Steady-state Optimal Control Problem Research Articles

Dynamics and Control on a Discrete Multi-Inventory System

In this paper, a discrete two item inventory model for deteriorating items with a linear stock dependent demand rate without regular supply is given first; then, regular supply is taken into account, which may be regarded as feedback control. An objective function is formed to calculate the net profit with respect to possible profits and possible loss. A necessary criterion for the steady state optimal control problem for optimizing the objective function subjected to the constraints given by the difference equations of the inventory is obtained. At last, an improved model is put forward.

On multi-item inventory

The paper gives a new approach towards a two––item inventory model for deteriorating items with a linear stock––dependent demand rate. In fact, for the first time, the interacting terms showing the mutual increase in the demand of one commodity due to the presence of the other is accommodated in the model. Again, from the linear demand rate, it follows that more is the inventory, more is the demand. So a control parameter is introduced, such that it maintains the continuous supply to the inventory. Next an objective function is formed to calculate the net profit with respect to all possible profits and all possible loss (taken with negative sign). The paper obtains a necessary criterion for the steady state optimal control problem for optimizing the objective function subjected to the constraints given by the ordinary differential equations of the inventory. It also considers a particular choice of parameters satisfying the above necessary conditions. Under this choice, the optimal values of control parameters are calculated; also the optimal amount of inventories is found out. Finally, with respect to these optimal values of control parameters and those of the optimal inventories, the optimal value of the objective function is determined. Next another choice of parameters is considered for which the aforesaid necessary conditions do not hold. Obviously, in that case the steady state solution is non-optimal. In such a case a suboptimal problem is considered corresponding to the more profitable inventory. It is shown that such suboptimal steady state solution fails to exist in this case.

Aggregation of the policy iteration method for nearly completely decomposable Markov chains

A steady-state optimal control problem is considered for nearly completely decomposable Markov chains. In order to apply the policy iteration method of R.A. Howard (Dynamic Programming and Markov Processes, Cambridge, MA, MIT Press, 1960), a high-dimensional ill-conditioned system of algebraic equations must be solved in the value-determination step. Although algorithms exist for aggregation of the steady-state probability distribution problem, they only provide methods for computing the cost, not the dual variables. Using a singular perturbation approach, an aggregation method for the value-determination equation is developed. The aggregation method is developed in three steps. First, a class of similarity transformations that transform the system into a singularly perturbed form is developed. Second, an aggregation method to compute the steady-state probability distribution is derived. Third, this aggregation method is applied to the value determination step of Howard's method (1960). >

Boundary integral equation methods for steady-state optimal control problems

The necessary conditions for optimality of a steady-state optimal control problem are first derived by using calculus of variations. Two model control problems from continuum mechanics are then investigated by discretizing the optimality conditions in space via the boundary integral equation methods and by minimizing the performance index via the conjugate gradient methods of optimization.

Optimization of Thermal Conductivities of Isotropic and Orthotropic Solids

Optimization of thermal conductivities of isotropic and orthotropic solids is treated as a steady-state optimal control problem. Nonlinear necessary optimum conditions are first derived for the so-called material optimization problem, and a general numerical method of solution is then proposed. The iterative numerical procedure solves the linearized state and co-state equations by the finite element method and minimizes the performance index by the conjugate gradient method. Numerical solutions, checked with exact results when possible, are given for an isotropic infinite plate and a cylinder.

Optimal Boundary Tractions for Solids With Initial Strains

Optimal boundary loading of solids with initial strains has been analyzed as a steady-state optimal control problem. Discretization of the optimality conditions, obtained by calculus of variations, is achieved by the finite element method, while the minimization of a performance index is done via the conjugate gradient method. Numerical results are provided for two plane strain problems with initial thermal strains.

Deadbeat control and tracking of discrete-time systems

A new approach for forcing the state of a linear discrete-time system to zero in a minimum number of steps is discussed. The problem is formulated as the solution to a steady-state optimal control problem with no cost on the control. This problem in turn is set up as the solution to an associated eigenvalue problem. No special assumption on the open loop system matrix and/or the ratio of the number of states to controls is required. Stable numerical techniques are presented for solving for the feedback gain. Robust deadbeat tracking is also discussed.

A steady-state optimal control problem

A steady-state optimal control problem