IDENTIFICATION FROM A "SMALL" NUMBER OF SAMPLES

Subspace identification methods may produce unreliable model estimates when a small number of noisy measurements are available. In such cases, the accuracy of the estimated parameters can be improved by using prior knowledge about the system. The prior knowledge considered in this work is constraints on the impulse response. It is motivated by availability of information about the steady-state gain, overshoot, and rise time of the system, which in turn can be expressed as constraints on the impulse response. The method proposed has two steps: 1) estimation of the impulse response with linear equality and inequality constraints, and 2) realization of the estimated impulse response. The problem on step 1 is shown to be a convex quadratic programming problem. In the case of prior knowledge expressed as equality constraints, the problem on step 1 admits a closed form solution. In the general case of equality and inequality constraints, the solution is computed by standard numerical optimization methods. We illustrate the performance of the method on a mass-springdamper system.