A View of SDRE Control Methods as One Branch of Indirect Adaptive Control

Abstract

Current popular State Dependent Riccati Equation (SDRE) control methods, which have recently received a lot of attention in the control community, have been perceived as one branch of adaptive control. Their ability to re-compute the controller gain in real time based on the State Dependent Coefficient (SDC) matrix pair [A(x(t)), B(x(t))] can be viewed as an equivalent approach to the indirect adaptive control design paradigm. The SDC pair captures new knowledge of the vehicle's dynamics from the dynamic state vector signatures without explicitly relying on an onboard parameter estimator. This paper presents such a view with a detailed comparison using an architecture-based functional block diagram to justify that observation. The premise that SDRE control methods can be viewed as an equivalent Indirect Adaptive Control DesignMethodology (i.e., self tuning regulator (STR) with an onboard parameter estimator) is supported by the following statement. SDRE design methods adaptively compute the gain matrix via an approximation to the Hamilton Jacobi Bellman (HJB) based optimization process (i.e., self tuning aspect) using an implicit on-board parameter estimator. This is virtually achieved by having the SDRE actual state vector x(t) driving the SDC pair [A(x(t)), B(x(t))] as the provider of new knowledge which is supplied to the controller tuning process. A satellite attitude pointing and control system is used to illustrate the comparison of both architectures and simulation assessments. The results from this example lead to the conclusion that the SDRE method is truly one branch of Indirect Adaptive Control. Discussion of the SDRE control performance as an indirect adaptive controller is provided to facilitate practitioners use of this design methodology for problems requiring adaptive control and to facilitate theorists to further solidify this thinking.