An adaptive method with weight matrix as a function of the state to design the rotatory flexible system control law

One of the most well-known techniques of optimal control is the theory of Linear Quadratic Regulator (LQR). This method was originally applied only to linear systems but has been generalized for non-linear systems: the State Dependent Riccati Equation (SDRE) technique. One of the advantages of SDRE is that the weight matrix selection is the same as in LQR. The difference is that weights are not necessarily constant: they can be state dependent. Then, it gives an additional flexibility to design the control law. Many are applications of SDRE for simulation or real time control but generally SDRE weights are chosen constant so no advantage of this flexibility is taken. This work serves to show through simulation that state dependent weights matrix can improve SDRE control performance. The system is a non-linear flexible rotatory beam. In a brief first part SDRE theory will be explained and the non-linear model detailed. Then, influence of SDRE weight matrix associated with the state Q will be analyzed to get some insight in order to assume a state dependent law. Finally, these laws are tested and compared to constant weight matrix Q. Based on simulation results; one concludes showing the benefits of using an adaptive weight Q rather than a constant one.