In this note we consider the cooperative linear quadratic control problem. That is, the problem where a number of players, all facing a (different) linear quadratic control problem, decide to cooperate in order to optimize their performance. It is well-known, in case the performance criteria are positive definite, how one can determine the set of Pareto efficient equilibria for these games. In ...

In this paper we present stability and convergence results for Dynamic Programming-based reinforcement learning applied to Linear Quadratic Regulation (LQR). The spe-ciic algorithm we analyze is based on Q-learning and it is proven to converge to the optimal controller provided that the underlying system is controllable and a particular signal vector is persistently excited. The performance of ...

We formulate stochastic robust optimal control problems, motivated by applications arising in interconnected economic systems, or spatially extended economies. We study in detail linear quadratic problems and nonlinear problems. We derive optimal robust controls and identify conditions under which concerns about model misspecification at specific site(s) could cause regulation to break down, to...

In Chapters 8 and 9 of this book we have designed dynamic controllers such that the closed-loop systems display the desired transient response and steady state characteristics. The design techniques presented in those chapters have sometimes been limited to trial and error methods while searching for controllers that meet the best given specifications. Furthermore, we have seen that in some cas...

For discrete-time linear time invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly, the state feedback control law which minimizes a quadratic performance criterion. We show that the control law is piece-wise linear and continuous for both the "nite horizon problem (model predictive control) and the usual in"nite time measure (constrained line...