Optimal Tracking Research Articles

Optimizing Photovoltaic Systems: A Decision Matrix Approach for Selecting the Optimal Maximum Power Point Tracking Technique

Numerous strategies exist for improving maximum power point tracking (MPPT) techniques, which vary in terms of tracking speed, accuracy, sensor usage, complexity, and cost. Due to the importance of sustainable energy use and related challenges, it is essential to choose an appropriate algorithm that can reliably provide energy without exhausting resources. While much research has examined the benefits and drawbacks of different MPPT algorithms, guidance on selecting the best suited algorithm for a particular solar system application is lacking. For a fair and thorough comparison, this study analyzes four MPPT algorithms, including two artificial intelligence-based techniques, an adaptive neuro-fuzzy inference system, and a conventional technique. A decision matrix model and requirement analysis are used to determine their suitability for a standalone PV application, using particularly ranked evaluation criteria, which include tracking efficiency, implementation costs, rise time, settling time, tracking error and variance. Simulation results show that the perturb and observe technique has the fastest settling and rise times and high tracking efficiency for varying irradiance and temperature levels, with little implementation effort required for a stand-alone photovoltaic application.

Near-Optimal Tracking Control of Partially Unknown Discrete-Time Nonlinear Systems Based on Radial Basis Function Neural Network

This paper proposes an optimal tracking control scheme through adaptive dynamic programming (ADP) for a class of partially unknown discrete-time (DT) nonlinear systems based on a radial basis function neural network (RBF-NN). In order to acquire the unknown system dynamics, we use two RBF-NNs; the first one is used to construct the identifier, and the other one is used to directly approximate the steady-state control input, where a novel adaptive law is proposed to update neural network weights. The optimal feedback control and the cost function are derived via feedforward neural network approximation, and a means of regulating the tracking error is proposed. The critic network and the actor network were trained online to obtain the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation within the ADP framework. Simulations were carried out to verify the effectiveness of the optimal tracking control technique using the neural networks.

Reinforcement Q-learning and Optimal Tracking Control of Unknown Discrete-time Multi-player Systems Based on Game Theory

Reinforcement Q-learning and Optimal Tracking Control of Unknown Discrete-time Multi-player Systems Based on Game Theory

Optimal trajectory tracking of tractor-trailer wheeled platforms taken into account wheel dynamics

Tractor-trailer wheeled platforms are recognized as articulated robotic systems which consist of a frontrunner active mobile platform (known as tractor) that pulls one or more passive platforms (known as trailers). Regarding to their novel features such as maximum load carrying capacity and minimum energy consumption, this category of mobile platforms is widely employed for conveying purposes and transportation. The presented article deals with path tracking optimization of the tractor-trailer platform using the indirect method of the optimal control. First, nonlinear motion relations of the modular platform are obtained considering kinematic constraints and inertia characteristics of the wheels. Then, the obtained dynamic equations are considered as constraints of the optimal problem, and as a result an appropriate objective criterion is determined for the optimal trajectory tracking. In the following, a proper solution for the optimal problem is developed and accordingly some simulations are presented. In view of the wheels dynamics, the obtained results reveal competency and applicability of the proposed procedure for the optimal tracking of the tractor-trailer wheeled mobile platforms.

Estimating 3D kinematics and kinetics from virtual inertial sensor data through musculoskeletal movement simulations

Portable measurement systems using inertial sensors enable motion capture outside the lab, facilitating longitudinal and large-scale studies in natural environments. However, estimating 3D kinematics and kinetics from inertial data for a comprehensive biomechanical movement analysis is still challenging. Machine learning models or stepwise approaches performing Kalman filtering, inverse kinematics, and inverse dynamics can lead to inconsistencies between kinematics and kinetics. We investigated the reconstruction of 3D kinematics and kinetics of arbitrary running motions from inertial sensor data using optimal control simulations of full-body musculoskeletal models. To evaluate the feasibility of the proposed method, we used marker tracking simulations created from optical motion capture data as a reference and for computing virtual inertial data such that the desired solution was known exactly. We generated the inertial tracking simulations by formulating optimal control problems that tracked virtual acceleration and angular velocity while minimizing effort without requiring a task constraint or an initial state. To evaluate the proposed approach, we reconstructed three trials each of straight running, curved running, and a v-cut of 10 participants. We compared the estimated inertial signals and biomechanical variables of the marker and inertial tracking simulations. The inertial data was tracked closely, resulting in low mean root mean squared deviations for pelvis translation (≤20.2 mm), angles (≤1.8 deg), ground reaction forces (≤1.1 BW%), joint moments (≤0.1 BWBH%), and muscle forces (≤5.4 BW%) and high mean coefficients of multiple correlation for all biomechanical variables (≥0.99). Accordingly, our results showed that optimal control simulations tracking 3D inertial data could reconstruct the kinematics and kinetics of individual trials of all running motions. The simulations led to mutually and dynamically consistent kinematics and kinetics, which allows researching causal chains, for example, to analyze anterior cruciate ligament injury prevention. Our work proved the feasibility of the approach using virtual inertial data. When using the approach in the future with measured data, the sensor location and alignment on the segment must be estimated, and soft-tissue artifacts are potential error sources. Nevertheless, we demonstrated that optimal control simulation tracking inertial data is highly promising for estimating 3D kinematics and kinetics for a comprehensive biomechanical analysis.

Primary-Frequency-Tuning and Secondary-Impedance-Matching IPT Converter With Programmable Constant Power Output and Optimal Efficiency Tracking Against Variation of Coupling Coefficient

Primary-Frequency-Tuning and Secondary-Impedance-Matching IPT Converter With Programmable Constant Power Output and Optimal Efficiency Tracking Against Variation of Coupling Coefficient

Optimal time-invariant distributed formation tracking for second-order multi-agent systems

This paper addresses the optimal time-invariant formation tracking problem with the aim of providing a distributed solution for multi-agent systems with second-order integrator dynamics. In the literature, most of the results related to multi-agent formation tracking do not consider energy issues while investigating distributed feedback control laws. In order to account for this crucial design aspect, we contribute by formalizing and proposing a solution to an optimization problem that encapsulates trajectory tracking, distance-based formation control and input energy minimization, through a specific and key choice of potential functions in the optimization cost. To this end, we show how to compute the inverse dynamics in a centralized fashion by means of the Projector-Operator-based Newton’s method for Trajectory Optimization (PRONTO) and, more importantly, we exploit such an offline solution as a general reference to devise a stabilizing online distributed control law. Finally, numerical examples involving a cubic formation following a chicane-like path in the 3D space are provided to validate the proposed control strategies.

Integral reinforcement learning-based angular acceleration autopilot for high dynamic flight vehicles

During the synthesis of acceleration autopilots for high dynamic flight vehicles (HDFV), autopilots with feedback of angular acceleration (AFAA) have become more perspective with stringent requirements on response speed and high maneuverability, compared with autopilots with feedback of angular rate (AFAR). Integral reinforcement learning (IRL) method has now proved to be an effective technique for adaptive optimal control of partially unknown nonlinear systems. In this paper, a novel data-driven IRL algorithm with “actor-critic” structure is proposed for HDFV utilizing AFAA. As an advanced model-free approach, actor-critic based IRL algorithm learns optimal behaviors by observing the real-time responses from the environment under the action of nonoptimal control policies. Instead of solving algebraic Riccati equation directly, the control policy updates online via the solution of proposed IRL Bellman equation with sensed quantities. Numerical simulation is carried out to validate the effectiveness of proposed online IRL-based angular acceleration autopilot for HDFVs. Besides, the tracking performance under different wave commands, the robustness against parameter uncertainties and the noise attenuation capacity between classical optimal tracking approach and proposed IRL method are analyzed for AFAR and AFAA, respectively. Simulation results show that, angular acceleration autopilot with proposed integral RL algorithm possesses better tracking performance against various disturbances.

Optimal Tracking of Networked Control Systems Over the Fading Channel With Packet Loss

Optimal Tracking of Networked Control Systems Over the Fading Channel With Packet Loss

Optimal Tracking Control of Heterogeneous MASs Using Event-Driven Adaptive Observer and Reinforcement Learning.

This article considers the output tracking control problem of nonidentical linear multiagent systems (MASs) using a model-free reinforcement learning (RL) algorithm, where partial followers have no prior knowledge of the leader's information. To lower the communication and computing burden among agents, an event-driven adaptive distributed observer is proposed to predict the leader's system matrix and state, which consists of the estimated value of relative states governed by an edge-based predictor. Meanwhile, the integral input-based triggering condition is exploited to decide whether to transmit its private control input to its neighbors. Then, an RL-based state feedback controller for each agent is developed to solve the output tracking control problem, which is further converted into the optimal control problem by introducing a discounted performance function. Inhomogeneous algebraic Riccati equations (AREs) are derived to obtain the optimal solution of AREs. An off-policy RL algorithm is used to learn the solution of inhomogeneous AREs online without requiring any knowledge of the system dynamics. Rigorous analysis shows that under the proposed event-driven adaptive observer mechanism and RL algorithm, all followers are able to synchronize the leader's output asymptotically. Finally, a numerical simulation is demonstrated to verify the proposed approach in theory.

Asymmetric Constrained Optimal Tracking Control With Critic Learning of Nonlinear Multiplayer Zero-Sum Games.

By utilizing a neural-network-based adaptive critic mechanism, the optimal tracking control problem is investigated for nonlinear continuous-time (CT) multiplayer zero-sum games (ZSGs) with asymmetric constraints. Initially, we build an augmented system with the tracking error system and the reference system. Moreover, a novel nonquadratic function is introduced to address asymmetric constraints. Then, we derive the tracking Hamilton-Jacobi-Isaacs (HJI) equation of the constrained nonlinear multiplayer ZSG. However, it is extremely hard to get the analytical solution to the HJI equation. Hence, an adaptive critic mechanism based on neural networks is established to estimate the optimal cost function, so as to obtain the near-optimal control policy set and the near worst disturbance policy set. In the process of neural critic learning, we only utilize one critic neural network and develop a new weight updating rule. After that, by using the Lyapunov approach, the uniform ultimate boundedness stability of the tracking error in the augmented system and the weight estimation error of the critic network is verified. Finally, two simulation examples are provided to demonstrate the efficacy of the established mechanism.

Detection of tracker misalignments and estimation of cross-axis slope in photovoltaic plants

Photovoltaic (PV) energy production is becoming a more significant part of the energy mix world-wide due to its clean origin, supportive and cost reductions. Therefore, it is increasingly important to develop methodologies to improve efficiency and reduce energy losses. Solar tracking is a way of increasing the irradiance over the PV field and, subsequently, boosting energy production. Both single-axis and double-axis tracking systems (SATS & DATS) are well known methods but both require not only a proper estimation of the sun’s position but also precise knowledge of the tracker’s position and orientation. Several factors (construction, design, configuration) can cause the values used to calculate the optimal tracking to be inaccurate, thus increasing production losses. This paper proposes a methodology to calculate the actual orientation of the trackers’ axis based on the energy production of its associated strings. Additionally, it provides the height differences between adjacent trackers by detecting shading patterns. This information is key to defining more efficient tracking and backtracking strategies the avoid row-to-row shading and, overall increasing energy production. The proposed method is applied to a real 5 MW facility, identifying misalignments of several degrees in most trackers that were causing annual losses (1 %), not only due to inaccurate tracking but also row-to-row shading.

Data‐driven disturbance compensation control for discrete‐time systems based on reinforcement learning

SummaryIn this article, a self‐learning disturbance compensation control method is developed, which enables the unknown discrete‐time (DT) systems to achieve performance optimization in the presence of disturbances. Different from traditional model‐based and data‐driven state feedback control methods, the developed off‐policy Q‐learning algorithm updates the state feedback controller parameters and the compensator parameters by actively interacting with the unknown environment, thus the approximately optimal tracking can be realized using only data. First, an optimal tracking problem for a linear DT system with disturbance is formulated. Then, the design for controller is achieved by solving a zero‐sum game problem, leading to an off‐policy disturbance compensation Q‐learning algorithm with only a critic structure, which uses data to update disturbance compensation controller gains, without the knowledge of system dynamics. Finally, the effectiveness of the proposed method is verified by simulations.

Adjustable iterative Q-learning for advanced neural tracking control with stability guarantee

In this article, an accelerated Q-learning algorithm with evolving control is established to solve the optimal tracking control problem. First, an accelerated Q-learning scheme is constructed with an advanced Q-function. By utilizing the advanced Q-function, calculating of the feedforward control input can be avoided and the terminal tracking error can be eliminated. Then, by introducing the relaxation factor, the convergence rate of the iterative Q-function sequence is accelerated significantly, which is a potential way to diminish the computational burden. Furthermore, the convergence, positive definiteness, and stability conditions of the accelerated Q-learning algorithm are analyzed with some preconditions of the relaxation factor. Thus, the developed algorithm can achieve evolving control. Finally, the fantastic performance of the developed algorithm with critic network implementation is verified through two simulation examples.

Model‐free learning‐based distributed cooperative tracking control of human‐in‐the‐loop multi‐agent systems

AbstractThis article studies the model‐free learning‐based distributed cooperative tracking control of human‐in‐the‐loop multi‐agent systems in the presence of an active leader. The core role of human‐in‐the‐loop is to use the ground station to send control commands to the non‐zero control input of the leader, and then directly or indirectly control a group of agents to complete complex tasks. Meanwhile, three essential demands including the completely unknown system model, the control objective obtained optimally, as well as no initial admissible control strategy requirement, are satisfied simultaneously. It is worth emphasizing that the relevant results only satisfy one or two demands at most, which are essentially not applicable to this problem. In this article, a model‐based human‐in‐the‐loop learning algorithm is first presented to achieve the optimal tracking control, as well as the convergence of the proposed learning algorithm is proved. Then, a bias‐based data‐driven learning algorithm is proposed, which provides the potential opportunities to overcome the difficulties caused by the above‐mentioned three demands. Finally, the validity of theoretical results is testified by a numerical example.

Human and Small Animal Detection Using Multiple Millimeter-Wave Radars and Data Fusion: Enabling Safe Applications.

Millimeter-wave (mmWave) radars attain high resolution without compromising privacy while being unaffected by environmental factors such as rain, dust, and fog. This study explores the challenges of using mmWave radars for the simultaneous detection of people and small animals, a critical concern in applications like indoor wireless energy transfer systems. This work proposes innovative methodologies for enhancing detection accuracy and overcoming the inherent difficulties posed by differences in target size and volume. In particular, we explore two distinct positioning scenarios that involve up to four mmWave radars in an indoor environment to detect and track both humans and small animals. We compare the outcomes achieved through the implementation of three distinct data-fusion methods. It was shown that using a single radar without the application of a tracking algorithm resulted in a sensitivity of 46.1%. However, this sensitivity significantly increased to 97.10% upon utilizing four radars using with the optimal fusion method and tracking. This improvement highlights the effectiveness of employing multiple radars together with data fusion techniques, significantly enhancing sensitivity and reliability in target detection.

Reliability-based optimization of supported pendulum TMDs’ nonlinear track shape using Padé approximants

Supported Pendulum Tuned Mass Dampers (PTMDs) are vibration absorbers whose mass is constrained to oscillate along a curved path, enabling to use gravity as a restoring force. Through a proper track shape selection, they can adapt to the so-called Nonlinear Energy Sinks (NES) concept, consolidated for spring–mass–damper TMDs. Accordingly, NESs are recognized for their ability to resonate in a wide range of frequencies due to their nonlinear nature, becoming more effective when variations on the host structure’s natural frequencies occur. However, regardless of the recent advances in the last few years, gaps remain to be explored in the track shape optimization of supported PTMDs. For instance, a comprehensive literature review shows that Reliability-Based Design Optimization (RBDO) studies to determine the track shape of supported PTMDs cannot be found to the best of the author’s knowledge. Within this context, this paper proposes an original RBDO approach to define the track shape of supported PTMDs in buildings subjected to seismic excitation. For this purpose, a generic rational function with an arbitrary curvature, determined from the Padé approximation of the circle equation, is constructed to allow the PTMD’s path shape search. This procedure allows optimizing fewer parameters than required in Taylor series expansions while providing a wider range of alternatives for numerical optimization. Finally, an active-learning Kriging-based Efficient Global Optimization (EGO) procedure is employed to find the optimum solutions with few objective function evaluations. The application case consists of a typical soft story building subjected to seismic loadings. The optimal track differs from the circle equation, with a higher slope for moderate displacements.

Adaptive dynamic programming based attitude optimal tracking control for a quadrotor with unmeasured velocities and model uncertainties

Adaptive dynamic programming based attitude optimal tracking control for a quadrotor with unmeasured velocities and model uncertainties

Combining hybrid metaheuristic algorithms and reinforcement learning to improve the optimal control of nonlinear continuous-time systems with input constraints

This paper proposes an innovative method for achieving optimal tracking control in nonlinear continuous-time systems with input constraints. The method combines reinforcement learning and hybrid metaheuristics to enhance the controller’s performance. Specifically, a hybrid metaheuristic algorithm is employed to optimize the hyperparameters of a critic neural network, which serves as the system’s controller. The proposed approach is evaluated through extensive simulation studies on a nonlinear system with input constraints. Results demonstrate its superiority over traditional control techniques in terms of accuracy, timeliness, and stability. Notably, the approach effectively eliminates overshoot and steady-state error while providing precise and prompt tracking and showcasing remarkable robustness against model uncertainties. By synergistically integrating reinforcement learning and hybrid metaheuristics, this approach represents a significant advancement in enhancing the control performance of complex nonlinear systems. The simulation studies confirm superiority of the proposed approach over existing techniques, offering a promising solution for achieving optimal tracking control in nonlinear systems with input constraints. This approach holds potential for a wide range of applications, including robotics, aerospace, and manufacturing, where precise and prompt tracking control is critical.

Optimal leader-following consensus under switching topologies based on event-triggered NN-based observer

This paper proposes a novel control strategy for multi-agent systems (MASs) to achieve optimal leader-following consensus under jointly connected topologies. The devised approach incorporates two key components: an event-triggered neural network (NN)-based leader observer and an NN-based optimal controller. The proposed leader observer allows followers to locally reconstruct the leader’s dynamics, even in scenarios where the communication topology is jointly connected. The implementation of an event-triggered communication protocol significantly reduces the communication burden, enhancing the overall efficiency of information exchange. As the observer’s state converges to the actual leader’s state, the simplification of achieving leader-follower consensus becomes evident by directly setting the state of the leader observer as the tracking goal. An NN-based optimal controller is utilized to approximate the solution to the Hamilton–Jacobi–Bellman (HJB) equation, thus enabling optimal tracking of the leader by followers. Finally, the performance of the proposed control strategy is verified by simulations.