Global optimization of linear hybrid systems with explicit transitions

• Published in: Systems & control letters Vol. 51; no. 5; pp. 363 - 375
• Main Authors: Lee, Cha Kun, Singer, Adam B, Barton, Paul I
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2004; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control parametrization; Control theory. Systems; Convex underestimators; Dynamic optimization; Exact sciences and technology; Fixed time events; Linear hybrid systems; Multistage dynamic optimization; Convex underestimators; Control parametrization; Linear hybrid systems; Fixed time events; Multistage dynamic optimization; Dynamic optimization; Gradient; Multistage; Differential equation; Branch and bound method; Global optimum; Linear time; Discrete system; Parameterization; Optimization; Hybrid system; Boarded computer; Time varying system; Transition system; Relaxation method; Objective function; Dynamic programming
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/j.sysconle.2003.09.005

The global optimization of hybrid systems described by linear time-varying ordinary differential equations is examined. A method to construct convex relaxations of general, nonlinear Bolza-type objective functions or constraints subject to an embedded hybrid system with explicit transitions is presented. The optimization problem can be solved using gradient-based algorithms in a branch and bound framework that is shown to be infinitely convergent when the implied state bounds are employed.