摘要:
首先, 利用 Backstepping 方法设计了简单的控制器将系统控制到不稳定的平衡点(0,0,0), 相空间中任一指定点 (0,0,1+b+p(1-p)) (0p1),以及实现利用第一个状态变量跟踪任意指定的函数 r(t). 其次,在假设有一个参数未知的条件下, 设计了一个单向偶合格式和未知参数的自适应律,使得该系统与其自身达到全局完全同步. 用Lyapunov 函数方法从理论上证明了设计的正确性,并用 Matlab 作了数值模拟说明设计的可行性.
Abstract:
By using the backstepping design method we formulated a simple controller to control the system to its unstable equilibrium (0,0,0), any point of the form (0,0,1+b+p(1-p))(0p1) in phase space, and forced the first state variable to trace arbitrary given function r(t). Suppose one parameter was unknown, we proposed a unidirectional coupled scheme and a parameter update role to assure the new Lorenz-like system to globally synchronize with a copy of itself. We presented a rigorous proof of our design by constructing proper Lyapunov function. Numerical simulations using Matlab were presented to show the feasibility of our design.
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