Permanent magnet synchronous motor(PMSM)speed control systems with conventional linear active disturbance rejection control(CLADRC)strategy encounter issues regarding the coupling between dynamic response and disturba...Permanent magnet synchronous motor(PMSM)speed control systems with conventional linear active disturbance rejection control(CLADRC)strategy encounter issues regarding the coupling between dynamic response and disturbance suppression and have poor performance in suppressing complex nonlinear disturbances.In order to address these issues,this paper proposes an improved two-degree-of-freedom LADRC(TDOF-LADRC)strategy,which can enhance the disturbance rejection performance of the system while decoupling entirely the system's dynamic and anti-disturbance performance to boost the system robustness and simplify controller parameter tuning.PMSM models that consider total disturbances are developed to design the TDOF-LADRC speed controller accurately.Moreover,to evaluate the control performance of the TDOF-LADRC strategy,its stability is proven,and the influence of each controller parameter on the system control performance is analyzed.Based on it,a comparison is made between the disturbance observation ability and anti-disturbance performance of TDOF-LADRC and CLADRC to prove the superiority of TDOF-LADRC in rejecting disturbances.Finally,experiments are performed on a 750 W PMSM experimental platform,and the results demonstrate that the proposed TDOF-LADRC exhibits the properties of two degrees of freedom and improves the disturbance rejection performance of the PMSM system.展开更多
The elastic thickness parameter was estimated using the mobile correlation technique between the observed isostatic disturbance and the gravity disturbance calculated through direct gravimetric modeling. We computed t...The elastic thickness parameter was estimated using the mobile correlation technique between the observed isostatic disturbance and the gravity disturbance calculated through direct gravimetric modeling. We computed the vertical flexure value of the crust for a specific elastic thickness using a given topographic dataset. The gravity disturbance due to the topography was determined after the calculation. A grid of values for the elastic thickness parameter was generated. Then, a moving correlation was performed between the observed gravity data(representing actual surface data) and the calculated data from the forward modeling. The optimum elastic thickness of the particular point corresponded to the highest correlation coefficient. The methodology was tested on synthetic data and showed that the synthetic depth closely matched the original depth, including the elastic thickness value. To validate the results, the described procedure was applied to a real dataset from the Barreirinhas Basin, situated in the northeastern region of Brazil. The results show that the obtained crustal depth is highly correlated with the depth from known models. Additionally, we noted that the elastic thickness behaves as expected, decreasing from the continent towards the ocean. Based on the results, this method has the potential to be employed as a direct estimate of crustal depth and elastic thickness for any region.展开更多
An observer-based adaptive backstepping boundary control is proposed for vibration control of flexible offshore riser systems with unknown nonlinear input dead zone and uncertain environmental disturbances.The control...An observer-based adaptive backstepping boundary control is proposed for vibration control of flexible offshore riser systems with unknown nonlinear input dead zone and uncertain environmental disturbances.The control algorithm can update the control law online through real-time data to make the controller adapt to the environment and improve the control precision.Specifically,based on the adaptive backstepping framework,virtual control laws and Lyapunov functions are designed for each subsystem.Three direction interference observers are designed to track the timevarying boundary disturbance.On this basis,the inverse of the dead zone and linear state transformation are used to compensate for the original system and eliminate the adverse effects of the dead zone.In addition,the stability of the closed-loop system is proven by Lyapunov stability theory.All the system states are bounded,and the vibration offset of the riser converges to a small area of the initial position.Finally,four examples of flexible marine risers are simulated in MATLAB to verify the effectiveness of the proposed controller.展开更多
This paper is concerned with anti-disturbance Nash equilibrium seeking for games with partial information.First,reduced-order disturbance observer-based algorithms are proposed to achieve Nash equilibrium seeking for ...This paper is concerned with anti-disturbance Nash equilibrium seeking for games with partial information.First,reduced-order disturbance observer-based algorithms are proposed to achieve Nash equilibrium seeking for games with firstorder and second-order players,respectively.In the developed algorithms,the observed disturbance values are included in control signals to eliminate the influence of disturbances,based on which a gradient-like optimization method is implemented for each player.Second,a signum function based distributed algorithm is proposed to attenuate disturbances for games with secondorder integrator-type players.To be more specific,a signum function is involved in the proposed seeking strategy to dominate disturbances,based on which the feedback of the velocity-like states and the gradients of the functions associated with players achieves stabilization of system dynamics and optimization of players'objective functions.Through Lyapunov stability analysis,it is proven that the players'actions can approach a small region around the Nash equilibrium by utilizing disturbance observerbased strategies with appropriate control gains.Moreover,exponential(asymptotic)convergence can be achieved when the signum function based control strategy(with an adaptive control gain)is employed.The performance of the proposed algorithms is tested by utilizing an integrated simulation platform of virtual robot experimentation platform(V-REP)and MATLAB.展开更多
In this context,a testing system to understand rock fracturing processes induced by different dynamic disturbances under true triaxial compression was developed.The system is mainly composed of a static loading subsys...In this context,a testing system to understand rock fracturing processes induced by different dynamic disturbances under true triaxial compression was developed.The system is mainly composed of a static loading subsystem,a dynamic loading subsystem,a specimen box subsystem,and a data measurement subsystem.The static loading subsystem uses low stiffness loss frame structure technology,which greatly improves the frame stiffness in the three principal stress directions(up to 20 GN/m)and ensures the demand of the disturbance experiment in both the prepeak and postpeak stages.The disturbance loads with frequency of 0e20 Hz and stress level of 0e30 MPa were applied using large flow parallel oil source technology characterized with high heat dissipation efficiency.For the disturbance loads with frequency of 100e500 Hz and stress level of 0e30 MPa,they were realized by using high-frequency and centimeter-per-second-scale low-speed disturbance rod technology.Three rigid self-stabilizing specimen boxes were utilized to provide support for the specimen and deformation sensors,ensuring the stability and accuracy of the data obtained.To verify the performance of the true triaxial test system,disturbance experiments were conducted on granite specimens.The results show that the experimental device satisfies the requirements of original design,with an excellent repeatability and reliable testing results.展开更多
This paper presents a subspace identification method for closed-loop systems with unknown deterministic disturbances.To deal with the unknown deterministic disturbances,two strategies are implemented to construct the ...This paper presents a subspace identification method for closed-loop systems with unknown deterministic disturbances.To deal with the unknown deterministic disturbances,two strategies are implemented to construct the row space that can be used to approximately represent the unknown deterministic disturbances using the trigonometric functions or Bernstein polynomials depending on whether the disturbance frequencies are known.For closed-loop identification,CCF-N4SID is extended to the case with unknown deterministic disturbances using the oblique projection.In addition,a proper Bernstein polynomial order can be determined using the Akaike information criterion(AIC)or the Bayesian information criterion(BIC).Numerical simulation results demonstrate the effectiveness of the proposed identification method for both periodic and aperiodic deterministic disturbances.展开更多
The fault-tolerant control problem is investigated for high-speed trains with actuator faults and multiple disturbances.Based on the novel train model resulting from the Takagi–Sugeno fuzzy theory, a sliding-mode fau...The fault-tolerant control problem is investigated for high-speed trains with actuator faults and multiple disturbances.Based on the novel train model resulting from the Takagi–Sugeno fuzzy theory, a sliding-mode fault-tolerant control strategy is proposed. The norm bounded disturbances which are composed of interactive forces among adjacent carriages and basis running resistances are rearranged by the fuzzy linearity technique. The modeled disturbances described as an exogenous system are compensated for by a disturbance observer. Moreover, a sliding mode surface is constructed, which can transform the stabilization problem of position and velocity into the stabilization problem of position errors and velocity errors, i.e., the tracking problem of position and velocity. Based on the parallel distributed compensation method and the disturbance observer, the fault-tolerant controller is solved. The Lyapunov theory is used to prove the stability of the closed-loop system. The feasibility and effectiveness of the proposed fault-tolerant control strategy are illustrated by simulation results.展开更多
In this paper, a disturbance observer-based safe tracking control scheme is proposed for a medium-scale unmanned helicopter with rotor flapping dynamics in the presence of partial state constraints and unknown externa...In this paper, a disturbance observer-based safe tracking control scheme is proposed for a medium-scale unmanned helicopter with rotor flapping dynamics in the presence of partial state constraints and unknown external disturbances. A safety protection algorithm is proposed to keep the constrained states within the given safe-set. A second-order disturbance observer technique is utilized to estimate the external disturbances. It is shown that the desired tracking performance of the controlled unmanned helicopter can be achieved with the application of the backstepping approach, dynamic surface control technique, and Lyapunov method. Finally, the availability of the proposed control scheme has been shown by simulation results.展开更多
With increasing global concerns about clean energy in smart grids,the detection of power quality disturbances(PQDs)caused by energy instability is becoming more and more prominent.It is well acknowledged that the PQD ...With increasing global concerns about clean energy in smart grids,the detection of power quality disturbances(PQDs)caused by energy instability is becoming more and more prominent.It is well acknowledged that the PQD effects on power grid equipment are destructive and hazardous,which causes irreversible damage to underlying electrical/electronic equipment of the concerned intelligent grids.In order to ensure safe and reliable equipment implementation,appropriate PQDdetection technologiesmust be adopted to avoid such adverse effects.This paper summarizes the newly proposed and traditional PQD detection techniques in order to give a quick start to new researchers in the related field,where specific scenarios and events for which each technique is applicable are also clearly presented.Finally,comments on the future evolution of PQD detection techniques are given.Unlike the published review articles,this paper focuses on the new techniques from the last five years while providing a brief recap on traditional PQD detection techniques so as to supply researchers with a systematic and state-of-the-art review for PQD detection.展开更多
Aiming at the problems of multiple types of power quality composite disturbances,strong feature correlation and high recognition error rate,a method of power quality composite disturbances identification based on mult...Aiming at the problems of multiple types of power quality composite disturbances,strong feature correlation and high recognition error rate,a method of power quality composite disturbances identification based on multiresolution S-transform and decision tree was proposed.Firstly,according to IEEE standard,the signal models of seven single power quality disturbances and 17 combined power quality disturbances are given,and the disturbance waveform samples are generated in batches.Then,in order to improve the recognition accuracy,the adjustment factor is introduced to obtain the controllable time-frequency resolution through multi-resolution S-transform time-frequency domain analysis.On this basis,five disturbance time-frequency domain features are extracted,which quantitatively reflect the characteristics of the analyzed power quality disturbance signal,which is less than the traditional method based on S-transform.Finally,three classifiers such as K-nearest neighbor,support vector machine and decision tree algorithm are used to effectively complete the identification of power quality composite disturbances.Simulation results showthat the classification accuracy of decision tree algorithmis higher than that of K-nearest neighbor and support vector machine.Finally,the proposed method is compared with other commonly used recognition algorithms.Experimental results show that the proposedmethod is effective in terms of detection accuracy,especially for combined PQ interference.展开更多
In this letter to the editor,the authors discuss the findings and shortcomings of a published retrospective study,including 120 patients undergoing surgery for gastric or colon cancer under general anesthesia.The stud...In this letter to the editor,the authors discuss the findings and shortcomings of a published retrospective study,including 120 patients undergoing surgery for gastric or colon cancer under general anesthesia.The study focused on perioperative dynamic respiratory and hemodynamic disturbances and early postsurgical inflammatory responses.展开更多
This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clock...This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clockdependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system,and assign to each system a controller scheduled by a clock.A necessary and sufficient convex stability criterion is presented for the nominal system,and is further extended to the stabilization controller design with a nominal clock.In the presence of bounded peak disturbances,another stabilization controller with an error clock is developed for the error system,with the purpose of‘‘minimizing’’the reachable set of the error system by the ellipsoidal techniques.It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system,i.e.,a union of a family of bounding ellipsoids,that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system.Two numerical examples are provided to verify the effectiveness of the developed results.展开更多
In this paper,guaranteed cost attitude tracking con-trol for uncertain quadrotor unmanned aerial vehicle(QUAV)under safety constraints is studied.First,an augmented system is constructed by the tracking error system a...In this paper,guaranteed cost attitude tracking con-trol for uncertain quadrotor unmanned aerial vehicle(QUAV)under safety constraints is studied.First,an augmented system is constructed by the tracking error system and reference system.This transformation aims to convert the tracking control prob-lem into a stabilization control problem.Then,control barrier function and disturbance attenuation function are designed to characterize the violations of safety constraints and tolerance of uncertain disturbances,and they are incorporated into the reward function as penalty items.Based on the modified reward function,the problem is simplified as the optimal regulation problem of the nominal augmented system,and a new Hamilton-Jacobi-Bellman equation is developed.Finally,critic-only rein-forcement learning algorithm with a concurrent learning tech-nique is employed to solve the Hamilton-Jacobi-Bellman equa-tion and obtain the optimal controller.The proposed algorithm can not only ensure the reward function within an upper bound in the presence of uncertain disturbances,but also enforce safety constraints.The performance of the algorithm is evaluated by the numerical simulation.展开更多
文摘Permanent magnet synchronous motor(PMSM)speed control systems with conventional linear active disturbance rejection control(CLADRC)strategy encounter issues regarding the coupling between dynamic response and disturbance suppression and have poor performance in suppressing complex nonlinear disturbances.In order to address these issues,this paper proposes an improved two-degree-of-freedom LADRC(TDOF-LADRC)strategy,which can enhance the disturbance rejection performance of the system while decoupling entirely the system's dynamic and anti-disturbance performance to boost the system robustness and simplify controller parameter tuning.PMSM models that consider total disturbances are developed to design the TDOF-LADRC speed controller accurately.Moreover,to evaluate the control performance of the TDOF-LADRC strategy,its stability is proven,and the influence of each controller parameter on the system control performance is analyzed.Based on it,a comparison is made between the disturbance observation ability and anti-disturbance performance of TDOF-LADRC and CLADRC to prove the superiority of TDOF-LADRC in rejecting disturbances.Finally,experiments are performed on a 750 W PMSM experimental platform,and the results demonstrate that the proposed TDOF-LADRC exhibits the properties of two degrees of freedom and improves the disturbance rejection performance of the PMSM system.
文摘The elastic thickness parameter was estimated using the mobile correlation technique between the observed isostatic disturbance and the gravity disturbance calculated through direct gravimetric modeling. We computed the vertical flexure value of the crust for a specific elastic thickness using a given topographic dataset. The gravity disturbance due to the topography was determined after the calculation. A grid of values for the elastic thickness parameter was generated. Then, a moving correlation was performed between the observed gravity data(representing actual surface data) and the calculated data from the forward modeling. The optimum elastic thickness of the particular point corresponded to the highest correlation coefficient. The methodology was tested on synthetic data and showed that the synthetic depth closely matched the original depth, including the elastic thickness value. To validate the results, the described procedure was applied to a real dataset from the Barreirinhas Basin, situated in the northeastern region of Brazil. The results show that the obtained crustal depth is highly correlated with the depth from known models. Additionally, we noted that the elastic thickness behaves as expected, decreasing from the continent towards the ocean. Based on the results, this method has the potential to be employed as a direct estimate of crustal depth and elastic thickness for any region.
基金financially supported by the Sichuan Science and Technology Program(Grant No.2023NSFSC1980)。
文摘An observer-based adaptive backstepping boundary control is proposed for vibration control of flexible offshore riser systems with unknown nonlinear input dead zone and uncertain environmental disturbances.The control algorithm can update the control law online through real-time data to make the controller adapt to the environment and improve the control precision.Specifically,based on the adaptive backstepping framework,virtual control laws and Lyapunov functions are designed for each subsystem.Three direction interference observers are designed to track the timevarying boundary disturbance.On this basis,the inverse of the dead zone and linear state transformation are used to compensate for the original system and eliminate the adverse effects of the dead zone.In addition,the stability of the closed-loop system is proven by Lyapunov stability theory.All the system states are bounded,and the vibration offset of the riser converges to a small area of the initial position.Finally,four examples of flexible marine risers are simulated in MATLAB to verify the effectiveness of the proposed controller.
基金supported by the National Natural Science Foundation of China(NSFC)(62222308,62173181,62073171,62221004)the Natural Science Foundation of Jiangsu Province(BK20200744,BK20220139)+3 种基金Jiangsu Specially-Appointed Professor(RK043STP19001)1311 Talent Plan of Nanjing University of Posts and Telecommunicationsthe Young Elite Scientists SponsorshipProgram by CAST(2021QNRC001)the Fundamental Research Funds for the Central Universities(30920032203)。
文摘This paper is concerned with anti-disturbance Nash equilibrium seeking for games with partial information.First,reduced-order disturbance observer-based algorithms are proposed to achieve Nash equilibrium seeking for games with firstorder and second-order players,respectively.In the developed algorithms,the observed disturbance values are included in control signals to eliminate the influence of disturbances,based on which a gradient-like optimization method is implemented for each player.Second,a signum function based distributed algorithm is proposed to attenuate disturbances for games with secondorder integrator-type players.To be more specific,a signum function is involved in the proposed seeking strategy to dominate disturbances,based on which the feedback of the velocity-like states and the gradients of the functions associated with players achieves stabilization of system dynamics and optimization of players'objective functions.Through Lyapunov stability analysis,it is proven that the players'actions can approach a small region around the Nash equilibrium by utilizing disturbance observerbased strategies with appropriate control gains.Moreover,exponential(asymptotic)convergence can be achieved when the signum function based control strategy(with an adaptive control gain)is employed.The performance of the proposed algorithms is tested by utilizing an integrated simulation platform of virtual robot experimentation platform(V-REP)and MATLAB.
基金This study was financially supported by the National Natural Science Foundation of China(Grant No.51839003),for which we are grateful.
文摘In this context,a testing system to understand rock fracturing processes induced by different dynamic disturbances under true triaxial compression was developed.The system is mainly composed of a static loading subsystem,a dynamic loading subsystem,a specimen box subsystem,and a data measurement subsystem.The static loading subsystem uses low stiffness loss frame structure technology,which greatly improves the frame stiffness in the three principal stress directions(up to 20 GN/m)and ensures the demand of the disturbance experiment in both the prepeak and postpeak stages.The disturbance loads with frequency of 0e20 Hz and stress level of 0e30 MPa were applied using large flow parallel oil source technology characterized with high heat dissipation efficiency.For the disturbance loads with frequency of 100e500 Hz and stress level of 0e30 MPa,they were realized by using high-frequency and centimeter-per-second-scale low-speed disturbance rod technology.Three rigid self-stabilizing specimen boxes were utilized to provide support for the specimen and deformation sensors,ensuring the stability and accuracy of the data obtained.To verify the performance of the true triaxial test system,disturbance experiments were conducted on granite specimens.The results show that the experimental device satisfies the requirements of original design,with an excellent repeatability and reliable testing results.
基金partially supported by National Key Research and Development Program of China(2019YFC1510902)National Natural Science Foundation of China(62073104)+1 种基金Natural Science Foundation of Heilongjiang Province(LH2022F024)China Postdoctoral Science Foundation(2022M710965)。
文摘This paper presents a subspace identification method for closed-loop systems with unknown deterministic disturbances.To deal with the unknown deterministic disturbances,two strategies are implemented to construct the row space that can be used to approximately represent the unknown deterministic disturbances using the trigonometric functions or Bernstein polynomials depending on whether the disturbance frequencies are known.For closed-loop identification,CCF-N4SID is extended to the case with unknown deterministic disturbances using the oblique projection.In addition,a proper Bernstein polynomial order can be determined using the Akaike information criterion(AIC)or the Bayesian information criterion(BIC).Numerical simulation results demonstrate the effectiveness of the proposed identification method for both periodic and aperiodic deterministic disturbances.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 62203246, 62003127, and 62003183)。
文摘The fault-tolerant control problem is investigated for high-speed trains with actuator faults and multiple disturbances.Based on the novel train model resulting from the Takagi–Sugeno fuzzy theory, a sliding-mode fault-tolerant control strategy is proposed. The norm bounded disturbances which are composed of interactive forces among adjacent carriages and basis running resistances are rearranged by the fuzzy linearity technique. The modeled disturbances described as an exogenous system are compensated for by a disturbance observer. Moreover, a sliding mode surface is constructed, which can transform the stabilization problem of position and velocity into the stabilization problem of position errors and velocity errors, i.e., the tracking problem of position and velocity. Based on the parallel distributed compensation method and the disturbance observer, the fault-tolerant controller is solved. The Lyapunov theory is used to prove the stability of the closed-loop system. The feasibility and effectiveness of the proposed fault-tolerant control strategy are illustrated by simulation results.
基金supported in part by the National Natural ScienceFoundation of China (U2013201)the National Science Fund for Distinguished Young Scholars (61825302)the Postgraduate Research&Practice Innovation Program of Jiangsu Province (KYCX20_0208)。
文摘In this paper, a disturbance observer-based safe tracking control scheme is proposed for a medium-scale unmanned helicopter with rotor flapping dynamics in the presence of partial state constraints and unknown external disturbances. A safety protection algorithm is proposed to keep the constrained states within the given safe-set. A second-order disturbance observer technique is utilized to estimate the external disturbances. It is shown that the desired tracking performance of the controlled unmanned helicopter can be achieved with the application of the backstepping approach, dynamic surface control technique, and Lyapunov method. Finally, the availability of the proposed control scheme has been shown by simulation results.
文摘With increasing global concerns about clean energy in smart grids,the detection of power quality disturbances(PQDs)caused by energy instability is becoming more and more prominent.It is well acknowledged that the PQD effects on power grid equipment are destructive and hazardous,which causes irreversible damage to underlying electrical/electronic equipment of the concerned intelligent grids.In order to ensure safe and reliable equipment implementation,appropriate PQDdetection technologiesmust be adopted to avoid such adverse effects.This paper summarizes the newly proposed and traditional PQD detection techniques in order to give a quick start to new researchers in the related field,where specific scenarios and events for which each technique is applicable are also clearly presented.Finally,comments on the future evolution of PQD detection techniques are given.Unlike the published review articles,this paper focuses on the new techniques from the last five years while providing a brief recap on traditional PQD detection techniques so as to supply researchers with a systematic and state-of-the-art review for PQD detection.
基金Foundation of China(No.52067013)the Key Natural Science Fund Project of Gansu Provincial Department of Science and Technology(No.21JR7RA280)+1 种基金the Tianyou Innovation Team Science Foundation of Intelligent Power Supply and State Perception for Rail Transit(No.TY202010)the Natural Science Foundation of Gansu Province(No.20JR5RA395).
文摘Aiming at the problems of multiple types of power quality composite disturbances,strong feature correlation and high recognition error rate,a method of power quality composite disturbances identification based on multiresolution S-transform and decision tree was proposed.Firstly,according to IEEE standard,the signal models of seven single power quality disturbances and 17 combined power quality disturbances are given,and the disturbance waveform samples are generated in batches.Then,in order to improve the recognition accuracy,the adjustment factor is introduced to obtain the controllable time-frequency resolution through multi-resolution S-transform time-frequency domain analysis.On this basis,five disturbance time-frequency domain features are extracted,which quantitatively reflect the characteristics of the analyzed power quality disturbance signal,which is less than the traditional method based on S-transform.Finally,three classifiers such as K-nearest neighbor,support vector machine and decision tree algorithm are used to effectively complete the identification of power quality composite disturbances.Simulation results showthat the classification accuracy of decision tree algorithmis higher than that of K-nearest neighbor and support vector machine.Finally,the proposed method is compared with other commonly used recognition algorithms.Experimental results show that the proposedmethod is effective in terms of detection accuracy,especially for combined PQ interference.
文摘In this letter to the editor,the authors discuss the findings and shortcomings of a published retrospective study,including 120 patients undergoing surgery for gastric or colon cancer under general anesthesia.The study focused on perioperative dynamic respiratory and hemodynamic disturbances and early postsurgical inflammatory responses.
基金supported by the Natural Sciences and Engineering Research Council of Canada(NSERC).
文摘This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clockdependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system,and assign to each system a controller scheduled by a clock.A necessary and sufficient convex stability criterion is presented for the nominal system,and is further extended to the stabilization controller design with a nominal clock.In the presence of bounded peak disturbances,another stabilization controller with an error clock is developed for the error system,with the purpose of‘‘minimizing’’the reachable set of the error system by the ellipsoidal techniques.It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system,i.e.,a union of a family of bounding ellipsoids,that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system.Two numerical examples are provided to verify the effectiveness of the developed results.
基金supported in part by the National Science Foundation of China(62173183)。
文摘In this paper,guaranteed cost attitude tracking con-trol for uncertain quadrotor unmanned aerial vehicle(QUAV)under safety constraints is studied.First,an augmented system is constructed by the tracking error system and reference system.This transformation aims to convert the tracking control prob-lem into a stabilization control problem.Then,control barrier function and disturbance attenuation function are designed to characterize the violations of safety constraints and tolerance of uncertain disturbances,and they are incorporated into the reward function as penalty items.Based on the modified reward function,the problem is simplified as the optimal regulation problem of the nominal augmented system,and a new Hamilton-Jacobi-Bellman equation is developed.Finally,critic-only rein-forcement learning algorithm with a concurrent learning tech-nique is employed to solve the Hamilton-Jacobi-Bellman equa-tion and obtain the optimal controller.The proposed algorithm can not only ensure the reward function within an upper bound in the presence of uncertain disturbances,but also enforce safety constraints.The performance of the algorithm is evaluated by the numerical simulation.