Reference Tracking Problem Research Articles

Improved hybrid sphere decoding algorithm for long horizon finite control set model predictive control of grid-tied inverter

In this paper, the reference tracking and switching loss minimization problem of grid-tied inverters has been formulated as an integer least square (ILS) problem. It is considered an NP-hard and combinatorial problem due to the binary nature of switching status. A novel modification to the traditional non-recursive sphere decoding algorithm is being proposed in this research to address the implementation of long-horizon control with reduced computational burden. The proposed algorithm demonstrates a significant reduction in computation cost for long horizons resulting in energy minimization. The proposed method exploits the state-space model of the system to predict the sector in the space vector two-dimensional plane in which reference voltage could exist, thereby reducing the search space and time to search for the optimal solution. The proposed algorithm optimizes the utilization of controller resources compared to the conventional approach. The algorithm’s performance has been validated through simulations and Hardware in loop verification, for the performance optimization of a three-phase grid-tied inverter coupled using RL filter.

Heat exchanger networks: A predictive control approach

This work demonstrates the development of a practical predictive control approach to regulate the outputs of a network of heat exchangers. The full nonlinear continuous-time dynamic of the network is introduced to simulate the real process. Whereas a discrete linear and simpler version of this dynamic is employed to construct the predictive controller as well as an extended Kalman estimator. The presented algorithm is a time-varying model predictive control (MPC) where the simplified model is successively linearized on-line around the current available measurements. For the closed-stability of the introduced MPC scheme, a modified method is suggested to design terminal stabilizing weights where reference tracking problem, external disturbance dynamics, as well as the proper dynamics of a heat exchanger with bypass are all considered. The on-line updated extended Kalman estimator is utilized to estimate both the process states and unknown disturbances. Thanks to the successive linearization technique, the introduced predictive controller benefits from efficient online computations and online adaptations in operation points. Nonetheless, an accurate model of the heat exchanger is essential. Compared with a typical linear MPC, it is concluded that the presented predictive algorithm produces satisfactory results for disturbance rejection and switched operation points circumstances.

Deep reinforcement learning with reward shaping for tracking control and vibration suppression of flexible link manipulator

This paper puts forward a novel deep reinforcement learning control using deep deterministic policy gradient (DRLC-DDPG) framework to address the reference tracking and vibration suppression problem of rotary flexible link (RFL) manipulator. Specifically, this study attempts to address the continuous action space DRLC problem through DDPG algorithm and presents a Lyapunov function based reward shaping approach for guaranteed deep reinforcement learning (DRL) convergence and enhanced speed of training. The proposed approach synthesizes the hard and soft constraints of the flexible manipulator as a constrained Markov decision problem (MDP) and evaluates the performance of DRLC-DDPG framework through hardware in loop (HIL) testing to realize precise servo tracking and suppressed vibration of the flexible manipulator. For identifying the dynamical model of the RFL, an empirical Auto-Regressive eXogenous (ARX) model using the closed loop identification technique is built. Moreover, to extract the true states (servo angle and deflection angle) from the actual measurements, which typically have the influence of sensor noise, an adaptive Kalman filter (AKF) is augmented with the DRLC scheme. The experimental results of DRLC-DDPG scheme compared with those of the model predictive control (MPC) for several test cases reveal that the proposed scheme is superior to MPC both in terms of trajectory tracking and robustness against the external disturbances and model uncertainty.

Reference Tracking for Multiagent Systems Using Model Predictive Control

In this note, the reference tracking problem for teams of unmanned vehicles subject to formation constraints is solved via a model predictive control (MPC) algorithm built up in a distributed fashion. By exploiting the properties deriving from a novel kinematic description of the swarm agents, the receding horizon control (RHC) approach is properly adapted to deal with tracking and formation constraints. In particular, neighbor interactions are translated into convex conditions, thanks to an in-depth analysis of the geometric properties arising from the combined use of swarm kinematics and state predictions tubes. Experimental results on Elisa-3 robots show the applicability and effectiveness of the proposed control architecture.

Virtual reference feedback tuning with robustness constraints: A swarm intelligence solution

The simplified modeling of a complex system allied with a low-order controller structure can lead to poor closed-loop performance and robustness. A feasible solution is to avoid the necessity of a model by using data for the controller design. The Virtual Reference Feedback Tuning (VRFT) is a data-driven design method that only requires a single batch of data and solves a reference tracking problem, although with no guarantee of robustness. In this work, the inclusion of an H∞ robustness constraint to the VRFT cost function is addressed. The estimation of the H∞ norm of the sensitivity transfer function is extended to maintain the one-shot characteristic of the VRFT. Swarm intelligence algorithms are used to solve the non-convex cost function. The proposed method is applied in two real-world inspired problems with four different swarm intelligence algorithms, which are compared with each other through a Monte Carlo experiment of 50 executions. The obtained results are satisfactory, achieving the desired robustness criteria.

A Strategy for Traffic Safety of Vehicular Platoons Under Connection Loss and Time-Delay

Autonomous platoons are good alternatives for cargo transportation, with many approaches to safety and efficiency issues. In the last decades, much effort has been employed in this context, with solutions ranging from low-level control laws to learning strategies. Although some papers have concentrated on methods robust to disturbances or resilient to disruptions, most of the current literature assumes that the platoon starts and remains connected all the time, even when subjecting vehicles to limited communication ranges and time-delay. Therefore, in this paper, we address the problem of connectivity maintenance and stability of platoons under the complete disconnection of vehicles. The main goal is to increase the tolerance to agent exits, external elements (such as traffic lights and human-driven vehicles), and non-ideal initial conditions, improving traffic safety in mixed traffic scenarios. By modeling the network connection as a Directed Acyclic Graph, we use a state-machine policy to recover connectivity and regulate the spacing distance to other vehicles under heterogeneous time-delays. We demonstrate that this state alteration can be interpreted as a reference tracking problem and propose a design procedure that provides stability and zero spacing error in steady-state. Our control protocol allows vehicles to reach a consensus with the team, even when they start disconnected from other ones. Results with agent-based and nonlinear simulations illustrate the effectiveness of our approach.

Energy Management of P2 Hybrid Electric Vehicle Based on Event-Triggered Nonlinear Model Predictive Control and Deep Q Network

Hybrid electric vehicles (HEVs) are used as a bridge during the transition to battery electric vehicles (BEVs) and to make energy consumption more efficient. The main problem in improving the efficiency of HEV energy consumption is torque management. In this study, a novel approach based on a nonlinear model predictive controller to solve the reference tracking and torque distribution problem is proposed. That is to say, in order to increase the efficiency of torque distribution, the weights of nonlinear model predictive control (NMPC) are trained with a Deep Q Network (DQN), and an event-triggered mechanism is designed with DQN to reduce the computational cost of MPC. The considered torque distribution problem varies according to the type and structure of the HEV. In this study, a parallel type 2 hybrid electric vehicle (P2 HEV) is considered and modeled via publicly shared passenger vehicle data of the engine, motor, high-voltage battery, transmission, clutch, differential, and wheel characteristics. NMPC is formulated so that the torque values remain within the physical limits of the engine, and the battery also operates at its physical limits. Namely, it is guaranteed that the battery works according to a certain state of charge (SOC) window and current limits. The state of health (SOH) of the battery is also considered in the optimization. The motor and engine efficiencies increase by 3.61% and 2.86%, respectively, with the proposed control structure, while the computational cost is reduced by 52.01% when utilizing the proposed event-triggering mechanism in the NMPC controller.

Asymptotic stabilization of a transformed quadrotor model using energy-shaping method: Theory and experiments

This note presents a new passivity-based controller that ensures asymptotic stability for quadrotor position without solving partial differential equations or performing a partial dynamic inversion. After a resourceful change of coordinates, a pre-feedback controller, and a backstepping stage on the yaw angle dynamic, it is possible to identify new quadrotor cyclo passive outputs. Then, a simple proportional-integral controller of these cyclo-passive outputs completes the design. The cyclo-passive outputs allow the construction of an energy-based Lyapunov function that includes five out of six quadrotor degrees of freedom and guarantees asymptotic stability of the desired equilibrium. Moreover, the constant velocity reference tracking problem is solved with a slight modification to the proposed controller. Finally, the approach is validated through simulations and real-time experimental results.

A reinforcement learning approach to Automatic Voltage Regulator system

An Automatic Voltage Regulator (AVR) system utilized to keep the terminal voltage of a synchronous generator at the desired level has received much attention among researchers. Designing an efficient and robust control scheme for the AVR system to maintain a specified voltage level is an important research area. From the control area perspective, reinforcement learning, an adaptive optimal control method, has received increasing attention in reference tracking problems. This article discusses a reinforcement learning approach to an AVR system and its experimental validation. A deep deterministic policy gradient (DDPG) agent working in continuous-time is designed offline to improve dynamic system characteristics of the AVR system besides its robustness against load disturbance, parameter uncertainties, and reference change. In the DDPG agent design process, the limits of the produced control signal are taken into account to perform a feasible simulation similar to a real-time application. The performance of the proposed learning-based controller is analyzed in three categories: transient and steady-state responses, stability analysis, and robustness analysis against parameter uncertainties, reference change, and load disturbance. A comparison with recently published papers employing Fuzzy-PID, PID-F, PIλDND2N2, PIDD2 ,and PID controllers in which various heuristic optimization algorithms were employed to optimally tune the controller parameters is made. Furthermore, to demonstrate that the behavior of the learning-based approach provides a stable and satisfactory performance, it is analyzed for a real synchronous generator connected to a 230 kV network using Matlab/Simulink environment. The results presented in this paper indicate that the proposed learning-based controller ensures the stability of the AVR system, significantly improves the regulating performance, and most impressively, is robust against parameter uncertainties, reference change, and load disturbance.

On the Adaptive Tracking Problem of Time-Varying Systems using the Congelation for Variables Method

This paper discusses the use of the so-called congelation of variables method in the reference tracking problem for a class of nonlinear systems with matched, time-varying, parametric uncertainty. It is shown that the tracking problem using the proposed framework can be decomposed into a zero-regulation problem and a disturbance rejection problem. To reduce the size of the disturbance term, a dynamical system with known input is incorporated into the parameter update law to generate a time-varying nominal parameter. To reject the remaining disturbance term, a sign-like function is exploited, which achieves an adjustable tracking performance in an average sense, while guaranteeing boundedness of all trajectories of the closed-loop system. The theory is illustrated by solving a path-tracking problem and it is shown that the proposed control scheme outperforms the classical scheme in the presence of time-varying parameters.

Constrained Reference Tracking via Structured Input–Output Finite-Time Stability

In this article, the control approach based on structured input–output finite-time stability (IO-FTS) is extended to tackle the reference tracking problem. IO-FTS was originally introduced to deal with the disturbance rejection problem. By applying the finite-time stability control to a properly augmented system, we show that it is possible to enforce a set of specific requirements on the response of the closed-loop system during the transients, taking also into account saturation constraints on the actuators. Adding IO-FTS constraints to classic-state-feedback control law leads to a feasibility problem with bilinear matrix inequality (BMI) constraints. Herein, we show how the original BMI problem can be relaxed to a linear matrix inequality (LMI) one, which comes at a price of more conservatism, but turns out to be computationally more efficient. To prove the effectiveness of the proposed approach, we consider the case of the longitudinal control of a missile.

Bridging Reinforcement Learning and Iterative Learning Control: Autonomous Motion Learning for Unknown, Nonlinear Dynamics.

This work addresses the problem of reference tracking in autonomously learning robots with unknown, nonlinear dynamics. Existing solutions require model information or extensive parameter tuning, and have rarely been validated in real-world experiments. We propose a learning control scheme that learns to approximate the unknown dynamics by a Gaussian Process (GP), which is used to optimize and apply a feedforward control input on each trial. Unlike existing approaches, the proposed method neither requires knowledge of the system states and their dynamics nor knowledge of an effective feedback control structure. All algorithm parameters are chosen automatically, i.e. the learning method works plug and play. The proposed method is validated in extensive simulations and real-world experiments. In contrast to most existing work, we study learning dynamics for more than one motion task as well as the robustness of performance across a large range of learning parameters. The method’s plug and play applicability is demonstrated by experiments with a balancing robot, in which the proposed method rapidly learns to track the desired output. Due to its model-agnostic and plug and play properties, the proposed method is expected to have high potential for application to a large class of reference tracking problems in systems with unknown, nonlinear dynamics.

Optimal Control Strategy for Energy Management of PV-Diesel-Battery Hybrid Power System of a Stand-Alone Micro-Grid

New control algorithms are required to deal with the intermittent, stochastic, and distributed nature of the generation and new consumption patterns. Control of micro-grids poses significant challenges that need to be addressed through advanced control techniques. This paper investigates an optimal control strategy that efficiently manages a stand-alone residential micro-grid comprising renewable and non-renewable energy sources. An adaptive model predictive control (AMPC) algorithm is implemented for choosing an optimal mode and set of inputs for the system to track both a constant and load-varying power demand profile. The problem to be solved by the AMPC control algorithm is to perform an optimal power reference tracking problem, where the consumption of energy from the diesel generator is minimized while maximizing the efficiency of the storage bank. The objective of the optimal control scheme is for the generation to meet the demand, minimize the use of fossil fuels and ensure the energy storage is always maintained around a nominal point such that it is not over-depleted. Therefore, the main goal is to maximize the use of renewable sources and minimize traditional sources. The design and simulation of the plant model and the AMPC controller are carried out on the MATLAB/Simulink environment.

Reference Tracking and Observer Design for Space Fractional Partial Differential Equation Modeling Gas Pressures in Fractured Media

This paper considers a class of space fractional partial differential equations (FPDEs) that describe gas pressures in fractured media. First, the well-posedness, uniqueness, and the stability in $L_(\infty{R})$of the considered FPDEs are investigated. Then, the reference tracking problem is studied to track the pressure gradient at a downstream location of a channel. This requires manipulation of gas pressure at the downstream location and the use of pressure measurements at an upstream location. To achiever this, the backstepping approach is adapted to the space FPDEs. The key challenge in this adaptation is the non-applicability of the Lyapunov theory which is typically used to prove the stability of the target system as, the obtained target system is fractional in space. In addition, a backstepping adaptive observer is designed to jointly estimate both the system's state and the disturbance. The stability of the closed loop (reference tracking controller/observer) is also investigated. Finally, numerical simulations are given to evaluate the efficiency of the proposed method.

Scaled Consensus and Reference Tracking in Multiagent Networks With Constraints

This paper considers the scaled consensus problem for networks of groups of agents having state constraints. We first address the problem by using a gradient projection approach and design distributed consensus protocols that implement state restriction and steer agents asymptotically to proportions in terms of pre-assigned scales. We then extend the method to multiagent systems with static reference values. We propose and analyze sufficient conditions on agent dynamics such that scaled reference tracking problem is solved. The results are applied to a ship steering system and numerical examples to verify the effectiveness of the proposed cooperative coordination system scheme.

Reference tracking problem for boundary controlled time fractional advection dispersion equation in the presence of disturbances

In this paper, the output regulation problem of the time fractional advection-dispersion equation is considered, in the presence of disturbances. A generalized backstepping method is designed to allow the output to track a desired trajectory by manipulating the system’s control input located at the boundary. In addition, the paper provides the fundamental solution of the considered problem and the proof of its uniqueness.

ISS control for continuous‐time systems with filtered time‐varying parameter and saturating actuators

AbstractThis paper presents new convex conditions to design robust and linear parameter varying (LPV) gains for continuous time‐varying systems subject to saturating actuator and energy bounded disturbances. The input‐to‐state stability conditions are used to design controllers ensuring the minimization of the ‐gain between the disturbance input and the controlled output. Furthermore, optimization procedures to maximize the estimate of the region of attraction, and the bound to the control signal as well, are formulated. The efficacy of the proposed methods is illustrated with numerical examples, including a reference tracking problem, where realistic simulations are performed.

Evaluation of a NMPC Flowrate Controller for a Hot Rolling Finishing Mill for Steel Bars

In this work, the material flowrate control of a hot rolling finishing mill for steel bars is evaluated in simulation. First, a reduced model for control purpose is developed and described. This model uses nonlinear equations from the rolling theory and leads to the nonlinear control structure. The simulations are tested on a hot rolling mill simulator that implements a more detailed process behavior and is outside of the scope of this work. For controlling this plant, a Nonlinear Model Predictive Control (NMPC) is tested in various conditions. It is compared as a benchmark with a classical Linear Quadratic Regulator with integral action (LQI). The controller is implemented with help of CasADi and the control problem is solved by a SQP solver. The NMPC uses an underlying EKF as disturbance observer to handle the reference tracking problem.

Discrete-Time Sliding Mode Energy Control of sine-Gordon Chain with Adaptive Augmentation*

The present paper focuses on the robustness issues of the speed-gradient energy control design for the one-dimensional sine-Gordon system. The energy stabilization of a non-zero level is addressed as the energy reference tracking problem. In the paper, the “relay” speed gradient algorithm, using state feedback with in-domain actuators, is designed and its adaptive augmentation is proposed. The properties of the closed-loop energy feedback for sampling-in-time control algorithms are studied numerically. In the PDE setting, such an adaptive adjustment of the sliding mode control gain has not been investigated so far. This modification is demonstrated to ensure the closed-loop system robustness with respect to the time sampling.

Actuator fault-tolerant iterative learning control of the magnetic brake system

Design of fault-tolerant control for nonlinear systems is usually focused on maxi-mizing some criteria defining the level of robustness with respect to potential faults without significant degradation of the system performance. Therefore, strong interest is produced by compromise approaches which would generate decent control quality for the broadest possible class of potential faulty scenarios. Here, an approach is proposed with the application to magnetic brake system making use of the repetitive character of the control task. The concept of iterative learning control driven by measurement data is utilized to properly update the control signal in order to adapt to possible actuator fault states. A learning controller is adopted build on a mixture of neural networks for various operating points. Thus, it is able to adapt to changing working conditions of the device. Moreover, using the procedure employing an ensemble of inverse models, actuator faults can be successfully accommodated. The paper provides the complete iterative learning procedure including the system identification, fault estimation and fault-tolerant control. The numerical example on the reference tracking problem for magnetic brake system is discussed, taking into account various faulty scenarios.