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

Abstract

application-oriented approach to dual control with excitation for closed-loop identification. European Abstract System identification of systems operating in closed loop is an important problem in industrial applications, where model-based control is used to an increasing extent. For model-based controllers, plant changes over time eventually result in a mismatch between the dynamics of any initial model in the controller and the actual plant dynamics. When the mismatch becomes too large, control performance suffers and it becomes necessary to re-identify the plant to restore performance. Often the available data are not informative enough when the identification is performed in closed loop and extra excitation needs to be injected. This article considers the problem of generating such excitation with the least possible disruption to the normal operations of the plant. The methods explicitly take time domain constraints into account. The formulation leads to optimal control problems which are in general very difficult optimization problems. Computationally tractable solutions based on Markov decision processes and model predictive control are presented. The performance of the suggested algorithms is illustrated in two simulation examples comparing the novel methods and algorithms available in the literature.

Active exploration in adaptive model predictive control

“…The state and input constraints defined in (4) and the set dynamics proposed in (12) must be robustly satisfied for all θ ∈ Θ k and disturbances in W. To reformulate these in a convex manner, the following notation is defined…”

“…Proposition 1: Let the state tube {X l|k } N l=0 be parameterized according to (14). Then, the constraints (4) and setdynamics (12) are satisfied if and only if…”

“…However, a lower covariance of the parameter uncertainty might not always translate into improved performance, and the cost function requires tuning the probing effect. These problems can be mitigated by using an application-oriented approach to dual control [12], [13]. Here the probing effect is induced by using a measure of the robust performance, such as worst-case cost, instead of geometric measures of uncertainty.…”

Beyond Persistent Excitation: Online Experiment Design for Data-Driven Modeling and Control

“…Online approaches appear in various contexts in systems and control. We mention iterative feedback tuning [21] that utilizes repeated (closed-loop) experiments, contributions to dual control [22]- [24] that trade-off exploration and exploitation, and adaptive experiment design [25], [26] where optimal experiment design is combined with adaptive parameter estimation. Nonetheless, in the context of Willems' lemma, online input design has not received any attention.…”

Active exploration in adaptive model predictive control

“…These problems can be mitigated by using an applicationoriented approach to dual control [14]. Here, the probing effect is induced by using a measure of the robust performance of the system instead of geometric measures of uncertainty.…”