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Real-Time System Identification Using Deep Learning for Linear 1 Real-time System Identification Using Deep Learning for Linear Processes with Application to Unmanned Aerial Vehicles Abdulla Ayyad*1, Mohamad Chehadeh*1, Mohammad I. Awad1, and Yahya Zweiri1,2 1Khalifa University Center for Autonomous Robotic Systems, Khalifa University, Abu Dhabi United Arab Emirates 2Faculty of Science, Engineering and computing, Kingston University, London SW15 3DW, UK *Equal contribution authors Abstract—This paper proposes a novel parametric identifi- depending on the control requirements and design constraints. cation approach for linear systems using Deep Learning (DL) Parametric means are data-driven approaches where model and the Modified Relay Feedback Test (MRFT). The proposed parameters of a Process Under Test (PUT) are identified methodology utilizes MRFT to reveal distinguishing frequencies about an unknown process; which are then passed to a trained based on observation data. Such approaches include prediction DL model to identify the underlying process parameters. The error methods (PEM) [6], [7], [8], maximum likelihood (ML) presented approach guarantees stability and performance in methods [9], [10], least square (LS) methods [11], frequency the identification and control phases respectively, and requires response identification methods [12], [13], [14], and neural few seconds of observation data to infer the dynamic system network based methods [15], [16], [17]. Several studies in parameters. Quadrotor Unmanned Aerial Vehicle (UAV) attitude and altitude dynamics were used in simulation and experimen- the literature applied these techniques to UAV operation with tation to verify the presented methodology. Results show the accurate identification results [18], [19], [20], [21], [22], [23]. effectiveness and real-time capabilities of the proposed approach, Nonetheless, these methods require extensive data generation which outperforms the conventional Prediction Error Method in and accurate selection of optimizer initial conditions, which terms of accuracy, robustness to biases, computational efficiency demand human experience and cause susceptibility to data and data requirements. biases and overfitting. Furthermore, most of these methods Index Terms—System Identification, Unmanned Aerial Vehi- are computationally expensive and not suitable for real-time cles, Robot Learning, Sliding Mode Control, Process Control. application. On the other hand, non-parametric identification includes methods which rely on the partial knowledge of the PUT to MULTIMEDIA MATERIAL tune a predefined controller structure. Such methods include, A supplementary video for the work presented in this for example, the classical Ziegler-Nichols method [24], the paper can be accessed at: https://www.youtube.com/watch?v= Relay Feedback Test (RFT) [25], and the Modified Relay dz3WTFU7W7c Feedback Test (MRFT) [26]. In all these methods, the knowl- edge of the PUT response to a single excited frequency is enough to get controller parameters tuning. It was shown in I. INTRODUCTION recent work [27] that a near optimal controller for quadcopter Since the third industrial revolution, system identification attitude dynamics can be designed using MRFT based tuning arXiv:2004.08603v2 [eess.SY] 21 Apr 2020 has been a key element in the development of autonomous rules. However, non-parametric methods in the literature are technologies in a wide set of industrial applications. Accurate limited to PID tuning and do not provide full insight to the knowledge of system dynamics enables the design of robust system dynamics as they cannot be used to obtain model and high-performance systems for prediction, planning and parameters. control. Unmanned Aerial Vehicles (UAVs) are an example of Recent advancements in the fields of Iterative Learning an autonomous system that has seen diverse utilization in areas Control (ILC), Reinforcement Learning (RL) and Deep Learn- of agriculture, disaster relief, remote sensing, surveillance, etc. ing (DL), and the growth of computational capabilities have [1], [2], [3], [4], [5]. UAVs are often deployed in uncontrolled given rise to new approaches of controller design and tuning environments, and are hence required to adapt to dynamic [28], [29], [30], [31], [32], [33], [34]. These approaches conditions in real-time with minimal sacrifice to functionality have introduced advantages in regards to accuracy of models and performance. and controllers, adaptation time, and the ability to handle To meet the aforementioned requirements of autonomy, nonlinearities in the PUT; with the limiting requirement of extensive research have been carried out to develop effective abundant observation data. Similar to non-parametric tuning, methods of system identification and adaptation. These meth- these approaches do not generate explicit estimates of model ods are generally classified as parametric or non-parametric parameters, but rather implicitly consider these parameters in 2 Fig. 1: The proposed system identification scheme. The control switch starts at position (a) where MRFT is used to excite an unknown plant G(s) with stable oscillations. These oscillations are pre-processed and forwarded to a DL classifier to identify the system parameters as G^(s). After the PUT was identified, a suitable controller C∗(s) can be designed and applied to the plant by shifting the control switch to position (b). controller design. which highlight its advantages over other existing methods. This paper bridges the gap between parametric and non- First, the required amount of data needed for identification parametric methods and presents a novel methodology to is minimal as it consists of a single excited frequency of the infer accurate estimates of model parameters with the prime system. In contrast, other data driven classical identification motivation of designing high-performance controllers online methods used in the literature require extensive data generation and in real-time. The novelty of the proposed methodology lies [6], [7], [8], [9], [10], [13], [14]. Due to the reduction in in utilizing self-excited oscillations (i.e. chattering) resulting data requirements, the proposed methodology does not re- from a sliding mode controller, which is the MRFT, to reveal quire human experience for data generation, and the model distinguishing information about the PUT. The information fitting process is not prone to data bias. This makes the revealed by MRFT are then fed to a DL classifier which proposed method precise and accurate in identifying unknown selects model parameters that best represents the PUT. Fig. model parameters. Other advantages of data reduction include 1 illustrates the proposed comprehensive system identification minimizing computational requirements and shortening the approach. We show that this identification method can be period of the identification phase. In fact, we have found performed in real-time such that a UAV adapts to changes that the required computational time on modern commercial to its own physical dynamics during a flight mission. The processors is in the order of milliseconds; and the identification suggested online identification methodology is safe with guar- phase lasts for a maximum of a few seconds (this depends on anteed stability, and results in controllers with assessable levels the PUT dynamics, e.g. mass). of robustness and performance. The presented approach is The second inherent feature of the presented identification mainly applied to Second Order with Integrator Plus Time method is the guarantee of stability during the identification Delay (SOIPTD) linear systems; but is also applicable to other phase. This relieves the need for hand-tuned initial stabilizing system models with equal or lower number of model parame- controllers as opposed to classical identification methods, ters. Due to its real-time capabilities, the proposed technique and makes the presented method less prone to estimation can handle static nonlinearities by applying the identification biases and non-optimality caused by the selection of initial process in multiple operation modes (e.g. near ground hovering control parameters (i.e. initial parameters for the optimizer or drag dynamics caused by large translational speeds); to decision variables). As stability is guaranteed, the PUT can obtain locally linear descriptions of the system. be directly started in the identification phase as demonstrated There are two inherent features of the proposed approach in the results section; thus further minimizing the required 3 TABLE I: Qualitative comparison with selected recent methods from literature addressing the problem of automatic controller tuning and adaptation for UAVs Method Experimental data gen- Computational Stability Comments eration Resources This work Single steady-state oscil- A few millisec- Guaranteed in data gener- Not investigated for lateral lation at a specified phase onds with mod- ation phase by Loeb crite- UAV motion yet. Provides ern on-board pro- rion [35], [26] PUT model parameters cessors Sim-to-(Multi)-Real using Not required Inference model No stability guarantees This work’s problem proximal policy optimiza- is running in real- statement is closest to tion (PPO) RL [32] time the one presented in this paper, but with no guarantee of stability or explicit inference of model parameters ILC [28] Requires a lot of iterations Computationally Stability guaranteed Feedforward expensive within ILC iterations compensation terms Deep Model-Based Rein- Requires a lot of experi- Computationally Not guaranteed Early adaptation of
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