Continuous and inverse optimal control designs for chained systems: A global state-scaling transformation and a time-scaling method

In this paper, the inverse optimal control designs for chained systems are investigated. The presented designs are based on the thorough study of controllability of chained systems. Particularly, two methods are proposed to recover uniform complete controllability for the chained system. One involves a global singularity-free state-scaling transformation, the other is based on a time transform, and both of them require an innovative design of dynamic control component for its subsystem. Using either of the approaches, the chained system is mapped into a controllable linear time-varying system for which control can systematically be designed to ensure exponential convergence or asymptotic stability. Both state-feedback and output-feedback designs are presented and literally shown to be inversely optimal. Simulation results are used to verify the effectiveness of the proposed controls. Copyright q 2008 John Wiley & Sons, Ltd.