Nonlinear adaptive control and applications to biped robots

有些系统可以用一组常微分方程和一组代数方程，即所谓的微分代数方程（DAEs）来建模，有些系统可以用常微分方程（ode）来建模。所有物理系统都包含参数，其中一些可以测量，而另一些则不可接近。即使对于可测量的参数，有时也不容易获得准确的值。因此，设计控制器来实现控制目标和设计自适应律来估计未知参数具有重要的现实意义。具有自适应律的控制器称为自适应控制器。

Some systems can be modelled by a set of ordinary differential equations, together with a set of algebraic equations, so called differential-algebraic equations (DAEs) and some by ordinary differential equations (ODEs). All physical systems contain parameters, some of which can be measured and some of which are not accessible. Even for measurable parameters, sometimes it is not an easy task to obtain the exact values. Therefore, it is of practical importance to design controllers to achieve control objectives and to design adaptive laws to estimate unknown parameters. Controllers with adaptive laws are called adaptive controllers. Adaptive control theory has been well established for linear ODE systems and has attracted a lot of attention for nonlinear ODE systems. Almost all the research results for nonlinear adaptive control are obtained with structural assumptions of either matching condition or lower triangular form. There have been no research results on adaptive control for either linear or nonlinear DAE systems so far. Biped robots are robots which have two legs and are able to walk. The biped robots can be modeled by nonlinear ODEs for single support phase with only one foot on the ground and by nonlinear DAEs for double support phase with both feet on the ground. There are few results reported on adaptive control of biped robots. The main goals of this project are to relax the structural assumptions by using the existing design methods or by developing a new design approach for adaptive control of nonlinear ODE systems, to develop a design method for adaptive control of nonlinear DAE systems, and to apply adaptive control theory to biped robots. The anticipated outcomes are to build a biped robot, to enrich adaptive control theory for nonlinear ODE systems, to create adaptive control theory for nonlinear DAE systems, and to reduce the gap between adaptive control theory and practical applications. Since many real-world processes, such as chemical processes, mechanical systems, power systems, and so on, are nonlinear, contain unknown parameters, and are subjected to disturbances and delays, this research program has its practical importance in industrial processes.