The paper investigates the stability of the solutions of linearquadratic optimal control problems with bang-bang controls in terms of metric sub-regularity and bi-metric regularity. New sufficient conditions for these properties are obtained, which strengthen the known conditions for sub-regularity and extend the known conditions for bi-metric regularity to Bolza-type problems.

The operations number was evaluated for different design strategies to select the optimal or quasioptimal strategy that has the minimal computer time. The general methodology for the system design was elaborated by means of the optimal control theory approach. The problem of the time-optimal system design has been formulated as the classical problem of the optimal control for the some functiona...

We study the duality theory for hyperbolic equations. Also, we consider distributed control systems with positive control and convex cost functionals.

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 consider the optimal control of an unreliable manufacturing system with restarting costs. In 1986 and 1988, Akella and Kumar (for the in nite horizon discounted cost) and Bielecki and Kumar (for the in nite horizon average expected cost) show that the optimal policy is given by an optimal inventory level (“hedging point policy”). Inspired by these simple systems, we explore a new class of mo...

In critical energy infrastructure sectors (e.g. electric power generation, natural gas transportation, oil refining capacity) maintaining certain level of excess capacity is socially valuable (as it serves to protect against unexpected market conditions) but not necessarily compatible with the incentives for individual firms in the market. In this paper, we develop a dynamic oligopoly model wit...