CLF-based control design with good transient performance for known and unknown multi-input nonlinear systems

This paper tackles the problem of constructing semi-global state-feedback stabilizers that guarantee good transient closed-loop performance when applied to general nonlinear multi-input state-feedback stabilizable systems whose vector-fields are either known or totally unknown. In the case where the system vector-fields are known, a convex optimization design is proposed (which is based on the work of by Prajna et al. [6]) that provides an efficient semi-global state-feedback design for arbitrary smooth state-feedback stabilizable systems. In the case of systems with unknown vector-fields the aforementioned convex optimization design is appropriately combined with the adaptive Control Lyapunov Function (CLF)-based control scheme recently proposed by the author [5]. The resulting adaptive scheme guarantees arbitrarily good closed-loop transient performance outside the regions where the system is uncontrollable, provided the controlled system is state-feedback stabilizable and, moreover, it admits a controllability-like property.