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In this article, an optimized backstepping (OB) control scheme is proposed for a class of stochastic nonlinear strict-feedback systems with unknown dynamics by using reinforcement learning (RL) strategy of identifier-critic-actor architecture, where the identifier aims to compensate the unknown dynamic, the critic aims to evaluate the control performance and to give the feedback to the actor, and the actor aims to perform the control action. The basic control idea is that all virtual controls and the actual control of backstepping are designed as the optimized solution of corresponding subsystems so that the entire backstepping control is optimized. Different from the deterministic system, stochastic system control needs to consider not only the stochastic disturbance depicted by the Wiener process but also the Hessian term in stability analysis. If the backstepping control is developed on the basis of the published RL optimization methods, it will be difficult to be achieved because, on the one hand, RL of these methods are very complex in the algorithm thanks to their critic and actor updating laws deriving from the negative gradient of the square of approximation of Hamilton-Jacobi-Bellman (HJB) equation; on the other hand, these methods require persistence excitation and known dynamic, where persistence excitation is for training adaptive parameters sufficiently. In this research, both critic and actor updating laws are derived from the negative gradient of a simple positive function, which is yielded on the basis of a partial derivative of the HJB equation. As a result, the RL algorithm can be significantly simplified, meanwhile, two requirements of persistence excitation and known dynamic can be released. Therefore, it can be a natural selection for stochastic optimization control. Finally, from two aspects of theory and simulation, it is demonstrated that the proposed control can arrive at the desired system performance.

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In this article, an optimized leader-following consensus control scheme is proposed for the nonlinear strict-feedback-dynamic multi-agent system by learning from the controlling idea of optimized backstepping technique, which designs the virtual and actual controls of backstepping to be the optimized solution of corresponding subsystems so that the entire backstepping control is optimized. Since this control needs to not only ensure the optimizing system performance but also synchronize the multiple system state variables, it is an interesting and challenging topic. In order to achieve this optimized control, the neural network approximation-based reinforcement learning (RL) is performed under critic-actor architecture. In most of the existing RL-based optimal controls, since both the critic and actor RL updating laws are derived from the negative gradient of square of the Hamilton-Jacobi-Bellman (HJB) equation's approximation, which contains multiple nonlinear terms, their algorithm are inevitably intricate. However, the proposed optimized control derives the RL updating laws from the negative gradient of a simple positive function, which is correlated with the HJB equation; hence, it can be significantly simple in the algorithm. Meanwhile, it can also release two general conditions, known dynamic and persistence excitation, which are required in most of the RL-based optimal controls. Therefore, the proposed optimized scheme can be a natural selection for the high-order nonlinear multi-agent control. Finally, the effectiveness is demonstrated by both theory and simulation.

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In this article, the game-based backstepping control method is proposed for the high-order nonlinear multi-agent system with unknown dynamic and input saturation. Reinforcement learning (RL) is employed to get the saddle point solution of the tracking game between each agent and the reference signal for achieving robust control. Specifically, the approximate optimal solution of the established Hamilton-Jacobi-Isaacs (HJI) equation is obtained by policy iteration for each subsystem, and the single network adaptive critic (SNAC) architecture is used to reduce the computational burden. In addition, based on the separation operation of the error term from the derivative of the value function, we achieve the different proportions of the two agents in the game to realize the regulation of the final equilibrium point. Different from the general use of the neural network for system identification, the unknown nonlinear dynamic term is approximated based on the state difference obtained by the command filter. Furthermore, a sufficient condition is established to guarantee that the whole system and each subsystem included are uniformly ultimately bounded. Finally, simulation results are given to show the effectiveness of the proposed method.

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This article addresses a distributed time-varying optimal formation protocol for a class of second-order uncertain nonlinear dynamic multiagent systems (MASs) based on an adaptive neural network (NN) state observer through the backstepping method and simplified reinforcement learning (RL). Each follower agent is subjected to only local information and measurable partial states due to actual sensor limitations. In view of the distributed optimized formation strategic needs, the uncertain nonlinear dynamics and undetectable states may jointly affect the stability of the time-varying cooperative formation control. Furthermore, focusing on Hamilton-Jacobi-Bellman optimization, it is almost incapable of directly dealing with unknown equations. Above uncertainty and immeasurability processed by adaptive state observer and NN simplified RL are further designed to achieve desired second-order formation configuration at the least cost. The optimization protocol can not only solve the undetectable states and realize the prescribed time-varying formation performance on the premise that all the errors are SGUUB, but also prove the stability and update the critics and actors easily. Through the above-mentioned approaches offer an optimal control scheme to address time-varying formation control. Finally, the validity of the theoretical method is proven by the Lyapunov stability theory and digital simulation.

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In this article, an adaptive optimized control scheme based on neural networks (NNs) is developed for a class of perturbed strict-feedback nonlinear systems. An optimized backstepping (OB) technique is employed for breaking through the limitation of the matching condition. The disturbance of existing nonlinear systems may degrade system performance or even lead to instability. In order to improve the system's robustness, a disturbance observer is constructed to compensate for the impact coming from the external disturbance. Because the proposed optimized scheme needs to train the adaptive parameters not only for reinforcement learning (RL) but also for the disturbance observer, it will become more challenging no matter designing the control algorithm or deriving the adaptive updating laws. Finally, by virtue of the Lyapunov stability theory, it is proved that all internal signals of the closed-loop systems are semiglobal uniformly ultimately bounded (SGUUB). Simulation results are provided to illustrate the validity of the devised method.

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In this article, a control scheme based on optimized backstepping (OB) technique is developed for a class of nonlinear strict-feedback systems with unknown dynamic functions. Reinforcement learning (RL) is employed for achieving the optimized control, and it is designed on the basis of the neural-network (NN) approximations under identifier-critic-actor architecture, where the identifier, critic, and actor are utilized for estimating the unknown dynamic, evaluating the system performance, and implementing the control action, respectively. OB control is to design all virtual controls and the actual control of backstepping to be the optimized solutions of corresponding subsystems. If the control is developed by employing the existing RL-based optimal control methods, it will become very intricate because their critic and actor updating laws are derived by carrying out gradient descent algorithm to the square of Bellman residual error, which is equal to the approximation of the Hamilton-Jacobi-Bellman (HJB) equation that contains multiple nonlinear terms. In order to effectively accomplish the optimized control, a simplified RL algorithm is designed by deriving the updating laws from the negative gradient of a simple positive function, which is generated from the partial derivative of the HJB equation. Meanwhile, the design can also release the condition of persistence excitation, which is required in most existing optimal controls. Finally, effectiveness is demonstrated by both theory and simulation.

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This paper presents an adaptive neural network output feedback control method for stochastic nonlinear systems with full state constraints. The barrier Lyapunov functions are used to conquer the effect of state constraints to system performance. The neural network state observer is established to estimate the unmeasured states. By using dynamic surface control technique, the "explosion of complexity" issue existing in the backstepping design is overcome. The proposed control scheme can guarantee that all signals of the system are bounded and the system output can follow the desired signal. Finally, two examples are given to verify the effectiveness of our control method.

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In this paper, a tracking control approach for surface vessel is developed based on the new control technique named optimized backstepping (OB), which considers optimization as a backstepping design principle. Since surface vessel systems are modeled by second-order dynamic in strict feedback form, backstepping is an ideal technique for finishing the tracking task. In the backstepping control of surface vessel, the virtual and actual controls are designed to be the optimized solutions of corresponding subsystems, therefore the overall control is optimized. In general, optimization control is designed based on the solution of Hamilton-Jacobi-Bellman equation. However, solving the equation is very difficult or even impossible due to the inherent nonlinearity and complexity. In order to overcome the difficulty, the reinforcement learning (RL) strategy of actor-critic architecture is usually considered, of which the critic and actor are utilized for evaluating the control performance and executing the control behavior, respectively. By employing the actor-critic RL algorithm for both virtual and actual controls of the vessel, it is proven that the desired optimizing and tracking performances can be arrived. Simulation results further demonstrate effectiveness of the proposed surface vessel control.

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In this paper, a control technique named optimized backstepping is first proposed by implementing tracking control for a class of strict-feedback systems, which considers optimization as a design philosophy of the high-order system control. The basic idea is that designing the actual and virtual controls of backstepping is the optimized solutions of the corresponding subsystems so that overall control of the high-order system is optimized. In general, optimization control is designed based on the solution of Hamilton-Jacobi-Bellman equation, but solving the equation is very difficult due to the inherent nonlinearity and intractability. In order to overcome the difficulty, the neural network (NN)-based reinforcement learning strategy of actor-critic architecture is used. In every backstepping step, the actor and critic NNs are constructed for executing control behavior and evaluating control performance, respectively. According to the Lyapunov stability theorem, it is proven that the desired control performance can be obtained. Finally, a simulation example is carried out to further demonstrate the effectiveness of the proposed control approach.

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Combined with backstepping techniques, an observer-based adaptive consensus tracking control strategy is developed for a class of high-order nonlinear multiagent systems, of which each follower agent is modeled in a semi-strict-feedback form. By constructing the neural network-based state observer for each follower, the proposed consensus control method solves the unmeasurable state problem of high-order nonlinear multiagent systems. The control algorithm can guarantee that all signals of the multiagent system are semi-globally uniformly ultimately bounded and all outputs can synchronously track a reference signal to a desired accuracy. A simulation example is carried out to further demonstrate the effectiveness of the proposed consensus control method.

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This paper studies an adaptive tracking control for a class of nonlinear stochastic systems with unknown functions. The considered systems are in the nonaffine pure-feedback form, and it is the first to control this class of systems with stochastic disturbances. The fuzzy-neural networks are used to approximate unknown functions. Based on the backstepping design technique, the controllers and the adaptation laws are obtained. Compared to most of the existing stochastic systems, the proposed control algorithm has fewer adjustable parameters and thus, it can reduce online computation load. By using Lyapunov analysis, it is proven that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded in probability and the system output tracks the reference signal to a bounded compact set. The simulation example is given to illustrate the effectiveness of the proposed control algorithm.

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This brief studies an adaptive neural output feedback tracking control of uncertain nonlinear multi-input-multi-output (MIMO) systems in the discrete-time form. The considered MIMO systems are composed of n subsystems with the couplings of inputs and states among subsystems. In order to solve the noncausal problem and decouple the couplings, it needs to transform the systems into a predictor form. The higher order neural networks are utilized to approximate the desired controllers. By using Lyapunov analysis, it is proven that all the signals in the closed-loop system is the semi-globally uniformly ultimately bounded and the output errors converge to a compact set. In contrast to the existing results, the advantage of the scheme is that the number of the adjustable parameters is highly reduced. The effectiveness of the scheme is verified by a simulation example.

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BACKGROUND: In China recruitment and retention of sufficient numbers of safe blood donors continues to be a challenge. Understanding who donates blood, particularly those who donate larger (>200 mL) whole blood (WB) units, will help blood centers to target more effective recruitment and retention strategies. STUDY DESIGN AND METHODS: Demographic characteristics of 226,489 allogeneic WB donors from January to December 2008 at five geographically and ethnically diverse, urban blood centers were analyzed. RESULTS: The typical Chinese WB donor can be characterized as first-time volunteer (67.9%), male (56.9%), less than 45 years old (93.8%), and Han ethnicity (86.1%). Most donors had some college or below educational level (77.5%), donated at a mobile collection site (97.6%), and donated 300- or 400-mL units (76.0%). Differences in WB volume donations and donor demographics exist among the five centers. CONCLUSION: In China compared to the United States, donations are made by younger donors and donors give infrequently and make smaller WB donations. To help ensure supply adequacy, continued efforts are needed to have donors give larger volumes of WB in China.

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BACKGROUND: A multi-blood center study was conducted to evaluate a human immunodeficiency virus type 1 (HIV-1) and hepatitis C virus (HCV) multiplex nucleic acid testing (NAT) donor screening test and to determine the residual risk for HIV-1 and HCV infection. STUDY DESIGN AND METHODS: A commercially available HIV-1 and HCV assay (Procleix, Chiron Corp.) was used for simultaneous detection of HIV-1 RNA and HCV RNA on 89,647 unlinked donor samples. NAT was performed with pools of 16 samples that had passed all routine screening tests. Single-donor NAT was performed for samples that had been disqualified by any reactive screening test result(s). Anti-HCV (Ortho third-generation HCV enzyme immunoassay [EIA]), alanine aminotransferase, and HCV NAT (Roche COBAS Amplicor HCV test) confirmatory tests were used for HCV EIA-nonreactive, HCV NAT-reactive samples. RESULTS: Three HCV NAT yield cases and no HIV-1 yield cases were detected. The yield rate for HCV NAT was 3.4 per 10(5) (95 percent confidence interval [CI], 0.7-9.8). The estimated incidence rate for HCV is 24.2 per 100,000 person-years (95% CI, 3.4-88.0). If minipool NAT is added to routine donor screening, the residual risk for HCV is estimated to be reduced to 1 in 20.4x10(4) (95% CI, 1 in 5.2x10(4)-1 in 165.5x10(4)). CONCLUSION: The residual risk for transfusion-transmitted HCV infection is still relatively high in China. Incorporating NAT technology into blood donor screening would be estimated to reduce the residual risk of HCV infections eightfold over current EIA screening.

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BACKGROUND: The recruitment and retention of voluntary, nonremunerated blood donors continues to be a challenge in China. Understanding donor demographics and donor characteristics is crucial for any blood center in developing strategies to recruit potential donors. STUDY DESIGN AND METHODS: The study population included all 29,784 whole blood donors from January 1 to December 31, 2003, at the Urumqi City Blood Center or one of its mobile blood collection buses. Demographic data, location, and frequency of donation and results of testing for transfusion-transmissible infection (TTI) were evaluated. RESULTS: The typical blood donor in Urumqi is male, less than 36 years of age, and Han Chinese; has at least a high school education; is a first-time donor; and donated at a mobile blood collection bus. The majority, 71 percent, were first-time donors. Among all donors, the seroprevalence rate of TTI was 3.5 percent for first-time donors, 2.7 percent for donors who donated twice, and 2.1 percent for donors who had donated three or more times. Han Chinese had lower seroprevalence rates of TTIs than ethnic minorities. Lower seroprevalence rates of TTIs were found among donors at mobile buses than at the blood centers. CONCLUSION: Similar to other donor populations, higher rates of TTIs were observed among first-time donors, and the prevalence decreased among repeated donors. One possible strategy for improving the safety of the blood supply might be for the blood center to recruit a cadre of donors who donate repeatedly, instead of relying on campaigns to recruit new donors from workplaces at each donation cycle.

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