Viscosity Approximating Solutions to ODE Systems That Admit Shocks, and Their Limits

Hybrid Control Systems and Viscosity Solutions

We investigate a model of hybrid control system in which both discrete and continuous controls are involved. In this general model, discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, namely, an autonomous jump set A or a controlled jump set C where the controller can choose to jump or not. At...

Approximating NP-hard Problems Efficient Algorithms and their Limits

Viscosity Solutions and Computation for Dissipative Systems

Recent activity in nonlinear H∞ control has sparked renewed interest in the theory of dissipative nonlinear systems. This theory was initiated byWillems (1972) and developed further by Hill & Moylan (1976). Central to this theory are the so-called storage functions. These functions are generalized energy functions defined in terms of dissipation inequalities. The natural infinitesimal versions ...

Singular solutions to systems of conservation laws: shocks, δ- and δ′-shocks

Using the definitions of δand δ′-shocks for the systems of conservation laws [12], [13], [39], the Rankine–Hugoniot conditions for δand δ′-shocks are derived. We present a construction of solutions to the Cauchy problems admitting δand δ′-shocks. In particular, the Riemann problem admitting shocks, δ-shocks, δ′-shocks, and vacuum states is considered. The geometric aspects of δand δ′-shocks are...

Unbounded Viscosity Solutions of Hybrid Control Systems

We study a hybrid control system in which both discrete and continuous controls are involved. The discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, namely, an autonomous jump set A or a controlled jump set C where controller can choose to jump or not. At each jump, trajectory can move to a d...