A Feedback Optimal Control Algorithm with Optimal Measurement Time Points

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.

Inverse Tangent Functional Nonlinear Feedback Control and Its Application to Water Tank Level Control

“…Similarly, references [15][16][17] researched nonlinear control, such as a robust adaptive fuzzy neural network control algorithm to design a PID controller for heading control of unmanned marine vehicles and a Non-Linear Dynamic Inversion Control to compare the primary differences between three multi-rotor platforms, and a closed-loop control system were implemented where applicable. Some other nonlinear control models were also established and proposed from different perspectives [18][19][20][21]. Be that as it may, all aforementioned references were researched thoroughly from different points of view and attained certain achievements with respects to water tank level control by using different control modes.…”

Mathematical Models for the Influence of Cytarabine on White Blood Cell Dynamics in Acute Myeloid Leukemia

“…If predictions from personalised mathematical models were reliable and accurate, they could be used for providing better care to AML patients receiving Ara-C consolidation treatment, e.g. in an automatized measurement–decision support loop [4, 5]. Precisely identifying the period of Ara-C-induced profound leukopenia and modification of treatment schedules based on such predictions might enable prevention of severe infectious complications, sepsis, and thus delay to undergo subsequent treatment cycles.…”

Optimal Experimental Design for Parameter Estimation of an IL-6 Signaling Model

“…While these measurements y are discrete in nature, the assumption that y is a continuous variable can be made if the sampling frequency is sufficiently high. Optimal experimental design involves maximizing a criterion function that indicates the quantity of information gained by a given experiment, often in the context of model identification [8][9][10][11][12]14,[17][18][19][20][21][22][23]29,31]. Several commonly used criterion functions for experimental design exist.…”

“…Recently, as biological modeling and systems biology have emerged as an important area in biomedical research, optimal experimental design applied to biological experimental systems has become more popular [17][18][19][20][21][22][23][24][25][26][27][28]; additionally, optimal experimental design has been recognized as a valuable tool in optimal control for several decades [29]. For example, Jones et al [13] maximized production of an exogenous commodity chemical in metabolically engineered E. coli using an empirical modeling method similar to those used in [15,16] to maximize the efficacy of drug delivery.…”