In this chapter we present a brief description of 1 robust control. We first motivate the use of the 1norm and then show how it is used in formulating a control problem with the objective of minimizing the effect of unknown by bounded disturbances. This leads to formulation of the 1 optimal control problem, for which we present a solution using the Scaled-Q method. We then address the problem o...

We solve optimal transportation problem using stochastic optimal control theory. Indeed, for a super linear cost at most quadratic at infinity, we prove Kantorovich duality theorem by a zero noise limit (or vanishing viscosity) argument.. We also obtain a characterization of the support of an optimal measure in Monge-Kantorovich minimization problem (MKP) as a graph. Our key tool is a duality r...

Backstepping design is proposed to control a Lorenz chaotic system. A major advantage of this method is that it has the flexibility to build the control law by avoiding cancellations of useful nonlinearities. Consequently, the goals of stabilization of chaotic motion and tracking of a reference signal are achieved with a reduced control effort. A comparison with the differential geometric metho...

This paper analyzes the implications of potential offenders caring about their relative status. We establish that subjects’ status concerns can result in multiple-equilibrium crime rates and may modify the standard comparative-statics results regarding how the crime rate changes in response to a higher detection probability and higher sanctions. In addition, we argue that the socially optimal l...

The Lyapunov based approach for synchronizing and identifying the unknown parameters in the Duffing system is presented in this paper. The strategy consists of proposing a slave system which has to follow asymptotically the desired Duffing system. The gains of the slave system are adjusted continually according to a convenient adaptation control law, until the measurable output error converges ...

We develop a martingale approach for studying continuous-time stochastic differential games of control and stopping, in a non-Markovian framework and with the control affecting only the drift term of the state-process. Under appropriate conditions, we show that the game has a value and construct a saddle pair of optimal control and stopping strategies. Crucial in this construction is a characte...

background: determining the optimal and effective scheme for administrating the chemotherapy agents in breast cancer is the main goal of this scientific research. the most important issue here is the amount of drug or radiation administrated in chemotherapy and radiotherapy for increasing patient's survival. this is because in these cases, the therapy not only kills the tumor cells, but also ki...