Nonlinear adaptive control and applications to biped robots

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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.