No abstract

Many dynamical systems experience inputs that are difficult to measure. Knowledge of these unknown inputs, from estimation techniques, may improve the performance of a system. However, there may be uncertainty in both the linear model of the plant and the unknown input. An architecture for the estimation of an unknown input simultaneously with the plant internal states is presented. The architecture allows for error in the realization of the dynamical model, which is corrected using an adaptive feedback term. This allows the estimator to recover the correct physical structure of the plant dynamics. Crucial to the approach is an internal model of the unknown input which is generated by an ordinary differential equation. Discussion on the advantages and disadvantages of the input generator follow, along with general considerations for the selection of basis functions for an unknown function space. Convergence proofs are presented along with illustrative examples to demonstrate the theoretical results. This novel scheme will allow for the reliable online estimates of an unknown input with known waveform while also recovering the physical structure of the internal dynamics.

No abstract

Quantum statistical mechanics offers an increasingly relevant theory for a wide variety of probabilistic systems including thermodynamics, particle dynamics, and robotics. Quantum dynamical systems can be described by linear time invariant systems and so there is a need to build out traditional control theory for quantum statistical mechanics. The probability information in a quantum dynamical system evolves according to the quantum master equation, whose state is a matrix instead of a column vector. Accordingly, the traditional notion of a full rank observability matrix does not apply. In this work, we develop a proof of observability for quantum dynamical systems including a rank test and algorithmic considerations. A qubit example is provided for situations where the dynamical system is both observable and unobservable.