Adaptive parameter identification and state estimation with partial state information and bounded disturbances

In this paper, we present a joint state and adaptive parameter identification scheme for the cases when all the states of the system are measured and when only some states of the system are measured. When all the states are measured, we show that, in the presence of process and measurement noise, the state and parameter estimation errors are bounded. To this end, we show that this is possible only through the appropriate design of a virtual input which ensures that the system error signals are bounded. As a special case of all the states being measured, we show that in the case of a noise free system, the state estimation errors converge to the origin. For the case when only some states are measured, we show that for a linear system with n states, m inputs and p measurements, we can estimate at most p² entries of the system matrix and pm entries of the input matrix.