Optimal Control Design Research Articles

Bisimulations of Probabilistic Boolean Networks

A probabilistic Boolean network (PBN) is a collection of Boolean networks endowed with a probability structure describing the likelihood with which a constituent network is active at each time step. This paper proposes a definition of bisimulation for PBNs. The notion is inspired by the analogous notions for probabilistic chains and for stochastic linear systems. Necessary and sufficient conditions to check the proposed notion are derived, model reduction of PBNs via bisimulation is addressed, and a discussion on the use of probabilistic bisimulation for optimal control design is given. The present results extend the theory of bisimulation known for deterministic Boolean networks to a stochastic setting.

Design and implementation of optimal controller for DFIG-WT using autonomous groups particle swarm optimization

<span>There are many types of generators used within wind energy such as doubly fed induction generator (DFIG). Particle swarm optimization (PSO) algorithm is simple, robust and easy to implement. In addition to the privilege of PSO, autonomous groups particle swarm optimization (AGPSO) has the advantages of using diverse autonomous groups which result in more randomized and directed search. Applying AGPSO to tune PI controller to control DFIG is proposed in this paper. An implemented laboratory prototype consists of brushless DC motor (BLDC) for simulating the various wind speeds. Wound rotor induction machine, working as DFIG. This system is a stand-alone system. System identification strategy was introduced in this work. In this study, AGPSO is suggested for tuning the PI controller. Different case studies are performed, such as step changes in both speed and electrical load for showing the effectiveness of the proposed algorithm. For comparison PSO is used to tune the PI controller. Results from experiments clarify the feasibility of the proposed methodology. It is approved that AGPSO achieves the prevalent control execution (quicker transient response and more modest steady state error (ess)) contrasted with the PSO in tuning PI controller when applied to be used with off-grid systems. </span>

Online Value Iteration for Intelligent Discounted Tracking Design of Constrained Systems

In this brief, in order to solve the discounted optimal tracking control problem for discrete-time systems with control constraints, an advanced online value iteration (VI) algorithm is developed. First, we revisit discounted general value iteration (GVI) for optimal tracking control design. Second, the stability condition of GVI is established, which can be applied to evaluate the current iterative tracking control policy. Third, based on the concept of attraction domain, the evolving tracking control policies generated by online VI can be obtained through judging the location of the current tracking error. Finally, we prove system stability based on online VI for the present tracking control problem. A simulation example is shown to illustrate the effectiveness of the developed algorithm.

Design of Optimal Sliding Mode Control of Elbow Wearable Exoskeleton System Based on Whale Optimization Algorithm

The high nonlinearity and time-varying coefficients characterize the elbow exoskeleton system for rehabilitation. To deal with these difficult control challenges, nonlinear and reliable controllers are needed. This paper shows the use of Sliding Mode Control (SMC) to track the trajectory of an Elbow Exoskeleton System (EES) with presence of parameter uncertainty. The Whale Optimization Algorithm (WOA) algorithm is used to tuning the design parameters of suggested controllers for performance improvement. Computer simulation based on MATLAB software has been implemented to conduct a comparison study between optimal and non-optimal SMC. The simulation findings shows that the optimal SMC outperforms the non-optimal version of controller in terms of performance.

Reliability-based optimal control design for seismic-excited structures: A hybrid IS-MTLBO pseudo-double loop method

This study addressed a reliability-based optimal control design (RBOCD) approach for seismic-excited structures. For this aim, a hybrid importance sampling-modified teaching-learning based optimization (IS-MTLBO) pseudo-double loop method is developed. Uncertainty sources such as structural model, stochastic model of the ground acceleration, structural response measurements in sensors, and designed/applied forces in actuators are considered in this study. Numerical studies are carried out on a 10-story building subjected to earthquake excited. A deterministic optimal control design (DOCD) approach based on the MTLBO algorithm is firstly conducted for the structure. Then, a sensitivity analysis using the Borgonovo sensitivity method is carried out to identify and measure the effectiveness of the mentioned uncertainty sources on the seismic responses. Finally, the IS-MTLBO pseudo-double loop approach as an RBOCD approach is implemented for the studied structure. The average reductions of the seismic responses in terms of maximum displacement, acceleration, and drift of floors are obtained as 18.95%, 27.7%, and 24.65% for the RBOCD approach, while, the corresponding reduction are 7.30%, 19.45%, and 14.05% for the DOCD approach. It is shown that although the designed controller based on the DOCD approach satisfies the limitation considered for the maximum floor drift in the nominal model, it is not able to satisfy it in the presence of uncertainties. In other words, the RBOCD approach represents a robust control design against uncertainties, while the DOCD approach gives an uncertainty-sensitive control scheme. Considering four well-known earthquakes, the failure probabilities of the structure controlled by both DOCD and RBOCD approaches are compared. The results indicate the failure probability of the structure controlled by the RBOCD approach is much less than those given using the DOCD approach.

Nonlinear optimal controller design for three-degrees of freedom robotic arm

Nonlinear optimal controller design for three-degrees of freedom robotic arm

Reinforcement Learning Applications in Unmanned Vehicle Control: A Comprehensive Overview

This paper briefly reviews the dynamics and the control architectures of unmanned vehicles; reinforcement learning (RL) in optimal control theory; and RL-based applications in unmanned vehicles. Nonlinearities and uncertainties in the dynamics of unmanned vehicles (e.g. aerial, underwater, and tailsitter vehicles) pose critical challenges to their control systems. Solving Hamilton–Jacobi–Bellman (HJB) equations to find optimal controllers becomes difficult in the presence of nonlinearities, uncertainties, and actuator faults. Therefore, RL-based approaches are widely used in unmanned vehicle systems to solve the HJB equations. To this end, they learn the optimal solutions by using online data measured along the system trajectories. This approach is very practical in partially or completely model-free optimal control design and optimal fault-tolerant control design for unmanned vehicle systems.

A multi-objective energy coordinative and management policy for solid oxide fuel cell using triune brain large-scale multi-agent deep deterministic policy gradient

In this paper, a data-driven multi-objective energy coordinative management policy is proposed in order to enhance the net output power and efficiency of a solid oxide fuel cell (SOFC) and prevent constraint violations. This study focuses on the optimization agent and controller design for a SOFC power system to maintain stable oxygen excess ratio (OER) and fuel utilization (FU) ratio as well as meet the load demand simultaneously. The optimization agent is responsible for output the reference OER and FU, aiming to achieve maximum net output power and operational efficiency as well as dynamic constraint satisfaction times in terms of OER and FU in real time. By applying reference OER and FU settings, the air and hydrogen flow within the SOFC can be effectively controlled by coordination of the air control agent and hydrogen control agent, respectively. In addition, a triune brain large-scale multi-agent deep deterministic policy gradient algorithm (TBL-MADDPG) is proposed. In order to improve the robustness of the proposed policy, the design of TBL-MADDPG entails curriculum learning, imitation learning and a large-scale multi-agent training framework. The performance of this proposed method is verified by the experiment.

Diversified-Intensified Current Search Algorithm and Its Application to Optimal State-Feedback Controller Design for Tractor Active Suspension System

Wydawnictwo SIGMA-NOT wydaje czasopisma fachowe informujące swoich czytelników o najnowszych osiągnięciach naukowych i nowoczesnych rozwiązaniach technicznych w Polsce i na świecie, popularyzuje problemy techniczne oraz poszerza wiedzę i kulturę techniczną.

Optimal negative derivative feedback controller design for collocated systems based on [formula omitted] and [formula omitted] method

In this paper, a direct procedure is presented in order to design negative derivative feedback (NDF) controller for collocated systems. Collocated systems have embedded sensors and actuators, which have an alternating poles and zeroes in frequency domain, which creates asymptotic stability. NDF is a band-pass filter, cutting off the control action far from the natural frequencies associated with the controlled modes, which reduces the spillover effect. Since it is a band-pass filter, it can effectively control the lower and higher frequency disturbances. Also, it is very efficient controller for higher frequencies’ vibration mitigation. An approach for an optimal design of NDF controller to implement on collocated system is presented. A simple, collocated system is considered and a mode of it is targeted to damp. Maximum damping method is used to extract all of the controller constants dependent on closed-loop damping value. Afterward, H2 and H∞ methods are utilized to determine the closed-loop damping value optimally. The results show that NDF not only can easily damp the targeted mode impactfully but also can reduce some level of vibrations in the modes after that as well. This shows the power of NDF filter on vibration mitigation of modes located in a band of frequency. The proposed method is applicable for any general system and for any zero/pole patterns of collocated system, easily. It can be applied for any collocated system with zero before pole pattern or zero after pole pattern.

Impedance Variation and Learning Strategies in Human-Robot Interaction.

In this survey, various concepts and methodologies developed over the past two decades for varying and learning the impedance or admittance of robotic systems that physically interact with humans are explored. For this purpose, the assumptions and mathematical formulations for the online adjustment of impedance models and controllers for physical human-robot interaction (HRI) are categorized and compared. In this systematic review, studies on: 1) variation and 2) learning of appropriate impedance elements are taken into account. These strategies are classified and described in terms of their objectives, points of view (approaches), and signal requirements (including position, HRI force, and electromyography activity). Different methods involving linear/nonlinear analyses (e.g., optimal control design and nonlinear Lyapunov-based stability guarantee) and the Gaussian approximation algorithms (e.g., Gaussian mixture model-based and dynamic movement primitives-based strategies) are reviewed. Current challenges and research trends in physical HRI are finally discussed.

Optimal Design of PIDA Controller for Wind Turbine Systems by Cuckoo Search

Wydawnictwo SIGMA-NOT wydaje czasopisma fachowe informujące swoich czytelników o najnowszych osiągnięciach naukowych i nowoczesnych rozwiązaniach technicznych w Polsce i na świecie, popularyzuje problemy techniczne oraz poszerza wiedzę i kulturę techniczną.

An Optimal Quantitative PID Controller Design for Ball and Beam System

In this paper, the design of two degree of freedom controller for ball and beam system is proposed. The Quantitative Feedback Theory (QFT) constraints are used to design two PID controllers to stabilize and compensate the nonlinear system with robust stability, robust performance and more desirable time response specifications. A multi objective cost function is proposed in this work to represent the function of QFT. The Black Hole Optimization (BHO) technique is a useful method to automate the design procedure of the proposed controller. The results of simulation indicate that the suggested optimal quantitative PID controller can give a desirable performance in comparison to other controllers designed in previous work.

A coupled numerical framework for hybrid floating offshore wind turbine and oscillating water column wave energy converters

Integrating floating offshore wind turbines with oscillating-water-column wave energy converters has been seen as a promising solution for hybrid offshore renewable energy production, as the cost-effective wave energy devices could possibly help increase the overall power absorption, reduce platform dynamic responses, and mitigate loads for critical wind turbine structures etc. As most existing research works on dynamic analysis of these hybrid concepts are based on frequency-domain simulations or scale model experiments, this work focuses on establishing an aero-hydro-elastic-servo-mooring coupled numerical framework for integrated time-domain dynamic analysis. In particular, the water column dynamics are characterised based on an equivalent virtual oscillating body approach so that the time-domain analysis capability for oscillating-water-columns with power take-off control is enabled. For validation, a novel combined concept is designed, and its time-domain numerical results under various environmental conditions have been compared against the 1:50 scale model wave basin test data. Good agreement has been observed between the numerical and experimental results, demonstrating the feasibility of the proposed numerical framework. Furthermore, different power take-off control strategies for the oscillating-water-column wave energy converters have been proposed, and it is found that the designed gain-scheduling control schemes are more beneficial for mitigating the platform motion responses and wind turbine structural loads compared with traditional linear damping control, resulting in 15% platform pitch motion mitigation and 6% tower base fatigue load reduction. Further studies on multi-objective optimal power take-off control design regarding both load reduction and power maximisation could be conducted for hybrid energy platforms based on the established numerical framework.

Optimal design of fuzzy-PID controller for automatic generation control of multi-source interconnected power system

This paper suggests a fuzzy logic controller (FLC) structure from seven membership functions (MFs) and its input–output relationship rules to design a secondary controller to reduce load frequency control (LFC) issues. The FLC is coupled to a proportional–integral–derivative (PID) controller as the proposed FPID controller, which is tuned by an optimized water cycle algorithm (WCA). The proposed WCA: FPID scheme was implemented with two models from the literature under the integral time absolute error cost function. Initially, a two-area non-reheat unit was implemented, and the gains of PID and FPID controllers were adjusted to verify the suitability of WCA in solving LFC issues. Then, in order to identify the robustness of the closed-loop system, sensitivity analysis is carried out. Additionally, a two-area non-reheat unit was tested under the governor dead band nonlinearity. To guarantee the suitability of the proposed FPID controller, a model with a mixture of power plants, such as reheat, hydro, and gas unit in each area was carried out with and without the HVDC link, which can increase practical issues with LFC. The proposed controller's robustness was studied for all models under numerous scenarios, step load perturbations (SLP), and different objective functions. Simulation results proved that the proposed FPID controller provided superior performance compared to recently reported techniques in terms of peaks and settling time.

Robust control for a class of nonlinear systems with input constraints based on actor‐critic learning

AbstractThis article focuses on establishing a general robust actor‐critic online learning control structure for disturbed nonlinear continuous systems with input constraints. It enriches the existing studies for the robustness of input constraint systems. First, the problem of robust controller design is successfully transformed into optimal controller design, and this process is proven, in which a particular nonquadratic discount cost function is defined. Then, build two neural networks (NNs) to estimate the cost function together and update each other. In the update process of actor NN, a robust term related to the state is introduced, which can guarantee the system's stability during the online learning process, and the state information is more fully utilized. Furthermore, using Lyapunov's direct method, it is proved that the estimated weights of the closed‐loop optimal control system and the actor‐critic NNs are uniformly ultimately bounded (UUB). It also provides extended discussions and a simulation example to demonstrate the robustness verification results of the novel algorithm.

Performance Analysis and Optimization of NOMA-Based Cell-Free Massive MIMO for IoT

This article investigates the performance of nonorthogonal multiple access (NOMA)-based cell-free massive multiple-input–multiple-output (mMIMO) for the Internet of Things (IoT) considering spatially correlated Rician fading channels. The exact closed form of downlink spectral efficiency (SE) and energy efficiency expressions is derived with three estimators and the maximum ratio transmission by taking the impacts of imperfect successive interference cancellation and pilot contamination into account. Subsequently, the performance of a local-MMSE precoder with the three aforementioned estimators is analyzed. Then, a large-scale fading-based user pairing scheme is proposed to further analyze the system SE. Besides, we formulate the optimum power control design as a max–min problem and a computational efficient suboptimal algorithm is proposed based on the successive convex approximation. Furthermore, our results reveal that the magnitude of the spatial correlation negligibly effects the SE in spatially correlated Rician fading channels. Then, numerical results confirm the positive effect of the proposed power control scheme. Also, our results further illustrate that NOMA-based cell-free mMIMO for IoT provides significant performance gain compared with its counterpart deploying conventional orthogonal multiple-access schemes.

Optimal Signal Control Design for Isolated Intersections Using Sample Travel-Time Data

Increased travel times are often observed on urban roads, with signalized intersections being the major bottlenecks. The inability of existing static signal timings in accommodating the actual demand fluctuations could be one of the contributing factors. A traffic-responsive signal control system that changes signal timings according to traffic volume fluctuations may alleviate this problem. However, such problems are conventionally formulated based on the data collected from location-based sensors, which are infrastructure intensive and costly and fail to capture mixed and disordered traffic conditions. Considering these limitations, this paper presents an optimal signal design using sample travel time information collected from mobile data sources such as GPS/Bluetooth/Wi-Fi sensors that work independently of the traffic conditions and are relatively cost-effective. The proposed adaptive signal design minimizes total intersection delay at isolated intersections for every cycle based on the traffic conditions observed in the previous cycle. The mathematical programming-based formulation uses shock waves formed during the red and green phases to estimate optimal-phase durations. Results revealed that the proposed design is capable of handling traffic flow fluctuations without requiring the entire traffic stream data. The system demonstrated that sample data from four probe vehicles per phase is adequate for real-time optimal signal design. Results showed that the proposed model outperformed the existing Webster’s signal design procedure with a delay reduction of 11.78% when compared theoretically and 10.41% when implemented in VISSIM.

Bilinearization, Reachability, and Optimal Control of Control-Affine Nonlinear Systems: A Koopman Spectral Approach

This article considers the problem of bilinearization and optimal control of a control-affine nonlinear system by projecting the system dynamics onto the Koopman eigenspace. Although there are linearization techniques like Carleman linearization for embedding a finite-dimensional nonlinear system into an infinite-dimensional space, they depend on the analytic property of the vector fields and work only on polynomial space. The proposed method utilizes the Koopman canonical transform, specifically the Koopman eigenfunctions of the drift vector field, to transform the dynamics into a bilinear system under certain assumptions. While the bilinearization is exact, if there exists a Koopman-invariant finite-dimensional subspace for the drift vector field, sometimes this condition is too conservative. An approximate approach is to minimize an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}^2$</tex-math></inline-formula> norm on the truncated state-space. The approximation can be carried out from time-series data without explicit knowledge of the drift vector field. Controllability of the bilinear system is analyzed using the Myhill semigroup method and Lie algebraic structures. Pontryagin’s principle is applied to the bilinear system to yield a two-point boundary-value problem for the optimal control design. A single shooting method solves the boundary value problem in order to determine the control signal. Alternatively, a gradient-based method is also outlined to find the optimal control which exploits the bilinear structure. Several examples of control-affine nonlinear systems numerically illustrate the bilinearization and optimal control design, assuming a cost function quadratic in the states and control input.

Learning-Based Adaptive Optimal Control for Connected Vehicles in Mixed Traffic: Robustness to Driver Reaction Time.

Through vehicle-to-vehicle (V2V) communication, both human-driven and autonomous vehicles can actively exchange data, such as velocities and bumper-to-bumper distances. Employing the shared data, control laws with improved performance can be designed for connected and autonomous vehicles (CAVs). In this article, taking into account human-vehicle interaction and heterogeneous driver behavior, an adaptive optimal control design method is proposed for a platoon mixed with multiple preceding human-driven vehicles and one CAV at the tail. It is shown that by using reinforcement learning and adaptive dynamic programming techniques, a near-optimal controller can be learned from real-time data for the CAV with V2V communications, but without the precise knowledge of the accurate car-following parameters of any driver in the platoon. The proposed method allows the CAV controller to adapt to different platoon dynamics caused by the unknown and heterogeneous driver-dependent parameters. To improve the safety performance during the learning process, our off-policy learning algorithm can leverage both the historical data and the data collected in real time, which leads to considerably reduced learning time duration. The effectiveness and efficiency of our proposed method is demonstrated by rigorous proofs and microscopic traffic simulations.