A Robust Control Framework for Direct Adaptive State Estimation with Known Inputs for Linear Time-Invariant Dynamic Systems

Many dynamic systems experience unwanted actuation caused by an unknown exogenous input. Typically, when these exogenous inputs are stochastically bounded and a basis set cannot be identified, a Kalman-like estimator may suffice for state estimation, provided there is minimal uncertainty regarding the true system dynamics. However, such exogenous inputs can encompass environmental factors that constrain and influence system dynamics and overall performance. These environmental factors can modify the system’s internal interactions and constitutive constants. The proposed control scheme examines the case where the true system’s plant changes due to environmental or health factors while being actuated by stochastic variances. This approach updates the reference model by utilizing the input and output of the true system. Lyapunov stability analysis guarantees that both internal and external error states will converge to a neighborhood around zero asymptotically, provided the assumptions and constraints of the proof are satisfied.