End-point Control Problems Research Articles

Epi-derivatives of integral functionals with applications

We study first- and second-order epi-differentiability for integral functionals defined on L 2 [ 0 , T ] {L^2}[0,T] , and apply the results to obtain first- and second-order necessary conditions for optimality in free endpoint control problems.

Solution of finite-time optimal control problems with mixed end constraints in the s-domain

The solution of linear quadratic optimal control problems having mixed end conditions is considered. The plant is assumed to be linear, time invariant, and multivariable, and the cost function is quadratic, and defined over a Finite time interval. At the terminal time some of the system responses are required to achieve desired values and the remaining responses are free. The solution in the s -domain is more direct than previous methods and simple problems can be solved by hand calculations. Open- and clused-loop solutions can be determined and the method enables new insight to be gained into the relationship between the fixed and free end-point control problems.

A General Minimum Principle for End-point Control Problems

ABSTRACT A very brood class of end-point control problems is formulated in general terms, and correspondingly general procedures in the calculus of variations are developed for their solution The generality of the treatment lies in a systematic application of the point of view of functional analysis. The state of the system being controlled is described by an abstract vector in a suitable linear space ; the evolution of the system state with time is described in terms of an operator on the state vector ; the measure of system performance to be maximized or minimized is taken as a functional of the final state. The linearized system operator and its adjoint with respect to an inner product in the state space play central roles in the variational arguments The variational methods are in the spirit of those leading to the familiar Pontrjagin maximum principle, and indeed this principle appears as the finite-dimensional case of the present results. These results however apply equally to infinite-dimensional cases such as systems with distributed parameters whose mathematical description is given in terms of partial rather than ordinary differential equations. The methods are illustrated here for a problem in heat exchanger control. General numerical procedures are discussed, but for distributed parameter systems the calculations required to solve practical problems will be/extrcmely_formidable.

Best Endpoint Control of Noisy Systems

ABSTRACT The endpoint control problem for noisy systems, as formulated in terms of dynamic programming (Bellman 1957), loads to a control policy which requires complete feedback information at every time when control action is to be taken. The problem formulation applies conceptually only to systems making discrete jumps at discrete times, although the functional equations solution can in certain cases (in particular where the random disturbances to the system equations appear as an additive Gaussian white noise) be taken to the limit of continuous time (Florentin 1961) The present work investigates an alternate formulation of the problem that aims in the first instance at a feed forward control schedule, although it can in principle be used to obtain feedback control policies as well. The policies obtained in this way differ in general from those arising from the formalism of dynamic programming. This formulation applies equally well to systems evolving continuously in time, and, under certain restrictiv...