Robust L2-gain control for nonlinear systems with projection dynamics and input constraints: an example from traffic control

We formulate the L2-gain control problem for a general nonlinear, state-space system with projection dynamics in the state evolution and hard constraints on the set of admissible inputs. We develope specific results for an example motivated by a traffic signal control problem. A statefeedback control with the desired properties is found in terms of the solution of an associated Hamilton-Jacobi-Isaacs equation (the storage function or value function of the associated game) and the critical point of the associated Hamiltonian function. Discontinuities in the resulting control as a function of the state and due to the boundary projection in the system dynamics lead to hybrid features of the closed-loop system, specifically jumps of the system description between two or more continuous-time models. Trajectories for the closed-loop dynamics must be interpreted as a differential set inclusion in the sense of Filippov. Construction of the storage function is via a generalized stable invarian...

• Type: Journal
• Year: 1999
• Where: AUTOMATICA
• Authors: Joseph A. Ball, Martin V. Day, Tungsheng Yu, Pushkin Kachroo
• Keywords: AUTOMATICA 1999, Control Problem, L2-gain Control Problem, Storage Function