Optimization of microalgal photobioreactor system using model predictive control with experimental validation.

To maximize biomass and lipid concentrations, various optimization methods were investigated in microalgal photobioreactor systems under mixotrophic conditions. Lipid concentration was estimated using unscented Kalman filter (UKF) with other measurable sources and subsequently used as lipid data for performing model predictive control (MPC). In addition, the maximized biomass and lipid trajectory obtained by open-loop optimization were used as target trajectory for tracking by MPC. Simulation studies and experimental validation were performed and significant improvements in biomass and lipid productivity were achieved in the case where MPC was applied. However, occurence of a lag phase was observed while manipulating the feed flow rates, which is induced by large amount of inputs. This is an important phenomenon that can lead to model-plant mismatch and requires further study for the optimization of microalgal photobioreactors.

Quantized-output-feedback practical prescribed-time design strategy for decentralized tracking of a class of interconnected nonlinear systems with unknown interaction delays.

This paper proposes a decentralized practical prescribed-time (PT) tracking design using quantized output feedback (QOF) for uncertain interconnected lower-triangular systems with unknown time-delay interconnections. The local output signals are assumed to be only measured and quantized for the PT tracker design under a band-limited network. By employing a PT-dependent scaling function, a decentralized memoryless PT observer based on quantized local outputs is developed to estimate local unmeasurable state variables. Owing to output quantization, the available output feedback signals become discontinuous. As a result, the tracking error between the actual (i.e., unquantized) local output and the local desired signal cannot be utilized in the local virtual controller. To address this issue, a novel adaptive compensation mechanism is derived to design the local PT neural network tracking laws using only quantized local outputs and estimated states. The proposed PT tracking controller does not require information on the interconnected nonlinear functions and interaction delays. During the Lyapunov stability analysis, the boundary layer error decomposition approach is employed to address the issue of non-differentiability in the local virtual control laws. The proposed QOF control system achieves practical PT stability. It is shown that the settling time of local tracking errors can be predetermined, regardless of the design parameters and initial conditions. Finally, the proposed QOF decentralization strategy is supported with illustrative examples and a comparison to demonstrate its benefits.

Adaptive-observer-based consensus tracking with fault-tolerant network connectivity of uncertain time-delay nonlinear multiagent systems with actuator and communication faults.

In this study, a distributed output-feedback design approach for ensuring fault-tolerant initial network connectivity and preselected-time consensus tracking performance is proposed for a class of uncertain time-delay nonlinear multiagent systems (TDNMSs) with unexpected actuator and communication faults. It is assumed that time-varying state delays and system nonlinearities in TDNMSs are unknown. The main contribution of this study is to provide a delay-independent output-feedback control strategy to address a fault-tolerant initial connectivity preservation problem in the consensus tracking field. A local delay-independent adaptive state observer using neural networks is designed for each follower, and the boundedness of local observation errors is proved by constructing a Lyapunov-Krasovskii functional and adaptive tuning laws. Then, the local nonlinear relative output errors using a time-varying function with a preselected convergence time are derived to design simple local delay-independent trackers. The stability of the proposed consensus tracking system is analyzed, and simulation comparison results demonstrate the validity of the proposed strategy.

Distributed Adaptive Formation Tracking for a Class of Uncertain Nonlinear Multiagent Systems: Guaranteed Connectivity Under Moving Obstacles.

This article explores a guaranteed network connectivity problem during moving obstacle avoidance within a distributed formation tracking framework for uncertain nonlinear multiagent systems with range constraints. We investigate this problem based on a new adaptive distributed design using nonlinear errors and auxiliary signals. Within the detection range, each agent regards other agents and static or dynamic objects as obstacles. The nonlinear error variables for formation tracking and collision avoidance are presented, and the auxiliary signals in formation tracking errors are introduced to maintain network connectivity under the avoidance mechanism. The adaptive formation controllers using command-filtered backstepping are constructed to ensure closed-loop stability with collision avoidance and preserved connectivity. Compared with the previous formation results, the resulting features are as follows: 1) the nonlinear error function for the avoidance mechanism is considered an error variable, and an adaptive tuning mechanism for estimating the dynamic obstacle velocity is derived in a Lyapunov-based control design procedure; 2) network connectivity during dynamic obstacle avoidance is preserved by constructing the auxiliary signals; and 3) owing to neural networks-based compensating variables, the bounding conditions of time derivatives of virtual controllers are not required in the stability analysis.

Neural-Network-Based Distributed Asynchronous Event-Triggered Consensus Tracking of a Class of Uncertain Nonlinear Multi-Agent Systems.

This article proposes a neural-network-based adaptive asynchronous event-triggered design strategy for the distributed consensus tracking of uncertain lower triangular nonlinear multi-agent systems under a directed network. Compared with the existing event-triggered recursive consensus tracking designs using multiple neural networks for each follower and continuous communications among followers, the primary contribution of this study is the development of an asynchronous event-triggered consensus tracking methodology based on a single-neural network for each follower under event-driven intermittent communications among followers. To this end, a distributed event-triggered estimator using neighbors' triggered output information is developed to estimate a leader signal. Subsequently, the estimated leader signal is used to design local trackers. Only a triggering law and a single-neural network are used to design the local tracking law of each follower, irrespective of unmatched unknown nonlinearities. The information of each follower and its neighbors is asynchronously and intermittently communicated through a directed network. Thus, the proposed asynchronous event-triggered tracking scheme can save communicational and computational resources. From the Lyapunov stability theorem, the stability of the entire closed-loop system is analyzed and the comparative simulation results demonstrate the effectiveness of the proposed control strategy.

Distributed Quantized Feedback Design Strategy for Adaptive Consensus Tracking of Uncertain Strict-Feedback Nonlinear Multiagent Systems With State Quantizers.

This study investigates a quantized feedback design problem for distributed adaptive leader-following consensus of uncertain strict-feedback nonlinear multiagent systems with state quantizers. It is assumed that all system nonlinearities of followers are unknown and heterogeneous, all state variables of each follower are quantized by a uniform state quantizer, and quantized states of followers are only communicated under a directed network. Compared with previous approximation-based distributed consensus tracking methods for uncertain lower triangular multiagent systems, the main contribution of this article is addressing the distributed quantized state communication problem in the adaptive leader-following consensus tracking field of uncertain lower triangular multiagent systems. A quantized-states-based local adaptive control law for each follower is derived by designing quantized-signals-based weight tuning laws for neural-network-based function approximators. By analyzing the boundedness of the local quantization errors, it is shown that the total closed-loop signals are uniformly ultimately bounded and the consensus tracking errors converge to a sufficiently small domain around the origin. Finally, simulation examples, including multiple ship steering systems, are considered to verify the effectiveness of the proposed theoretical approach.

Neural-Network-Based Adaptive Resilient Dynamic Surface Control Against Unknown Deception Attacks of Uncertain Nonlinear Time-Delay Cyberphysical Systems.

A neural-network-based dynamic surface design strategy against sensor and actuator deception attacks is presented to design a delay-independent adaptive resilient control scheme of uncertain nonlinear time-delay cyberphysical systems in the lower triangular form. It is assumed that all nonlinearities, time-varying delays, and sensor and actuator attacks are unknown. In the concerned problem, since the state information measured by sensors is compromised by additional attack signals, the exact state variables are not available for feedback. Thus, a memoryless adaptive resilient control design using compromised state variables is developed by employing the neural-network-based function approximation technique and designing the attack compensator. The resulting control scheme ensures the robust stabilization in the presence of unknown deception attacks and time-varying delays. It is shown from the Lyapunov stability analysis that all closed-loop signals are uniformly ultimately bounded and the stabilization errors converge to an adjustable neighborhood of the origin.

Distributed approximation-free design for ensuring network connectivity of uncertain nonholonomic multi-robot synchronized tracking systems with disturbances.

A distributed approximation-free design for maintaining initial connectivity of uncertain nonholonomic multi-robot synchronized tracking systems is developed under limited communication ranges where the models of followers are regarded as the kinematics and dynamics of uncertain nonholonomic mobile robots. All nonlinearities and external disturbances in the followers' dynamics are assumed to be unknown. The primary improvement in the current development is that local trackers for ensuring connectivity among robots are designed by using only relative posture errors and adaptive function approximators such as neural networks or fuzzy logic systems are not utilized despite unknown nonlinearities in the robot dynamics. This improvement has been done by transforming individual linear position errors among mobile robots to individual nonlinear position errors using connectivity-preserving functions with communication ranges. The predefined synchronized tracking performance and the guaranteed connectivity of the overall closed-loop system are proved via the Lyapunov stability theorem.

Decentralized adaptive quantized feedback tracking of a class of uncertain interconnected lower-triangular nonlinear systems.

A decentralized adaptive quantized feedback tracking problem is addressed for uncertain interconnected nonlinear systems in a strict-feedback form. All local state variables for each subsystem are quantized by a hysteresis quantizer. Different from the existing results in the literature, the primary contribution of this study is to establish an adaptive control design and stability analysis strategy using the local quantized state variables in the decentralized tracking field. A novel recursive design approach is presented to deal with unmatched interconnections and nonlinearities in the quantized feedback control framework, without any restrictions on virtual control laws. The total closed-loop stability is analyzed by deriving some technical lemmas on the boundedness of quantization error signals.

An Error Transformation Approach for Connectivity-Preserving and Collision-Avoiding Formation Tracking of Networked Uncertain Underactuated Surface Vessels.

This paper investigates a distributed connectivity-preserving and collision-avoiding formation tracking problem of networked uncertain underactuated surface vessels (USVs) with heterogeneous limited communication ranges. All nonlinearities in the dynamic model are assumed to be completely unknown. Compared with the existing formation tracking results for USVs, our primary contribution is to develop a new nonlinearly transformed formation error for achieving the initial connectivity preservation, the collision avoidance, and the distributed formation tracking without switching the desired formation pattern and using any additional potential functions. In other words, these three objectives can be achieved by using only one transformed formation error surface. The local tracker design strategy using the nonlinearly transformed error is established under the direct graph topology, where the adaptive function approximation technique and the auxiliary variables are employed to compensate for uncertain nonlinearities and to deal with the underactuated problem of USVs, respectively. Finally, the Lyapunov stability analysis and simulations are performed to verify the effectiveness of the proposed theoretic result.

Connectivity-Preserving Consensus Tracking of Uncertain Nonlinear Strict-Feedback Multiagent Systems: An Error Transformation Approach.

This brief addresses a distributed connectivity-preserving adaptive consensus tracking problem of uncertain nonlinear strict-feedback multiagent systems with limited communication ranges. Compared with existing consensus results for uncertain nonlinear lower triangular multiagent systems, the main contribution of this brief is to present an error-transformation-based design methodology to preserve initial connectivity patterns in the consensus tracking field, namely, both connectivity preservation and consensus tracking problems are considered for uncertain nonlinear lower triangular multiagent systems. A dynamic surface design based on nonlinearly transformed errors and neural network function approximators is established to construct the local controller of each follower. In addition, a technical lemma is derived to analyze the stability of the proposed connectivity-preserving consensus scheme in the Lyapunov sense.

Connectivity-Preserving Approach for Distributed Adaptive Synchronized Tracking of Networked Uncertain Nonholonomic Mobile Robots.

This paper addresses a distributed connectivity-preserving synchronized tracking problem of multiple uncertain nonholonomic mobile robots with limited communication ranges. The information of the time-varying leader robot is assumed to be accessible to only a small fraction of follower robots. The main contribution of this paper is to introduce a new distributed nonlinear error surface for dealing with both the synchronized tracking and the preservation of the initial connectivity patterns among nonholonomic robots. Based on this nonlinear error surface, the recursive design methodology is presented to construct the approximation-based local adaptive tracking scheme at the robot dynamic level. Furthermore, a technical lemma is established to analyze the stability and the connectivity preservation of the total closed-loop control system in the Lyapunov sense. An example is provided to illustrate the effectiveness of the proposed methodology.

Event-triggered decentralized adaptive fault-tolerant control of uncertain interconnected nonlinear systems with actuator failures.

This paper investigates the event-triggered decentralized adaptive tracking problem of a class of uncertain interconnected nonlinear systems with unexpected actuator failures. It is assumed that local control signals are transmitted to local actuators with time-varying faults whenever predefined conditions for triggering events are satisfied. Compared with the existing control-input-based event-triggering strategy for adaptive control of uncertain nonlinear systems, the aim of this paper is to propose a tracking-error-based event-triggering strategy in the decentralized adaptive fault-tolerant tracking framework. The proposed approach can relax drastic changes in control inputs caused by actuator faults in the existing triggering strategy. The stability of the proposed event-triggering control system is analyzed in the Lyapunov sense. Finally, simulation comparisons of the proposed and existing approaches are provided to show the effectiveness of the proposed theoretical result in the presence of actuator faults.

Memoryless disturbance-observer-based adaptive tracking of uncertain pure-feedback nonlinear time-delay systems with unmatched disturbances.

This paper presents a delay-independent nonlinear disturbance observer (NDO) design methodology for adaptive tracking of uncertain pure-feedback nonlinear systems in the presence of unknown time delays and unmatched external disturbances. Compared with all existing NDO-based control results for uncertain lower-triangular nonlinear systems where unknown time delays have been not considered, the main contribution of this paper is to develop a delay-independent design strategy to construct an NDO-based adaptive tracking scheme in the presence of unknown time-delayed nonlinearities and non-affine nonlinearities unmatched in the control input. The proposed delay-independent scheme is constructed by employing the appropriate Lyapunov-Krasovskii functionals and the same function approximators for the NDO and the controller. It is shown that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to an adjustable neighborhood of the origin.

Adaptive dynamic surface control of flexible-joint robots using self-recurrent wavelet neural networks.

A new method for the robust control of flexible-joint (FJ) robots with model uncertainties in both robot dynamics and actuator dynamics is proposed. The proposed control system is a combination of the adaptive dynamic surface control (DSC) technique and the self-recurrent wavelet neural network (SRWNN). The adaptive DSC technique provides the ability to overcome the "explosion of complexity" problem in backstepping controllers. The SRWNNs are used to observe the arbitrary model uncertainties of FJ robots, and all their weights are trained online. From the Lyapunov stability analysis, their adaptation laws are induced, and the uniformly ultimately boundedness of all signals in a closed-loop adaptive system is proved. Finally, simulation results for a three-link FJ robot are utilized to validate the good position tracking performance and robustness against payload uncertainties and external disturbances of the proposed control system.

Minimal-Approximation-Based Decentralized Backstepping Control of Interconnected Time-Delay Systems.

A decentralized adaptive backstepping control design using minimal function approximators is proposed for nonlinear large-scale systems with unknown unmatched time-varying delayed interactions and unknown backlash-like hysteresis nonlinearities. Compared with existing decentralized backstepping methods, the contribution of this paper is to design a simple local control law for each subsystem, consisting of an actual control with one adaptive function approximator, without requiring the use of multiple function approximators and regardless of the order of each subsystem. The virtual controllers for each subsystem are used as intermediate signals for designing a local actual control at the last step. For each subsystem, a lumped unknown function including the unknown nonlinear terms and the hysteresis nonlinearities is derived at the last step and is estimated by one function approximator. Thus, the proposed approach only uses one function approximator to implement each local controller, while existing decentralized backstepping control methods require the number of function approximators equal to the order of each subsystem and a calculation of virtual controllers to implement each local actual controller. The stability of the total controlled closed-loop system is analyzed using the Lyapunov stability theorem.

A comparative study of soft sensor design for lipid estimation of microalgal photobioreactor system with experimental validation.

This study examines the applicability of various nonlinear estimators for online estimation of the lipid concentration in microalgae cultivation system. Lipid is a useful bio-product that has many applications including biofuels and bioactives. However, the improvement of lipid productivity using real-time monitoring and control with experimental validation is limited because measurement of lipid in microalgae is a difficult and time-consuming task. In this study, estimation of lipid concentration from other measurable sources such as biomass or glucose sensor was studied. Extended Kalman filter (EKF), unscented Kalman filter (UKF), and particle filter (PF) were compared in various cases for their applicability to photobioreactor systems. Furthermore, simulation studies to identify appropriate types of sensors for estimating lipid were also performed. Based on the case studies, the most effective case was validated with experimental data and found that UKF and PF with time-varying system noise covariance is effective for microalgal photobioreactor system.

Dynamic modelling of mixotrophic microalgal photobioreactor systems with time-varying yield coefficient for the lipid consumption.

Microalgae have been suggested as a promising feedstock for producing biofuel because of their potential for lipid production. In this study, microalgal photobioreactor systems under mixotrophic conditions were investigated, for the purpose of developing a mathematical model that predicts biomass and lipid production. The model was developed based on the Droop model, and the optimal input design using D-optimality criterion was performed to compute the system input profile, to estimate parameters more accurately. From the experimental observations, the newly defined yield coefficient was suggested to represent the consumption of lipid and nitrogen within the cell, which reduces the number of parameters with more accurate prediction. Furthermore, the lipid consumption rate was introduced to reflect the experimental results that lipid consumption is related to carbon source concentration. The model was validated with experiments designed with different initial conditions of nutrients and input changes, and showed good agreement with experimental observations.

Distributed consensus tracking for multiple uncertain nonlinear strict-feedback systems under a directed graph.

In this brief, we study the distributed consensus tracking control problem for multiple strict-feedback systems with unknown nonlinearities under a directed graph topology. It is assumed that the leader's output is time-varying and has been accessed by only a small fraction of followers in a group. The distributed dynamic surface design approach is proposed to design local consensus controllers in order to guarantee the consensus tracking between the followers and the leader. The function approximation technique using neural networks is employed to compensate unknown nonlinear terms induced from the controller design procedure. From the Lyapunov stability theorem, it is shown that the consensus errors are cooperatively semiglobally uniformly ultimately bounded and converge to an adjustable neighborhood of the origin.

Real-time estimation of glucose concentration in algae cultivation system using Raman spectroscopy.

This work proposes a soft-sensor design for real-time estimation of glucose concentration under mixotrophic conditions using Raman spectroscopy. The suggested approach applies a Rolling-Circle Filter (RCF), Partial Least Squares (PLS), and a successive Savitzky-Golay (SG) smoothing filter. RCF is used to remove the background effects of Raman spectrum in the pre-processing step. PLS is used to reduce the dimensionality of spectrum data and relate them to the concentration. The SG filter is further employed as a post-processing step in a successive manner to adjust predicted glucose concentrations. Two sets of experiments using artificial assays and samples from a microalgae cultivation system were performed for verification. The proposed approach showed improved prediction performances compared to other data processing and regression techniques.