatched unknown parameters. The parameter update laws resemble a nonlinear reduced-order disturbance observer. Thus, the convergence of the estimated parameter values to the true ones is guaranteed. In each recursive design step, only single parameter update law is required in comparison to the existing standard adaptive backstepping techniques based on overparametrization and tuning functions. To make a fair comparison with the overparametrization and tuning function methods, a second-order nonlinear engine cooling system is taken as a benchmark problem. This system is subject to both matched and mismatched state-dependent lumped disturbances. Moreover, the proposed model-based controllers are compared with a classical PI control by using performance metrics, i.e., root-mean-square error and control effort. The comparative analysis based on these performance metrics, simulations as well as experiments highlights the effectiveness of the proposed novel adaptive backstepping control in terms of asymptotic tracking, global stability and guaranteed parameter convergence.