| Discrete Time Optimal Adaptive Control for Linear Stochastic Systems |
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| 作者姓名： | 姜睿 罗贵明 |
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| 作者单位： | Department of Computer Science and Technology Tsinghua University，School of Software Tsinghua University，Beijing 100084 China School of Software Tsinghua University，Beijing 100084 China，Beijing 100084 China |
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| 基金项目： | the National Natural Science Foundation of China(No.60474026)，the Asia Research Center at Tsinghua University |
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| 摘 要： | The least-squares (LS) algorithm has been used for system modeling for a long time. Without any excitation conditions, only the convergence rate of the common LS algorithm can be obtained. This paper analyzed the weighted least-squares (WLS) algorithm and described the good properties of the WLS algorithm. The WLS algorithm was then used for adaptive control of linear stochastic systems to show that the linear closed-loop system was globally stable and that the system identification was consistent. Compared to the past optimal adaptive controller, this controller does not impose restricted conditions on the coefficients of the system, such as knowing the first coefficient before the controller. Without any persistent excitation conditions, the analysis shows that, with the regulation of the adaptive control, the closed-loop system was globally stable and the adaptive controller converged to the one-step-ahead optimal controller in some sense.
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| 关 键 词： | 线性随机系统 优化自适应控制 离散时间 全局稳定 加权最小二乘法 |
| 收稿时间： | 10 March 2006 |
| 修稿时间： | 2006-03-10 |
Discrete Time Optimal Adaptive Control for Linear Stochastic Systems |
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| JIANG Rui,LUO Guiming.Discrete Time Optimal Adaptive Control for Linear Stochastic Systems[J].Tsinghua Science and Technology,2007,12(1):105-110. |
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| Authors: | JIANG Rui LUO Guiming |
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| Institution: | 1. Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China; 2. School of Software, Tsinghua University, Beijing 100084, China |
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| Abstract: | The least-squares (LS) algorithm has been used for system modeling for a long time. Without any excitation conditions, only the convergence rate of the common LS algorithm can be obtained. This paper analyzed the weighted least-squares (WLS) algorithm and described the good properties of the WLS algorithm. The WLS algorithm was then used for adaptive control of linear stochastic systems to show that the linear closed-loop system was globally stable and that the system identification was consistent. Compared to the past optimal adaptive controller, this controller does not impose restricted conditions on the coefficients of the system, such as knowing the first coefficient before the controller. Without any persistent excitation conditions, the analysis shows that, with the regulation of the adaptive control, the closed-loop system was globally stable and the adaptive controller converged to the one-step-ahead optimal controller in some sense. |
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| Keywords: | stochastic system weighted least-squares (WLS) algorithm optimal adaptive control globally stable |
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