Data-Driven Safety Filter: An Input-Output Perspective

Implementation of learning-based control remains challenging due to the absence of safety guarantees. Safe control methods have turned to model-based safety filters to address these challenges, but this is paradoxical when the ultimate goal is a model-free, data-driven control solution. Addressing the core question of "Can we ensure the safety of any learning-based algorithm without explicit prediction models and state estimation?" this paper proposes a Data-Driven Safety Filter (DDSF) grounded in Behavioral System Theory (BST). The proposed method needs only a single system trajectory available in an offline dataset to modify unsafe learning inputs to safe inputs. This contribution addresses safe control in the input-output framework and therefore does not require full state measurements or explicit state estimation. Since no explicit model is required, the proposed safe control solution is not affected by unmodeled dynamics and unstructured uncertainty and can provide a safe solution for systems with unknown time delays. The effectiveness of the proposed DDSF is illustrated in simulation for a high-order six-degree-of-freedom aerial robot and a time-delay adaptive cruise control system

Non-Iterative Data-Driven Model Reference Control

In model reference control, the objective is to design a controller such that the closed-loop system resembles a reference model. In the standard model-based solution, a plant model replaces the unknown plant in the design phase. The norm of the error between the controlled plant model and the reference model is minimized. The order of the resulting controller depends on the order of the plant model. Furthermore, since the plant model is not exact, the achieved closed-loop performance is limited by the quality of the model. In recent years, several data-driven techniques have been proposed as an alternative to this model-based approach. In these approaches, the order of the controller can be fixed. Since no model is used, the problem of undermodeling is avoided. However, closed-loop stability cannot, in general, be guaranteed. Furthermore, these techniques are sensitive to measurement noise. This thesis treats non-iterative data-driven controller tuning. This controller tuning approach leads to an identification problem where the input is affected by noise, and not the output as in standard identification problems. A straightforward data-driven tuning scheme is proposed, and the correlation approach is used to deal with measurement noise. For linearly parameterized controllers, this leads to a convex optimization problem. The accuracy of the correlation approach is compared to that of several solutions proposed in the literature. It is shown that, if the order of the controller is fixed, both the correlation approach and a specific errors-in-variables approach can be used. The model reference controller-tuning problem is extended with a constraint that ensures closed-loop stability. This constraint is derived from stability conditions based on the small-gain theorem. For linearly parameterized controllers, the resulting optimization problem is convex. The proposed constraint for stability is conservative. As an alternative, a non-conservative a posteriori stability test is developed based on similar stability conditions. The proposed methods are applied to several numerical and experimental examples

On identification methods for direct data-driven controller tuning

In non-iterative data-driven controller tuning, a set of measured input/output data of the plant is used directly to identify the optimal controller that minimizes some control criterion. This approach allows the design of fixed-order controllers, but leads to an identification problem where the input is affected by noise, and not the output as in standard identification problems. Several solutions that deal with the effect of measurement noise in this specific identification problem have been proposed in literature. The consistency and statistical efficiency of these methods are discussed in this paper and the performance of the different methods is compared. The conclusions offer a guideline on how to solve efficiently the data-driven controller tuning problem

Noniterative Data-driven Controller Tuning Using the Correlation Approach

Data-driven controller tuning for model reference control problem is investigated. A new controller tuning scheme for linear time-invariant single- input single-output systems is proposed. The method, which is based on the correlation approach, uses a single set of input/output data from open-loop or closed-loop operation. A specific choice of instrumental variables makes the correlation criterion an approximation of the model reference control criterion. The controller parameters and the correlation criterion are asymptotically not affected by noise. In addition, based on the small gain theorem, a sufficient condition for the stability of the closed-loop system is given in terms of the infinity norm of a transfer function. An unbiased estimate of this infinity norm can be obtained as the solution to a convex optimization problem using an infinite number of noise-free data. It is also shown that, for noisy data, the use of the correlation approach can improve significantly the estimate. The effectiveness of the proposed method is illustrated via a simulation example

Data-driven model reference control with asymptotically guaranteed stability

This paper presents a data-driven controller tuning method that includes a set of constraints for ensuring closed-loop stability. The approach requires a single experiment and can also be applied to nonminimum-phase or unstable systems. The tuning scheme uses an approximation of the closed-loop output error in the model-reference control problem. For linearly parameterized controllers, minimization of the correlation between this error and the reference signal leads to a convex optimization problem. A sufficient condition for closed-loop stability is introduced, which is implemented as a set of convex constraints on the Fourier transform of specific auto- and cross-correlation functions. As the data length tends to infinity, closed-loop stability is guaranteed. The quality of the estimated controller is analyzed for finite data length. The effectiveness of the proposed method is demonstrated in simulation as well as experimentally on a laboratory-scale mechanical setup

A Synthesis Method for Automatic Handling of Inter-patient Variability in Closed-loop Anesthesia

This paper presents a convex-optimization-based technique to obtain parameters for a PID feedback controller, used to control the infusion rate of the anesthetic drug propofol. The controller design is based on a set of identified patient models, relating propofol infusion to an EEG-based conciousness index. The main contribution lies in the method automatically taking inter-patient variability into account, i.e., it guarantees robustness (sensitivity peak) and performance (disturbance rejection) over a set of patient models, without the need for manual intervention. The method is demonstrated using a clinically relevant design example. A controller designed using the proposed method is currently scheduled for clinical evaluation

Quantification of the variability in response to propofol administration in children

Closed-loop control of anesthesia is expected to decrease drug dosage and wake up time while increasing patient safety and decreasing the work load of the anesthesiologist. The potential of closed-loop control in anesthesia has been demon- strated in several clinical studies. One of the challenges in the development of a closed-loop system that can be widely accepted by clinicians and regulatory authorities is the effect of inter- patient variability in drug sensitivity. This system uncertainty may lead to unacceptable performance, or even instability of the closed-loop system for some individuals. The development of reliable models of the effect of anesthetic drugs and charac- terization of the uncertainty is therefore an important step in the development of a closed-loop system. Model identification from clinical data is challenging due to limited excitation and the lack of validation data. In this paper, approximate models are therefore validated for controller design by evaluating the predictive accuracy of the closed-loop behavior. A set of 47 validated models that describe the inter-patient variability in the response to propofol in children is presented. This model set can be used for robust linear controller design provided that the experimental conditions are similar to the conditions during data collection

Optimizing robust PID control of propofol anesthesia for children; design and clinical evaluation

Objective: The goal of this study was to optimize robust PID control for propofol anesthesia in children aged 5-10 years to improve performance, particularly to decrease the time of induction of anesthesia while maintaining robustness.Methods: We analyzed results of a previous study conducted by our group to identify opportunities for system improvement. Allometric scaling was introduced to reduce the interpatient variability and a new robust PID controller was designed using an optimization based method. We evaluated this optimized design in a clinical study involving 16 new cases.Results: The optimized controller design achieved the performance predicted in simulation studies in the design stage. Time of induction of anesthesia was median [Q1, Q3] 3.7 [2.3, 4.1] minutes and the achieved global score was 13.4 [9.9, 16.8]. Conclusion: Allometric scaling reduces the interpatient variability in this age group, and allows for improved closed-loop performance. The uncertainty described by the model set, the predicted closedloop responses and the predicted robustness margins are realistic. The system meets the design objectives of improved speed of induction of anesthesia while maintaining robustness, improving clinically relevant system behavior.Significance: Control system optimization and ongoing system improvement are essential to the development of a clinically relevant commercial device. This paper demonstrates the validity of our approach, including system modeling, controller optimization and pre-clinical testing in simulation