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This paper presents a joint synthesis algorithm of trajectory and controlledinvariant funnel (CIF) for locally Lipschitz nonlinear systems subject tobounded disturbances. The CIF synthesis refers to a procedure of computingcontrolled invariance sets and corresponding feedback gains. In contrast toexisting CIF synthesis methods that compute the CIF with a pre-defined nominaltrajectory, our work aims to optimize the nominal trajectory and the CIFjointly to satisfy feasibility conditions without the relaxation of constraintsand obtain a more cost-optimal nominal trajectory. The proposed work has arecursive scheme that mainly optimize trajectory update and funnel update. Thetrajectory update step optimizes the nominal trajectory while ensuring thefeasibility of the CIF. Then, the funnel update step computes the funnel aroundthe nominal trajectory so that the CIF guarantees an invariance property. As aresult, with the optimized trajectory and CIF, any resulting trajectorypropagated from an initial set by the control law with the computed feedbackgain remains within the feasible region around the nominal trajectory under thepresence of bounded disturbances. We validate the proposed method via twoapplications from robotics.

Joint Synthesis of Trajectory and Controlled Invariant Funnel for Discrete-time Systems with Locally Lipschitz Nonlinearities