Unknown Dynamics Research Articles

Optimized backstepping‐based finite‐time containment control for nonlinear multi‐agent systems with prescribed performance

AbstractIn this article, a finite‐time optimal containment control method is proposed for nonlinear multi‐agent systems with prescribed performance. First, a neural network‐based reinforcement learning algorithm is developed under the optimized backstepping framework. The algorithm employs an identifier‐critic‐actor architecture, where the identifiers, critics and actors are used to estimate the unknown dynamics, evaluate the system performance, and optimize the system, respectively. Subsequently, in order to guarantee the transient performance of the tracking error, the original system is converted into an equivalent unconstrained system. Then, the tracking errors are allowed to converge to a prescribed set of residuals in finite time by combining prescribed performance control and finite‐time optimal control techniques. Furthermore, by using the Lyapunov stability theorem, it is verified that all signals are semi‐globally practical finite‐time stable, and all followers can converge to a convex region formed by multiple leaders. Finally, the effectiveness of the proposed scheme is demonstrated by a practical example.

Dynamics of actinotrichia, fibrous collagen structures in zebrafish fin tissues, unveiled by novel fluorescent probes

Abstract Collagen fibers provide physical support to animal tissues by orienting in the correct position and at optimal density. Actinotrichia are thick collagen fibers that are present at the tips of fish fins and serve as scaffolds for bone formation. The arrangement and density of actinotrichia must be constantly maintained with a high degree of regularity to form spatial patterns in the fin bones, but the mechanisms of this process are largely unknown. To address this issue, we first identified two fluorescent probes that can stain actinotrichia clearly in vivo. Using these probes and time-lapse observation of actinotrichia synthesized at different growth stages, we revealed the following previously unknown dynamics of actinotrichia. (i) Actinotrichia do not stay stationary at the place where they are produced; instead, they move towards the dorsal area during the notochord bending and (ii) move towards the distal tip during the fin growth. (iii) Actinotrichia elongate asymmetrically as new collagen is added at the proximal side. (iv) Density is maintained by the insertion of new actinotrichia. (v) Actinotrichia are selectively degraded by osteoclasts. These findings suggest that the regular arrangement of actinotrichia is the outcome of multiple dynamic processes.

Optimal trajectory tracking of uncertain nonlinear continuous-time strict-feedback systems with dynamic constraints

A novel method for optimal trajectory tracking of uncertain nonlinear systems by using adaptive dynamic programming (ADP)-based integral reinforcement learning (IRL) and neural networks (NNs) is proposed. The method utilises an actor-critic framework with optimal backstepping to minimise a discounted value function and uses a single-layer NN identifier for estimating the unknown dynamics. For safety assurance, a time-varying barrier Lyapunov function (TVBLF) is used in the control design to handle the constraints. A novel weight-tuning law by using the control input error, integral Bellman error, and the NN identifier is used for the actor-critic framework. A novel lifelong learning (LL)-based method for critic NN is utilised in an optimal framework by incorporating the Bellman error to mitigate catastrophic forgetting in multitasking scenarios. Stability analysis using Lyapunov stability theory is obtained for the overall closed-loop system. Simulations of leader-follower mobile robot formation control show a 25% reduction in the cost in multitasking scenarios.

Adaptive fault-tolerant control for a class of nonlinear multi-agent systems with multiple unknown time-varying control directions

In this paper, we investigate the consensus tracking control for a class of heterogeneous multi-agent systems with multiple unknown time-varying control directions and unknown direction actuator faults. Different from existing work, the directions of the multiple time-varying control coefficients are subject to fault-induced sign-switching. To address this challenge, a series of high-order Lyapunov functions and differentiable functions are introduced to avoid non-integrable terms. Then, a novel contradiction statement and some Nussbaum functions are used to handle the summation of multiple unknown control coefficients with time-varying amplitudes and directions. Meanwhile, a novel distributed observer with quantized communication is introduced to track a reference trajectory with unknown dynamics. It is shown that all closed-loop signals are globally uniformly bounded and the tracking errors converge to residual sets that can be made arbitrarily small. Simulation results illustrate the effectiveness of the proposed scheme.

Periodic event-triggered controller design with Bayesian optimization: An emulation-based approach

In recent years, event-triggered control has emerged as a promising strategy for addressing resource constraints in networked control systems (NCSs), such as limited life-time of battery capacity. This paper explores the development of a periodic event-triggered controller through a model-free design, assuming unknown plant dynamics. The design of the event-triggered controller employs an emulation-based approach, which is divided into solving two sub-problems: the problem for designing parameters for the time-triggered (periodic) control law, and the problem for designing parameters for the event-triggered condition. In particular, both problems will be solved through the usage of two distinct Bayesian optimization algorithms. The first problem is addressed by adapting basic Bayesian optimization to include network utilization by considering the number of communication time steps during optimization. The second problem employs constrained Bayesian optimization to incorporate explicit performance constraints within the optimization process. A numerical example is provided to demonstrate the effectiveness of the proposed method.

On neural networks application in integral sliding mode control

In this paper, the combined use of deep neural networks (DNNs) and integral sliding mode (ISM) control is investigated, giving rise to novel DNN-ISM control strategies for nonlinear systems affine in the control law, characterized by fully unknown dynamics and subject to disturbances. In particular, two feed-forward DNNs are used to approximate the drift term and the control effectiveness matrix of the nonlinear systems model. The DNNs weights are tuned online relying on adaptation laws derived from Lyapunov’s stability analysis. The DNNs with their weights tuning mechanism are exploited as building blocks in the design of an ISM control scheme to solve trajectory tracking problems. The proposed framework is then extended to the case in which the system dynamics is subject to time-varying state constraints, producing a second scheme, still of DNN-ISM type. Both control schemes are analyzed, providing interesting theoretical guarantees. Possible solutions to reduce, in practical implementations, the chattering effect, as well as the initial estimation error of the DNNs are also discussed. The proposed DNNs-based control schemes are finally assessed in simulation relying on a realistic model of an anthropomorphic 7-axes robot manipulator.

Identifying Community-Bridge Network Structures via Bayesian Learning With Mixed Sparsity Mode.

Identifying structures of complex networks based on time series of nodal data is of considerable interest and significance in many fields of science and engineering. This article presents a sparse Bayesian learning (SBL) method for identifying structures of community-bridge networks, where nodes are grouped to form communities connected via bridges. Using the structural information of such networks with unknown nodal dynamics and community formations, network structure identification is tackled similar to sparse signal reconstruction with mixed sparsity mode. The proposed method is theoretically proved to be convergent. Its superiority to mainstream baselines is demonstrated via extensive experiments without the need for manual adjustment of regularization parameters.

A High-Gain Observer Approach to Robust Trajectory Estimation and Tracking for a Multi-Rotor Uav

Abstract Using the context of trajectory estimation and tracking for multi-rotor UAVs, we explore the challenges in applying high-gain observers to highly dynamic systems. The multi- rotor will operate in the presence of external disturbances and modeling errors. At the same time, the reference trajectory is unknown and generated from a reference system with unknown or partially known dynamics. We assume the only measurements that are available are the position and orientation of the multi-rotor and the position of the reference sys- tem. We adopt an extended high-gain observer (EHGO) estimation framework to estimate the unmeasured multi-rotor states, modeling errors, external disturbances, and the reference trajectory. We design a robust output feedback con- troller for trajectory tracking that comprises a feedback linearizing controller and the EHGO. The proposed control method is rigorously analyzed to establish its stability properties. Finally, we illustrate our theoretical results through numerical simulation and experimental validation in which a multi-rotor tracks a moving ground vehicle with an unknown trajectory and dynamics and successfully lands on the vehicle while in motion.

Path-following control of an underactuated stratospheric airship with unknown dynamics and external disturbances using time-delay control

In this paper, the path-following problem for an underactuated stratospheric airship with unknown dynamics and external disturbances has been studied. Vector field guidance is employed to fix the underactuated issue and generate desired heading. Time-delay control (TDC) is utilised to track desired states and estimate the model uncertain and disturbances using simple delayed states. To compensate time-delay estimation (TDE) errors, terminal sliding-mode is utilised and combined with TDC. The stability of the proposed controller is provided by using Lyapunov function. A numerical simulation is demonstrated to prove the performance of the proposed control algorithm.

Reinforcement learning‐based finite‐time cross‐media tracking control for a cross‐media vehicle under unknown dynamics and disturbances

AbstractThis study proposes a reinforcement learning‐based finite‐time cross‐media tracking control approach for a slender body cross‐media vehicle encountering unknown hydrodynamics, wind, and wave disturbances. Initially, a reinforcement learning framework consisting of the actor neural network and critic neural network is constructed. The critic neural network monitors the actions of the actor neural network and approximates the cost function, while the actor neural network estimates the unknown hydrodynamics and disturbances, minimising the cost function to optimise performance. Subsequently, the command filter featuring finite‐time convergence is formulated, effectively managing the corresponding filter error through a proposed error compensating signal. By integrating these techniques, a reinforcement learning‐based finite‐time control strategy is developed, circumventing the singularity issue inherent in traditional finite‐time backstepping strategies. Comparative analysis with existing methods demonstrates the strong robustness of the proposed scheme against unknown hydrodynamics and disturbances, ensuring finite‐time convergence of the system's states and optimising controller performance. Finally, simulations confirm the effectiveness and superiority of the presented approach.

[formula omitted] tracking control for de-oiling hydrocyclone systems via event-triggered reinforcement learning

De-oiling hydrocyclone system is a crucial device in offshore oil and gas production. To reduce action frequency of actuators as well as energy costs, it is desired to apply event-triggered control (ETC) technique for coordination control of de-oiling hydrocyclone systems. However, the triggering errors and slugging disturbances will greatly affect oil-water separation efficiency and need to be well treated. Towards this end, this work studies the coordination control problem of de-oiling hydrocyclone systems subject to slugging disturbances and unknown system dynamics. Robust H∞ control approach is applied to reduce disturbances sensitivity and guaranteeing satisfactory oil-water separation performance. The coordination control problem is transformed into a 2-player zero-sum game problem. A model-based solution by solving the game algebraic Riccati equation (GARE) is obtained and an event-triggered (ET) off-policy reinforcement learning (RL) algorithm is developed to implement the model-based solution. The salient feature of the proposed algorithm is that the proposed model-free H∞ control method alleviates the affects of both triggering errors and slugging disturbances, which are handled together as a generalized disturbance in the algorithm. Stability and Zeno behavior avoidance of the proposed algorithm are analyzed. Simulation studies demonstrate the effectiveness of the proposed algorithm.

Optimal fuzzy event-triggered fault-tolerant control of fractional-order nonlinear stochastic systems

This paper considers the optimal fuzzy fault-tolerant control issue for fractional-order nonlinear stochastic systems (FONSS) using event-triggered mechanisms with fractional-order derivative α∈(0,1). First, in order to weaken the impacts of actuator and sensor faults, a fuzzy observer and augmented system are developed. Since stochastic disturbance can adversely affect stability, based on fractional Barbalat lemmas and Lyapunov theory, an adaptive fault-tolerant controller and the corresponding adaptive update law are designed to ensure the stability of FONSS. Then, the architecture of identifier-critic-actor NN, which is more concise than the traditional one, is described. This NN architecture recognizes unknown dynamics and completes control actions after evaluating the control performance, driving control toward optimization. Furthermore, the event-triggered mechanism is devised to save control resources and avoid Zeno behavior. Finally, simulation results demonstrate that under equivalent conditions, the proposed optimal event-triggered control reduces the number of information transmissions compared to traditional time-triggered control, saving communication resources and enhancing the overall control performance.

Data-driven fault detection for closed-loop T-S fuzzy systems with unknown system dynamics and its application to aero-engines

This paper considers the fault detection problem of closed-loop Takagi-Sugeno (T-S) fuzzy systems with unknown system dynamics. However, the unknown dynamics make the model-based detection methods being infeasible. To tackle this problem, a detection scheme is designed directly by using input/state data, and disturbance attenuation as well as fault sensitivity performance are then introduced within data-driven framework such that a multiobjective optimization problem is formulated to compute the parameters of detector. Moreover, to remove the existing limitation that sensor faults must occur, corresponding design conditions of detector are developed by considering the characteristics of fault frequency. In particular, a linearization approach via searching the minimum singular value of unknown matrix is further developed to handle the nonconvex problem caused by introducing the fault sensitivity performance. Finally, an aero-engine system is used to show the effectiveness and advantages of the developed method.

Insights of using control theory for minimizing induced seismicity in underground reservoirs

Deep Geothermal Energy, Carbon Capture, and Storage and Hydrogen Storage have significant potential to meet the large-scale needs of the energy sector and reduce the CO2 emissions. However, the injection of fluids into the earth’s crust, upon which these activities rely, can lead to the formation of new seismogenic faults or the reactivation of existing ones, thereby causing earthquakes. In this study, we propose a novel approach based on control theory to address this issue. First, we obtain a simplified model of induced seismicity due to fluid injections in an underground reservoir using a diffusion equation in three dimensions. Then, we design a robust tracking control approach to force the seismicity rate to follow desired references. In this way, the induced seismicity is minimized while ensuring fluid circulation for the needs of renewable energy production and storage. The designed control guarantees the achievement of the control objectives even in the presence of system uncertainties and unknown dynamics. Finally, we present simulations of a simplified geothermal reservoir under different scenarios of energy demand to show the reliability and performance of the control approach, opening new perspectives for field experiments based on real-time regulators.

Reinforcement learning-based secure synchronization for two-time-scale complex dynamical networks with malicious attacks

This paper studies the secure synchronization problem for two-time-scale complex dynamical networks with unknown dynamics information and malicious attacks. The challenge is that under complex dynamic networks with unknown dynamic information, all system matrices are unknown. To ameliorate this conundrum, we design a reinforcement learning algorithm, conjoined with a full-order processing of singularly perturbed parameters, with the express objective of securing the stability of the synchronization error system within a context devoid of adversarial intrusions. Second, in order to reduce the impact of malicious attacks, a switching function is developed based on feedback gain. Besides, it is proved that the proposed distributed controllers can still guarantee the convergence of the synchronization error system under malicious attacks. Finally, two numerical examples are given to illustrate the applicability and effectiveness of the proposed algorithm.

Event-Triggered Adaptive Containment Control for Heterogeneous Stochastic Nonlinear Multiagent Systems.

This article investigates the event-triggered adaptive containment control problem for a class of stochastic nonlinear multiagent systems with unmeasurable states. A stochastic system with unknown heterogeneous dynamics is established to describe the agents in a random vibration environment. Besides, the uncertain nonlinear dynamics are approximated by radial basis function neural networks (NNs), and the unmeasured states are estimated by constructing the NN-based observer. In addition, the switching-threshold-based event-triggered control method is adopted with the hope of reducing communication consumption and balancing system performance and network constraints. Moreover, we develop the novel distributed containment controller by utilizing the adaptive backstepping control strategy and the dynamic surface control (DSC) approach such that the output of each follower converges to the convex hull spanned by multiple leaders, and all signals of the closed-loop system are cooperatively semi-globally uniformly ultimately bounded in mean square. Finally, we verify the efficiency of the proposed controller by the simulation examples.

ℒ2 gain tracking control of linear completely unknown discrete‐time networked control systems with dropout

AbstractWe introduce an online, model‐free algorithm to address the gain optimal tracking problems in discrete linear networked control systems. The algorithm is specifically proposed to handle stochastic information dropout in the feedback loop. Our goal is to design a control law that achieves the system output reference tracking while attenuating the effect of the disturbance input. We first construct an augmented system consisting of the original system and the command generator system. Then, the performance index is expressed in a quadratic form taking into account packet loss. Next, we obtain the optimal solution by solving the dropout generalized algebraic riccati equation (GARE). Finally, a ‐learning algorithm is utilized to estimate the control and disturbance feedback gains of the system, using only measurement data with unknown system dynamics in the presence of dropout. Two algorithms are tested on a numerical example to demonstrate the validity and effectiveness of the proposed methodology.

Adaptive event‐triggered control and observer design for discrete‐time nonlinear Markov jump systems with DoS attacks using policy iteration‐based adaptive dynamic programming

AbstractThis article addresses adaptive event‐triggered discrete‐time nonlinear Markov jump systems (MJs) with DoS attacks, where the introduced DoS attacks are considered as more general stochastic models with fixed trigger frequency and duration. To solve the optimal control problem, we use an adaptive dynamic programming (ADP) algorithm based on policy iteration (PI). The approximate process is as follows: the performance index function (PIF) is first updated by the iteration policy in advance, and the control policy is obtained from the PIF. Subsequently, an approximate estimation of the optimal PIF and the optimal control policy is made using the actor‐critic structure obtained through neural network techniques. In order to reduce the occupied communication resources required for control policy iteration, we introduce an adaptive event triggering mechanism with an adaptive triggering threshold, which reduces the conservatism of resource occupation by the PIF compared to the fixed‐threshold ETM. In addition, an observer identifying the unknown dynamics part of the system is designed. Finally, using the Lyapunov function, it is shown that the designed control policy ensures the stability and convergence of the MJS, and the designed observer is effective. Simulation examples are given to verify the feasibility of the controller and the observer.

Coordinated discrete-time super-twisting sliding mode controller coupled with time-delay estimator for PWR-based nuclear steam supply system

The coordination control problem for the core thermal power of the nuclear reactor (NR) and the water level of the nuclear steam generator (SG) is a crucial challenge for real-time model-based control of a pressurized-water reactor (PWR)-based nuclear steam supply system (NSSS). In this paper, a new coordinated discrete-time super-twisting sliding mode controller (CDTSTSMC) coupled with time-delay estimators (TDEs) is proposed, tackling the coordination control problem for the core thermal power of the NR and the water level of the nuclear SG in the presence of unknown dynamics, such as unmeasured system states, model uncertainties, parameter perturbations, and disturbances. First of all, the continuous-time dynamical models of both the NR and the SG in the PWR-based NSSS are described with consideration of unknown dynamics and then are transformed into discrete-time forms using the Euler approximation method. Two TDEs capable of estimating the unknown dynamics existing in the NR and the SG, respectively, are developed, which rely merely on the measurements of the PWR-based NSSS without the upper bounds of the uncertain dynamics being known. After that, a CDTSTSMC strategy, based on the discrete-time dynamical models describing both the NR and the SG, is proposed, allowing the core thermal power to be driven to a desired value while at the same time maintaining the desired water level in the SG with the help of TDEs. It is proved from stability analysis using a Lyapunov approach that under the proposed CDTSTSMC strategy coupled with the TDEs, the stability of the controlled PWR-based NSSS can be ensured in a wide range of load, where the control errors of both the NR and the SG are driven to a neighbor of zero. Finally, the proposed CDTSTSMC strategy coupled with the TDEs is compared with the previous discrete-time optimized proportional–integral–derivative controller (DTOPIDC) and fuzzy weighting controller (FWC). The simulation results reveal that the proposed CDTSTSMC strategy coupled with the TDEs outperforms the DTOPIDC and the FWC, particularly in rejecting unknown dynamics while maintaining both the core thermal power in the NR and the water level in the SG in their desired ranges.

Backstepping based neural [formula omitted] optimal tracking control for nonlinear state constrained systems with input delay and disturbances

This paper focuses on the problem of H∞ optimal tracking control for a class of nonlinear state constrained systems with input delay and disturbances. With the aid of Pade approximation, an auxiliary variable is devised to eliminate the effects of input delay. Combining barrier Lyapunov functions (BLFs) with backstepping design technique, a feedforward adaptive controller is designed to transform the tracking control problem of nonlinear state constrained system into an equivalent H∞ control problem of input-affine error system without state constraints, wherein neural networks (NNs) are employed to approximate unknown system dynamics. Then based on single-network adaptive dynamic programming (ADP), an H∞ optimal feedback controller is developed by utilizing a single critic network to learn the Nash equilibrium related to Hamilton–Jacobi–Isaacs (HJI) equation. Therefore, the whole tracking controller can be constructed by integrating the feedforward adaptive controller with the optimal feedback controller. Moreover, it is proven by Lyapunov’s theory that all signals within the closed-loop system are uniformly ultimately bounded (UUB), and the tracking error converges to a small neighborhood of the origin without violating any state constraints. Two simulation examples are also presented to validate the effectiveness of the proposed approach.