Control of Nonlinear Complex System with Variable Constraint

1.提出了一种考虑内力和冲击产生的冲量约束的非线性复杂系统建模方法。该方法明确表达了多关节系统运动所需的约束力，并对其进行控制，使约束与运动同步调节。提出了一种显式控制冲力的变约束控制算法，并在摆式杂耍系统中实现。实验结果表明了该方法的有效性。利用状态相关Riccati方程（SDRE）设计了非线性系统的镇定控制器。确定了控制律的计算步骤。作为一个实现实例，实现了摆控制系统对摆起和倒立稳定的强鲁棒性。针对变约束系统在极限环中运动且约束连续变化的问题，设计了一种控制器。特别是在混沌镇定方法——OGY方法的基础上，提出了一种周期镇定控制器，使系统达到具有一定周期的极限环。在被动步行机器人上的实验结果表明了该方法的有效性。采用变结构控制方法，研究了在不同初始角度、不同初始转速、不同增益和超平面的变结构控制器下，倒立摆从上摆到稳定在倒立位置的时间间隔。提出用颜色表示系统相对于初始条件和控制器参数的稳定程度。所得到的彩色图是由Julia集和Mandelbrot集的类似思想给出的。针对非线性系统提出了一种带SDRE的滑动扇区控制方法，针对无稳定子系统的混合系统提出了一种混合滑动扇区控制方法，并提出了自适应变结构微分器。少

1.A modeling approach for nonlinear complex systems is proposed taking the internal constraint force and the impulse constraint force resulted from impacting into consideration. The constraint force, which is required for the movement of multi-joints systems, is expressed explicitly and controlled to adjust the constraint and the movement simultaneously. A variable constraint control algorithm is proposed to control the impulse force explicitly and implemented in a pendulum-type juggling system. The experimental results show the effectiveness.2.A stabilization controller for nonlinear systems is designed with the state-dependent Riccati Equation(SDRE). Steps for the calculation of the control law are confirmed. As an implementation example, strong robustness of a pendulum control system for both the swing-up and the stabilization at its inverted position was achieved.3.A controller is designed for variable constraint systems, which move in a limit cycle while the constraint changes dis … More continuously. Especially, based on the OGY approach known as a famous chaos stabilization approach, a period stabilization controller, which leads the system to a limit cycle with a certain period, is proposed. The experimental result with a passive walking robot shows the validity.4.With the variable structure control, the time interval for an inverted pendulum to be stabilized at its inverted position from being swung up is investigated for different initial angles, different initial rotation speeds and different gains and hyper planes of the variable structure controller. It is proposed to express the degree of stability with respect to the initial condition and controller parameters by the color. The resulted colored picture is given by a similar idea of the Julia and the Mandelbrot sets.5.A sliding sector control with SDRE for nonlinear systems, a hybrid sliding sector control for hybrid systems without stable subsystems and an adaptive variable structure differentiator are proposed. Less