Self-Tuning Control for Nonlinear Systems Using a State-Dependent Riccati Equation Approach

This paper presents a self-tuning algorithm for a nonlinear spring-mass damper system that uses a quasi-linear state-space representation and allows for automatic optimisation w.r.t. a chosen evaluation cost function (ECF). This algorithm addresses nonlinear system models with only approximately known system parameters. Using extended linearisation techniques, an equivalent quasi-linear system representation is established first. Based on this linear model representation, an optimal controller is calculated by solving state-dependent Riccati equations (SDREs) corresponding to a design cost function with weighting parameters to be optimised. Using a modified Nelder-Mead algorithm, the proposed self-tuning algorithm allows for the optimisation of the design cost function. The algorithm is applied to a nonlinear spring-mass-damper system and the main advantages of this approach are demonstrated in simulations. Moreover, the impact of model uncertainties as well as additional sensor noise and unknown disturbances on the optimisation routine is evaluated. Finally, the simulation results are compared to each other - showing clearly the efficiency and the benefits of the overall approach.