Research on geometric and algebraic structures of solutions and spectrums in hyperbolic - parabolic control systems

对于线性抛物型方程组，（1）证明了两个独立边界镇定方案的代数相似性，（2）用代数方法得到了镇定所需传感器和致动器的最小数目，（3）实现了具有第一类边界的耦合输运扩散方程组的镇定，（4）证明了两个独立边界镇定方案的代数相似性，（5）证明了两个独立边界镇定方案的代数相似性，（6）证明了两个独立边界镇定方案的代数相似性，（7）证明了两个独立边界镇定方案的代数相似性，（8）证明了两个独立边界镇定方案的代数相似性，（9）证明了两个独立边界镇定方案的代数相似性，（10）证明了两个独立边界镇定方案的代数相似性，（11）证明了两个独立边界镇定方案的代数相似性，（11）证明了两个独立边界镇定方案的代数相似性，（12）证明了两个独立边界镇定方案的代数相似性，（11）证明了两个独立边界镇定方案的代数相似性，（12）证明（4）设计了一种特殊的反馈控制方案，使得"状态"的某个线性泛函的衰减速度恰好快于状态的衰减速度。对于线性双曲型方程组，（5）利用backstepping方法解决了平行流换热过程的输出跟踪问题。

As for linear parabolic systems, (1) algebraic similarity of two independent boundary stabilization schemes was proven; (2) the smallest possible number of sensors and actuators necessary for stabilization was algebraically obtained; (3) stabilization of a coupled transport diffusion system with boundary of the firstkind was achieved; and (4) a specific feedback control scheme was designed, such that some linear functional of the "state" decays exactly faster than the state. As for linear hyperbolic systems, (5) an output tracking problem for a parallel-flow heat exchange process was achieved by the so-called backstepping approach.