Subspace identification with constraints on the impulse response

Subspace identification methods 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 paper is constraints on the impulse response, e.g., steady-state gain, overshoot, and rise time. 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-spring-damper system.