Abstract
Nonlinear model predictive control has been established as a powerful methodology to provide feedback for dynamic processes over the last decades. In practice it is usually combined with parameter and state estimation techniques, which allows to cope with uncertainty on many levels. To reduce the uncertainty it has also been suggested to include optimal experimental design into the sequential process of estimation and control calculation. Most of the focus so far was on dual control approaches, i.e., on using the controls to simultaneously excite the system dynamics (learning) as well as minimizing a given objective (performing). We propose a new algorithm, which sequentially solves robust optimal control, optimal experimental design, state and parameter estimation problems. Thus, we decouple the control and the experimental design problems. This has the advantages that we can analyze the impact of measurement timing (sampling) independently, and is practically relevant for applications with either an ethical limitation on system excitation (e.g., chemotherapy treatment) or the need for fast feedback. The algorithm shows promising results with a 36% reduction of parameter uncertainties for the Lotka-Volterra fishing benchmark example.
Highlights
We start by surveying recent progress of feedback via nonlinear optimal control under uncertainty, before we come to the main contribution of this paper, an investigation of the role of the measurement time grid
The initial values are obtained from a state and parameter estimation performed on the interval [0,15] with measurement time points derived from a optimal experimental design problem
Highlighting its flexibility, we exemplarily look at a possible robustification of the optimal control and of the optimal experimental design problem
Summary
We start by surveying recent progress of feedback via nonlinear optimal control under uncertainty, before we come to the main contribution of this paper, an investigation of the role of the measurement time grid. We propose a new feedback optimal control algorithm with sampling time points for the parameter and state estimation from the solution of an optimal experimental design problem. Our approach is complementary in the sense that, e.g., the numerical structure exploitation, the treatment of systematic disturbances, the treatment of robustness, the formulation of dual control objective functions, the use of scenario trees or set-based approaches can all be combined with an adaptive measurement grid This applies to the nature of the underlying control task, where many extensions are possible, e.g., multi-stage processes, mixed path- and control constraints, complicated boundary conditions and so on. The mathematical formulation of the underlying dynamical system and of the three different types of optimization problems, i.e., parameter and state estimation, optimal control, and optimal experimental design are introduced We explain the advantages of our decoupled dual control approach with respect to an efficient solution of the experimental design problem
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