2005/02/08 by Jean‐Guillaume Dumas, Dumas, Jean-Guillaume Luc, Aude Rondepierre +1
Engineering · Mathematics · #49J15 #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #FOS: Computer and information sciences #FOS: Mathematics #Guidance and Control Systems #Optimization and Control (math.OC) #Symbolic Computation (cs.SC)
paper · pdf · doi:10.48550/arxiv.math/0502172
openalex publication_date 2005/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced by piecewise affine approximations which allow an analytical resolution. The sequence of affine models then forms a sequence of states of a hybrid automaton. Given a sequence of states, we introduce an hybrid approximation of the nonlinear controllable domain and propose a new algorithm computing a controllable, piecewise convex approximation. The same way the nonlinear optimal control problem is replaced by an hybrid piecewise affine one. Stating a hybrid maximum principle suitable to our hybrid model, we deduce the global structure of the hybrid optimal control steering the system to the target.