A geometric derivation of numerical integrators for optimal control problems is proposed. It is based in the classical technique of generating functions adapted to the special features of optimal control problems.

Bayesian D-optimal designs supported on a xed number of points were found by Dette and Wong (1998) for estimating parameters in a polynomial model when the error variance depends exponentially on the explanatory variable. This work provides optimal designs under a broader class of error variance structures and investigates the robustness properties of these designs to model and prior distributi...

Optimal control problems in batch distillation involve finding a trajectory for the reflux ratio so as to maximize a performance index. Then the controller is asked to follow this trajectory in an open loop fashion. It is important to minimize the effect of uncertainties in thermodynamic models on the optimal control profiles to achieve a better operating performance. The non-linear parameter e...

ADiesel cycle enginewith internal and external irreversibilities of finite combustion rate of the fuel, friction and heat leakage is investigated in this paper. The heat transfer between the working fluid and the environment outside the cylinder obeys generalized radiative heat transfer law [q ∝ ∆(T n)]. Under the conditions of the fixed total cycle time and fuel consumed per cycle, the optimal...

In this article we develop a method of solving general one-dimensional Linear Quadratic Regulator (LQR) problems in optimal control theory, using a generalized form of Fibonacci numbers. We find the solution R (k) of the corresponding discrete-time Riccati equation in terms of ratios of generalized Fibonacci numbers. An explicit Binet type formula for R (k) is also found, removing the need for ...

where c > 0 and the supremum is taken over all admissible controls v satisfying vt 2 [ 0; 1] for all t up to = inf f t > 0 j Xt = 2 (`0; `1) g with 0 < 0 < 1 and `0 < 0 < `1 given and fixed. The following control v is proved to be optimal: ’Pull as hard as possible’ that is v t = 0 if Xt < g (St) , and ’push as hard as possible’ that is v t = 1 if Xt > g (St) , where s 7! g (s) is a switching c...

As follows from the Schwartz Impossibility Theorem, multiplication of two distributions is in general impossible. Nevertheless, often one needs to multiply a distribution by a discontinuous function, not by an arbitrary distribution. In the present paper we construct a space of distributions where the general operation of multiplication by a discontinuous function is defined, continuous, commut...

The paper extends quadratic optimal control theory to weakly regular linear systems, a rather broad class of infinite-dimensional systems with unbounded control and observation operators. We assume that the system is stable (in a sense to be defined) and that the associated Popov function is bounded from below. We study the properties of the optimally controlled system, of the optimal cost oper...

We consider the robust optimal control of a law of large numbers approximation of a stochastic network. The robust control problem is formulated as a di®erential game, with one player choosing the policies that determine service and routing assignments, and the other choosing quantities such as the arrival and service rates, subject to constraints. The cost to be minimized by the ̄rst player an...

In this paper we propose an iterative learning algorithm based on observer and linear quadratic performance function. We calculate the initial control value for the iteractive learning algorithm based on the estimation of the states, which guarantees the efficient asymptotic tracking of any desired trajectories. Furthermore, with Linear quadratic optimal control theory, we obtain the optimized ...