不确定非线性系统全局自适应跟踪控制分析与设计
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摘要
本文主要研究了几类不确定非线性系统的全局自适应实际输出跟踪问题.主要利用增加幂次积分方法、反推方法和通用控制及死区思想与技巧,分别设计了两类具有未知控制方向高阶非线性系统的全局自适应状态反馈跟踪控制器和两类具有未知增长率不确定非线性系统的全局自适应输出反馈跟踪控制器.本文主要内容分为以下四个部分：
一、控制方向未知高阶不确定非线性系统的全局实际跟踪控制设计
本部分在较弱的条件下,研究了一类具有未知控制方向的高阶不确定非线性系统的全局实际跟踪问题.受近期跟踪结果和通用控制及死区思想的启发,通过采用Nussbaum增益方法和增加幂次积分法,并引入一个新颖的坐标变换、新的调节律和拟符号函数,去除了密切相关跟踪文献中控制方向要求已知的这一本质性假设,给出了一个连续自适应状态反馈跟踪控制器的解析解.该控制器确保跟踪误差经有限时间后收敛于设定的原点的任意小邻域,同时闭环系统的所有信号皆有界.
二、更一般高阶不确定非线性系统的全局实际跟踪控制设计
本部分研究了一类更一般高阶不确定非线性系统的全局实际跟踪控制设计问题.特别地,将未知控制系数由上一部分中的上下界均为常数扩展成可以取任意大和／或任意小值.通过Nussbaum增益方法和增加幂次积分法,引入新的调节律和一个相对简单的连续可微函数,提出了新的全局自适应状态反馈实际跟踪控制设计方案.所得结果表明,该控制器能够确保闭环系统的所有状态皆有界,且跟踪误差经一个有限时间后收敛于设定的原点的任意小邻域.
三、增长率未知非线性系统全局输出反馈实际跟踪控制设计
本部分研究了一类具有依赖于不可测状态的增长且增长率为未知常数的不确定非线性系统的全局输出反馈实际跟踪问题.受相关镇定结果的启发,通过灵活运用通用控制和死区的方法与技巧,并引入一个基于新的动态高增益的观测器,设计出了全局自适应输出反馈跟踪控制器.结合所提出的性能分析新模式,证明了所设计的控制器能够确保跟踪误差经有限时间后收敛于设定的原点的任意小邻域,同时闭环系统的所有信号皆有界.
四、增长率和控制系数未知串联系统全局输出反馈实际跟踪控制设计
本部分考虑了一类具有更多不确定性非线性系统的全局输出反馈实际跟踪问题.所研究系统同时具有零动态、增长依赖于不可测状态且增长率为未知常数、未知时变控制系数且上界为未知常数.这些特征使得所研究系统大不同于密切相关文献,进而导致该问题较难解决.通过灵活将通用控制及死区思想与反推技巧相结合,并引入一个不同的基于新的动态高增益的观测器,成功提出了一种全局自适应实际跟踪控制设计的新方案.采用第三部分中所提出的性能分析模式,验证了所设计的控制器保证了所得闭环系统的所有状态是全局有界的,且跟踪误差在一个有限时间后收敛于设定的原点的任意小邻域.
以上四部分分别给出了相应的仿真算例,验证了所给出的全局自适应实际跟踪控制设计方案的有效性与可行性.
This dissertation investigates the problem of global adaptive practical out-put tracking for several classes of uncertain nonlinear systems. Mainly by the approaches of adding a power integrator and backstepping, and the ideas of uni-versal control and dead zone, global adaptive state-feedback tracking controllers and global adaptive output-feedback tracking controllers are designed respectively for two classes of high-order nonlinear systems with unknown control directions, and for two classes of uncertain nonlinear systems with unknown growth rate. The main contents of this dissertation are composed of the following four parts:
(I) Global practical tracking control design for high-order uncertain nonlinear systems with unknown control directions
This part addresses the global practical tracking problem for a class of high-order uncertain nonlinear systems with unknown control directions under fairly weak conditions. Motivated by the recent tracking works and the ideas of universal control and dead zone, by the approaches of Nussbaum-gain and adding a power integrator, and introducing a novel coordinate transformation, new updating laws, and pseudosign functions, the basic assumption that the control directions are required to be known in closely related tracking works is successfully removed, and a continuous adaptive state-feedback tracking controller is proposed. The designed controller is completely explicit, and guarantees that the tracking error becomes prescribed arbitrarily small after a finite time, and simultaneously all the closed-loop states are bounded.
(II) Global practical tracking control design for a large class of high-order uncertain nonlinear systems
This part addresses the global practical tracking problem for a more gen-eral class of high-order uncertain nonlinear systems, and particularly extends the unknown control coefficients with lower and upper constant bounds in the first part to the ones which may take arbitrarily large and/or small values. By the approaches of Nussbaum-gain and adding a power integrator, and introducing new updating laws, and a continuously differentiable function with a relatively simple structure, the new control design scheme of global adaptive state-feedback practical tracking is proposed. It is shown that the designed controller guarantees that all the closed-loop system states are bounded and the tracking error becomes prescribed arbitrarily small after a finite time.
(Ⅲ) Global practical tracking by output-feedback for nonlinear sys-tems with unknown growth rate
This part is devoted to the global practical tracking by output-feedback for a class of uncertain nonlinear systems which have unmeasured states dependent growth with unknown constant rate. Motivated by the related stabilization re-sults, flexibly using the ideas of universal control and dead zone, and introducing an observer with a new dynamic high-gain, a global adaptive output-feedback tracking controller is designed. Moreover, with the aid of the proposed new pat-tern of performance analysis, the designed controller can make the tracking error prescribed arbitrarily small after a finite time while keeping all the states of the closed-loop system bounded.
(Ⅳ) Global practical tracking via output-feedback for cascade sys-tems with unknown growth rate and unknown control coefficients
This part considers the global practical tracking problem by output-feedback for a class of uncertain cascade systems with more uncertainties. The systems in-vestigated are substantially different from the closely related work. The problem becomes much more difficult to solve due to the simultaneous existence of zero-dynamics, unmeasured states dependent growth with unknown constant rate, and unknown time-varying control coefficients with unknown constant bounds. By skillfully combining the methods of universal control and dead zone with backstep-ping technique, and introducing a distinct observer with a new dynamic high-gain, a new adaptive tracking control design scheme is successfully proposed. With the help of the pattern of performance analysis proposed in the third part, it is shown that the designed controller guarantees that all states of the resulting closed-loop system are globally bounded and the tracking error remains prescribed arbitrarily small after a finite time.
The above four parts also give the corresponding simulation examples, re-spectively, to illustrate the correctness and effectiveness of the proposed control design schemes of global adaptive practical tracking.
一、控制方向未知高阶不确定非线性系统的全局实际跟踪控制设计
本部分在较弱的条件下,研究了一类具有未知控制方向的高阶不确定非线性系统的全局实际跟踪问题.受近期跟踪结果和通用控制及死区思想的启发,通过采用Nussbaum增益方法和增加幂次积分法,并引入一个新颖的坐标变换、新的调节律和拟符号函数,去除了密切相关跟踪文献中控制方向要求已知的这一本质性假设,给出了一个连续自适应状态反馈跟踪控制器的解析解.该控制器确保跟踪误差经有限时间后收敛于设定的原点的任意小邻域,同时闭环系统的所有信号皆有界.
二、更一般高阶不确定非线性系统的全局实际跟踪控制设计
本部分研究了一类更一般高阶不确定非线性系统的全局实际跟踪控制设计问题.特别地,将未知控制系数由上一部分中的上下界均为常数扩展成可以取任意大和／或任意小值.通过Nussbaum增益方法和增加幂次积分法,引入新的调节律和一个相对简单的连续可微函数,提出了新的全局自适应状态反馈实际跟踪控制设计方案.所得结果表明,该控制器能够确保闭环系统的所有状态皆有界,且跟踪误差经一个有限时间后收敛于设定的原点的任意小邻域.
三、增长率未知非线性系统全局输出反馈实际跟踪控制设计
本部分研究了一类具有依赖于不可测状态的增长且增长率为未知常数的不确定非线性系统的全局输出反馈实际跟踪问题.受相关镇定结果的启发,通过灵活运用通用控制和死区的方法与技巧,并引入一个基于新的动态高增益的观测器,设计出了全局自适应输出反馈跟踪控制器.结合所提出的性能分析新模式,证明了所设计的控制器能够确保跟踪误差经有限时间后收敛于设定的原点的任意小邻域,同时闭环系统的所有信号皆有界.
四、增长率和控制系数未知串联系统全局输出反馈实际跟踪控制设计
本部分考虑了一类具有更多不确定性非线性系统的全局输出反馈实际跟踪问题.所研究系统同时具有零动态、增长依赖于不可测状态且增长率为未知常数、未知时变控制系数且上界为未知常数.这些特征使得所研究系统大不同于密切相关文献,进而导致该问题较难解决.通过灵活将通用控制及死区思想与反推技巧相结合,并引入一个不同的基于新的动态高增益的观测器,成功提出了一种全局自适应实际跟踪控制设计的新方案.采用第三部分中所提出的性能分析模式,验证了所设计的控制器保证了所得闭环系统的所有状态是全局有界的,且跟踪误差在一个有限时间后收敛于设定的原点的任意小邻域.
以上四部分分别给出了相应的仿真算例,验证了所给出的全局自适应实际跟踪控制设计方案的有效性与可行性.
This dissertation investigates the problem of global adaptive practical out-put tracking for several classes of uncertain nonlinear systems. Mainly by the approaches of adding a power integrator and backstepping, and the ideas of uni-versal control and dead zone, global adaptive state-feedback tracking controllers and global adaptive output-feedback tracking controllers are designed respectively for two classes of high-order nonlinear systems with unknown control directions, and for two classes of uncertain nonlinear systems with unknown growth rate. The main contents of this dissertation are composed of the following four parts:
(I) Global practical tracking control design for high-order uncertain nonlinear systems with unknown control directions
This part addresses the global practical tracking problem for a class of high-order uncertain nonlinear systems with unknown control directions under fairly weak conditions. Motivated by the recent tracking works and the ideas of universal control and dead zone, by the approaches of Nussbaum-gain and adding a power integrator, and introducing a novel coordinate transformation, new updating laws, and pseudosign functions, the basic assumption that the control directions are required to be known in closely related tracking works is successfully removed, and a continuous adaptive state-feedback tracking controller is proposed. The designed controller is completely explicit, and guarantees that the tracking error becomes prescribed arbitrarily small after a finite time, and simultaneously all the closed-loop states are bounded.
(II) Global practical tracking control design for a large class of high-order uncertain nonlinear systems
This part addresses the global practical tracking problem for a more gen-eral class of high-order uncertain nonlinear systems, and particularly extends the unknown control coefficients with lower and upper constant bounds in the first part to the ones which may take arbitrarily large and/or small values. By the approaches of Nussbaum-gain and adding a power integrator, and introducing new updating laws, and a continuously differentiable function with a relatively simple structure, the new control design scheme of global adaptive state-feedback practical tracking is proposed. It is shown that the designed controller guarantees that all the closed-loop system states are bounded and the tracking error becomes prescribed arbitrarily small after a finite time.
(Ⅲ) Global practical tracking by output-feedback for nonlinear sys-tems with unknown growth rate
This part is devoted to the global practical tracking by output-feedback for a class of uncertain nonlinear systems which have unmeasured states dependent growth with unknown constant rate. Motivated by the related stabilization re-sults, flexibly using the ideas of universal control and dead zone, and introducing an observer with a new dynamic high-gain, a global adaptive output-feedback tracking controller is designed. Moreover, with the aid of the proposed new pat-tern of performance analysis, the designed controller can make the tracking error prescribed arbitrarily small after a finite time while keeping all the states of the closed-loop system bounded.
(Ⅳ) Global practical tracking via output-feedback for cascade sys-tems with unknown growth rate and unknown control coefficients
This part considers the global practical tracking problem by output-feedback for a class of uncertain cascade systems with more uncertainties. The systems in-vestigated are substantially different from the closely related work. The problem becomes much more difficult to solve due to the simultaneous existence of zero-dynamics, unmeasured states dependent growth with unknown constant rate, and unknown time-varying control coefficients with unknown constant bounds. By skillfully combining the methods of universal control and dead zone with backstep-ping technique, and introducing a distinct observer with a new dynamic high-gain, a new adaptive tracking control design scheme is successfully proposed. With the help of the pattern of performance analysis proposed in the third part, it is shown that the designed controller guarantees that all states of the resulting closed-loop system are globally bounded and the tracking error remains prescribed arbitrarily small after a finite time.
The above four parts also give the corresponding simulation examples, re-spectively, to illustrate the correctness and effectiveness of the proposed control design schemes of global adaptive practical tracking.
引文
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