Studies of online optimization methods for experimental test design and state estimation.

摘要

This work investigates optimization approaches for test signal design for MIMO identification. In addition, an efficient approach to solving constrained estimation problems is proposed.;Model-based multivariable control requires good quality process models which, in addition to standard specifications for model quality, also satisfy the integral controllability condition. Satisfying the integral controllability condition guarantees that the resulting closed-loop controller is robustly stabilizing. The primary focus of the research is in developing a framework for designing experiments for linear 1 systems which satisfy the integral controllability condition. A challenge with the integral controllability condition is that it involves the unknown plant. However, we show how the uncertainty description for the model gains can be incorporated into an algebraic upper bound for the integral controllability condition. The resulting mathematical framework, which makes no distinction between well- and ill-conditioned systems, allows for the rigorous design of experiments to identify multivariable system models that satisfy the integral controllability condition. Experimental designs previously postulated are recovered, while a variety of new designs are proposed which are shown to depend on constraint specifications for the inputs and outputs.;Secondly, we investigate model predictive control and identification (MPCI) for multivariable systems. MPCI combines control and identification objectives into a single optimization problem. In addition to the standard MPC constraints associated with inputs and outputs, MPCI includes a constraint on the persistent excitation condition to satisfy identification objectives. Previous investigations with MPCI were limited to the SISO case. Here we extend MPCI to the multivariable case for the finite impulse response (FIR) model form. MPCI is shown to perform well on both ill- and well-conditioned examples, with the resulting models satisfying the integral controllability condition.;Lastly, a solution is proposed for efficiently solving the constrained moving horizon estimation problem (MHE) subject to inequality constraints, in a manner akin to Kalman filtering. The proposed method allows the on-line constrained optimization problem to be solved offline, requiring only a look-up table and simple function evaluations for real-time implementation. The method is illustrated via simulation.