Application set approximation in optimal input design for model predictive control

Abstract

Abstract-This contribution considers one central aspect of experiment design in system identification. When a control design is based on an estimated model, the achievable performance is related to the quality of the estimate. The degradation in control performance due to errors in the estimated model is measured by an application cost function. In order to use an optimization based input design method, a convex approximation of the set of models that satisfies the control specification is required. The standard approach is to use a quadratic approximation of the application cost function, where the main computational effort is to find the corresponding Hessian matrix. Our main contribution is an alternative approach for this problem, which uses the structure of the underlying optimal control problem to considerably reduce the computations needed to find the application set. This technique allows the use of applications oriented input design for MPC on much more complex plants. The approach is numerically evaluated on a distillation control problem.

Model Predictive Control oriented experiment design for system identification: A graph theoretical approach

“…The constraint (9) is in general non-convex. Thus, to further simplify the problem we will use its ellipsoidal approximation which results in the following Linear Matrix Inequality (LMI), see (Ebadat et al, 2014a) 1…”

An application-oriented approach to dual control with excitation for closed-loop identification

“…The expression (18) requires calculation of the Hessian of the application cost. This often requires numerical calculations and a simulations based scheme for this is given by Ebadat et al (2014a). The application-oriented input design above requires knowledge of the true system parameters, θ o .…”

Stochastic Model Predictive Control with Integrated Experiment Design for Nonlinear Systems

“…V app (θ) is defined in terms of the difference between the measured system states when the controller is designed using the true parameter values θ 0 and when the controller is designed using perturbed parameters θ (Ebadat et al, 2014)…”

“…where the second derivative V app (θ 0 ) can be approximated by the Hessian matrix of the system states (Ebadat et al, 2014). Notice that the application cost function and its derivatives are dependent on the true parameters θ 0 , which are unknown.…”