Min-Yen Lee

In this study, the robust H _∞ fuzzy observer-based fault-tolerant tracking control strategy is proposed for the stochastic polynomial fuzzy system (SPFS) under the effect of external disturbance, measurement noise, system/sensor fault signals and continuous/discontinuous internal random fluctuations. At first, the smoothed models of fault signals are constructed to describe their dynamic behavior. Then, by integrating the SPFS with the smoothed models of fault signals as one augmented system, the state/fault signal estimation problem can be transformed to a state estimation problem of augmented system by the proposed polynomial fuzzy observer. With the utilization of estimated state/fault signals and reference trajectory, a fuzzy polynomial fault-tolerant tracking controller can be implemented. To attenuate the effect of undesired external disturbance and measurement noise on the state/fault signal estimation and tracking control performance, the robust H _∞ fuzzy observer-based fault-tolerant tracking control strategy is proposed in this study. By utilizing the homogeneous Lyapunov function and Lipschiz condition, the Itô-Lévy formula is reformulated to relax the compensation terms of stochastic processes during the design. Then, the design conditions are derived in terms of interpolation function-dependent matrix inequality and consequently transformed to a two-step sum of square (SOS) condition design problem for the robust H _∞ fuzzy observer-based fault-tolerant tracking control strategy. A simulation example of double lane maneuvering task for autonomous ground vehicle (AGV) is provided to illustrate the effectiveness of proposed method. Index terms: Observer-based tracking control, polynomial fuzzy system, stochastic control, fault-tolerant control, sum of square (SOS).

For more practical applications, a simple decentralized $H_{\infty }$ proportional-integral-derivative (PID) team formation tracking strategy is proposed in this study for large-scale stochastic quadrotor unmanned aerial vehicles (UAVs) under external disturbance, intrinsic stochastic fluctuation and trailing vortex coupling. By adopting the virtual leader concept, the reference trajectory of each UAV is generated by the combination of virtual leader trajectory with a specific time-varying formation offset to form a desired flight formation shape. Then, by using the proposed optimal $\text{H}_{\infty }$ decentralized PID controller, each UAV can efficiently attenuate the effect of external disturbance and trailing vortex coupling from the neighboring quadrotor UAVs on the team formation reference tracking performance simultaneously. To avoid solving a complex nonlinear Hamiltion Jacobi inequality (HJI) for PID control of each UAV, the Takagi-Sugeno (T-S) fuzzy method is employed to interpolate several local linearized UAVs to approximate the nonlinear stochastic quadrotor UAV system so that the HJI can be transformed to a set of bilinear matrix inequalities (BMIs). By using novel variable transformation method, the optimal decentralized $\text{H}_{\infty }$ PID team formation tracking control problem of large-scale UAVs can be independently designed in terms of a set of independent LMIs-constrained optimization problems for each quadrotor UAV. Further, to simplify the design procedure in a single run, the large amount of decentralized $\text{H}_{\infty }$ PID controller parameters for each quadrotor UAV in the team formation can be efficiently obtained via the current convex optimization technique without any conventional parameter tuning procedure for PID design. Finally, a simulation example of team formation reference tracking control for 25 quadrotor UAVs with external disturbance and vortex coupling is given to validate the team formation tracking performance of the proposed decentralized $\text{H}_{\infty }$ PID tracking control method in comparison with conventional decentralized $H_{\infty }$ T-S fuzzy tracking control scheme.

The team formation of large-scale satellites for communication services of future smart cities in the 5G and 6G era is an important research topic currently. In this study, a robust $H_{\infty }$ tracking control with an event-triggered mechanism is proposed for the formation of large-scale satellites for communication tasks. At first, a satellite in the team formation is described by a nonlinear stochastic system with intrinsic random fluctuation, external disturbance, and coupling from other satellites. The proposed team formation tracking control for each satellite needs to consider the effect of network-induced delay and packet-dropout as well as save communication resources via an event-triggered mechanism. Further, the desired team formation of large-scale satellites can be prescribed by a set of reference models with the desired formation shape embedded in their reference inputs. Therefore, the large-scale team formation design problem can be simplified as an independent $H_{\infty }$ network model reference tracking control design problem for each satellite to efficiently attenuate the worst-effect of external disturbance, coupling of other satellites, intrinsic random fluctuation, network-induced delay, and packet-dropout on the model reference tracking performance. In order to avoid solving a nonlinear partial differential Hamillion-Jacobin inequality(HJI) for the $H_{\infty }$ decentralized network formation control for each satellite in the team the formation, the T-S fuzzy model is employed to interpolate several local linearized systems to approximate nonlinear satellite systems. Then the HJI in the $H_{\infty }$ decentralized network team formation design problem can be transformed into a set of linear matrix inequalities (LMIs) which can be easily solved by LMI TOOLBOX in MATLAB. Finally, a simulation example of team formation composed of ten satellites is given to illustrate the design procedure and to validate the proposed method in comparison with other methods.

In this study, a robust $H_{\infty }$ network observer-based attack-tolerant path tracking control design is proposed for the autonomous ground vehicle (AGV) under the effect of external disturbance, measurement noise and actuator/sensor attack signals. At first, a more practical AGV system is applied to describe the interaction among the longitudinal speed, lateral speed and yaw rate. Based on Controller Area Network (CAN), the information of local AGV is transmitted to remote control center through wireless channel and then the control command can be calculated from remote control center. To avoid the corruption of actuator/sensor attack signal from insecure CAN, two novel smoothed signal models are introduced to describe these attack signals and are embedded with the AGV dynamics system as an augmented system. Subsequently these attack signals can be simultaneously estimated with the AGV system state by the conventional Luenberger-type observer of the augmented system. By using the estimated state and attack signals, a robust $H_{\infty }$ network observer-based attack-tolerant path tracking controller is constructed to attenuate the effect of unknown disturbance on the energy of path tracking error and eliminate the influence of attacks signals. With the help of convex Lyapunov function, the design conditions of robust $H_{\infty }$ network observer-based attack-tolerant path tracking control design for AGV are derived in terms of a set of nonlinear difference inequalities. To reduce the difficulties in solving these nonlinear difference inequalities, Takagi-Sugeno fuzzy interpolation method is applied to approximate the nonlinear AGV system and the design can be simplified to a set of LMIs, which can be easily solved via LMI TOOLBOX in MATLAB. A double lane change task of AGV in CAN is provided as a simulation example to illustrate the design procedure and validate the effectiveness of proposed design method in comparison with the conventional steering control method.

In this study, we investigate multi-player noncooperative minmax $H_{\infty }$ target tracking game strategy with conflicting target strategies and cooperative $H_{\infty }$ target tracking game strategy with common target strategy of nonlinear mean-field stochastic jump diffusion (MFSJD) system with external disturbance. Due to the nonlinear terms and mean-field (average) behaviors in the stochastic nonlinear MFSJD system and minmax $H_{\infty }$ payoff function, the multi-player noncooperative and cooperative minmax $H_{\infty }$ mean-field game strategy of nonlinear MFSJD system are more difficult than the linear MFSJD system and conventional nonlinear stochastic system. To avoid solving complex Hamilton Jacobi Isaacs inequalities (HJIIs) of multi-player noncooperative minmax $H_{\infty }$ mean-field target tracking game strategy of nonlinear MFSJD system, the nonlinear MFSJD system is interpolated by a set of local linearized MFSJD system through smoothing functions by the global linearization method. Then the multi-player noncooperative minmax $H_{\infty }$ nonlinear mean-field target tracking game strategy design can be transformed to a linear matrix inequalities (LMIs)-constrained multi-objective optimization problem (MOP). The LMIs-constrained MOP could be efficiently solved by the help of the proposed LMIs-constrained multi-objective evolution algorithm (MOEA). We can prove that the Pareto optimal solution of LMIs-constrained MOP is the Nash equilibrium solution of noncooperative minmax $H_{\infty }$ mean-field target tracking strategy of nonlinear mean-field MFSJD system. Further, the cooperative minmax $H_{\infty }$ mean-field common target tracking strategy of nonlinear mean-field stochastic system is reduced to an LMIs-constrained single-objective optimization problem (SOP). Finally, two simulation examples of cyber-financial mean-field systems are given to illustrate the design procedure and compare the efficacies of the proposed noncooperative and cooperative minmax $H_{\infty }$ mean-field target tracking strategy of nonlinear MFSJD systems.

In this study, a robust $H_{\infty }$ networked security observer-based reference tracking control scheme is proposed for the stochastic quadrotor unmanned aerial vehicle (UAV) system under malicious attacks on the actuator and sensor of network control system (NCS). To reduce the computational burden on UAV system, the UAV system is connected with a remote computing unit and the complicated tracking control command can be calculated by remote computing unit. By using the novel discrete smoothed model, the model of attack signals on actuator and sensor can be embedded in system state of UAV and thus the attack signals as well as the quadrotor system state can be simultaneously estimated through a conventional Luenberger observer. Further, the corruption of attack signals on state estimation of UAV is also avoided. To eliminate the effect of unavailable external disturbance and intrinsic fluctuation during the reference tracking control process, a robust $H_{\infty }$ networked security observer-based reference tracking control scheme is introduced to attenuate their effects on the NCS of quadrotor UAV. By using the characteristic of convex Lyapunov function, the design condition of robust $H_{\infty }$ networked security observer-based tracking control is derived in terms of the nonlinear functional inequalities. Since the nonlinear functional inequalities are not easy to be solved analytically or numerically, the Takagi-Sugeno (T-S) fuzzy interpolation technique is employed to interpolate the nonlinear stochastic quadrotor NCS by a set of linear local systems via fuzzy bases. In this case, the nonlinear functional inequalities can be converted to a set of linear matrix inequalities (LMIs) which can be easily solved by the MATLAB LMI TOOLBOX. Simulation results are provided to validate the effectiveness of the proposed method in comparison with conventional robust observer-based T-S fuzzy tracking control scheme.

Recently, deep neural network (DNN) schemes based on big data-driven methods have been successfully applied to image classification, communication, translation of language, speech recognition, etc. However, more efforts are still needed to apply them to complex robust nonlinear filter design in signal processing, especially for the robust nonlinear $H_{\infty }$ filter design for robust state estimation of nonlinear stochastic signal system under uncertain external disturbance and output measurement noise. In general, the design problem of robust nonlinear $H_{\infty }$ filter needs to solve a complex Hamilton-Jacobi-Isaacs equation (HJIE), which is not easily solved analytically or numerically. Further, the robust nonlinear $H_{\infty }$ filter is not easily designed by training DNN directly via conventional big data schemes. In this paper, a novel robust $H_{\infty }$ HJIE-embedded DNN-based filter design is proposed as a co-design of $H_{\infty }$ filtering algorithm and DNN learning algorithm for the robust state estimation of nonlinear stochastic signal systems with external disturbance and output measurement noise. In the proposed robust $H_{\infty }$ DNN-based filter design, we have proven that when the approximation error of HJIE by the trained DNN through Adam learning algorithm approaches to 0, the HJIE-embedded DNN-based filter will approach the robust nonlinear $H_{\infty }$ filter of nonlinear stochastic signal system with uncertain external disturbance and output measurement noise. Finally, a trajectory estimation problem of 3-D geometry incoming nonlinear stochastic missile system by the proposed robust $H_{\infty }$ HJIE-embedded DNN-based filter scheme through the measurement by the sensor of radar system with external disturbance and measurement noise is given to illustrate the design procedure and validate its robust $H_{\infty }$ filtering performance when compared with the extended Kalman filter and particle filter.

In this study, the robust H _∞ stochastic observer-based attack-tolerant guidance control strategy is designed for the nonlinear stochastic missile guidance control system under the external disturbance and measurement noise as well as actuator attack signal and sensor attack signal. To simplify the attack signal estimation, a novel nonsingular smoothed dynamic model is introduced to efficiently describe the actuator and sensor attack signals. Consequently, the state/attack signal estimation can be easily achieved by using conventional Luenberger observer. Next, to attenuate the effect of external disturbance, measurement noise and approximation errors of attack signal on the missile guidance control system, the robust H _∞ attack-tolerant guidance control performance is considered and the design condition is derived in terms of nonlinear Hamilton-Jacobi inequality (HJI) constrained problem. Since HJI cannot be easily solved analytically or numerically, the Takagi-Sugeno (T-S) fuzzy modelling method is utilized to facilitate the robust H _∞ attack-tolerant guidance control strategy design. Thereafter, the H _∞ observer-based attack-tolerant control design problem is transformed into linear matrix inequalities problem (LMIP) which can be solved very efficiently by using the convex optimization techniques. Simulation example, with the comparison between the proposed method and conventional robust missile guidance strategy, is given to illustrate the design procedures and validate the performance of the proposed method.

In this study, a robust decentralized stochastic H _∞ tracking control design is proposed to deal with the team formation tracking problem for a large-scale biped robot team system with external disturbance and communication requirement on biped robots and leader. Under the concept of virtual leader and the decentralized control approach, biped robots walking in a large-scale team formation are controlled to track their own reference paths with the robust stochastic H _∞ tracking performance. Consequently, the original robust decentralized stochastic H _∞ large-scale biped robot team formation tracking control design problem can be transformed to a set of independent Hamilton-Jacobi inequality (HJI)-constrained optimization problems for each biped robot. To cope with the difficulties in solving the HJIs for the robust decentralized stochastic H _∞ team formation tracking control design, a numerical framework is introduced to approximate the walking biped robot systems. Based on the tensor-product model transformation technique, the set of independent HJI-constrained optimization problems for the robust decentralized stochastic H _∞ team formation tracking control design is converted into a set of independent linear-matrix-inequality-constrained optimization problems, which can be solved efficiently by the convex optimization methods. Since the robust decentralized stochastic H _∞ team formation tracking control can be designed individually, the magnitude of a biped robot team can be easily increased to a very large scale. Finally, a simulation example of decentralized H _∞ formation tracking control design for a 30-scale biped robot team is given to validate the effectiveness of the proposed scheme.