Data-Driven Self-Optimizing Control: Unconstrained Optimization Problem

Controlled variable (CV) selection plays an important role in determining the performance of a process plant. Existing methods for CV selection through self-optimizing control requires linearization of rigorous models around nominal operating points. This is a very difficult task which results to large losses. This work presents a novel method for CV design. A necessary condition of optimality (NCO) was proposed to be the CV. The approach does not require the analytical expression of the NCO to be derived but is approximated through a single regression step based on data. Finite difference was used to approximate the NCO (gradient) using data; three finite difference schemes were employed for this purpose, which are forward, backward and central differences. Seven different cases with respect to number of sampling points, neighborhood points and finite difference schemes were investigated. To demonstrate the efficacy of the method in simplest way, it is applied to a hypothetical unconstrained optimization problem. The proposed method was found to have outperformed some existing approaches in many instances. A zero loss was recorded by some designed CVs. Central difference was found to be the best schemes among the three. Keywords— controlled variable, disturbance, finite difference, monotonicity, regression.

Variation method solving of the inverse problems for Schrödinger-type equation

A variation method for solving the inverse problems of determining of the complex quantum potential in a nonlinear non-stationary Schrödinger-type equation with final and boundary observations is considered. The existence and uniqueness theorem of the solution of the variation formulation of the inverse problem is proved, the continuity and continuous differentiability of the quality criterion are established, the formula for its gradient is found, the necessary condition of optimality is proved and iterative regularization of the solution is indicated.

The Problem of the Optimal Control with a Lower Coefficient for Weakly Nonlinear Wave Equation in the Mixed Problem

In this paper, we consider the problem of determining the lowest coefficient of weakly nonlinear wave equation. The problem is reduced to the optimal control problem, in the new problem. In the this existence theorem of the optimal control and, the Fre ́echet differentiability of the functional is proved. Also the necessary condition of optimality is derived in view of variational inequality.

Optimal Control Problem for the Weak Nonlinear Equation of Thin Plate With Control at the Coefficient of Lowest Term

The paper deals with an inverse problem of determining the right-hand side of the linear equation of oscillations of thin plates. The problem is reduced to the optimal control problem. Differentiability of the functional is studied. Necessary condition of optimality is derived.

Optimal control problem for the equation of vibrations of an elastic plate

An optimal control problem for the vibration equation of an elastic plate is considered when the control function is included in the coefficient of the highest order derivative and the right-hand side of the equation. The solvability of the initial boundary value problem is shown, the theorem on the existence of an optimal control is proved and a necessary condition of optimality in the form of an integral equation is obtained.

Stochastic optimal control problem of constrained switching system with delay

This paper concerns the stochastic optimal control problem of switching systems with delay. The evolution of the system is governed by the collection of stochastic delay differential equations with initial conditions that depend on its previous state. The restriction on the system is defined by the functional constraint that contains state and time parameters. First, maximum principle for stochastic control problem of delay switching system without constraint is established. Finally, using Ekeland?s variational principle, the necessary condition of optimality for control system with constraint is obtained.

Optimal Control of Pseudoparabolic Variational Inequalities Involving State Constraint

We establish the necessary condition of optimality for optimal control problem governed by some pseudoparabolic differential equations involving monotone graphs. Some approximating control process and examples are given.

A Chebyshev-Based State Representation for Linear Quadratic Optimal Control

A computationally attractive method for determining the optimal control of unconstrained linear dynamic systems with quadratic performance indices is presented. In the proposed method, the difference between each state variable and its initial condition is represented by a finite-term shifted Chebyshev series. The representation leads to a system of linear algebraic equations as the necessary condition of optimality. Simulation studies demonstrate computational advantages relative to a standard Riccati-based method, a transition matrix method, and a previous Fourier-based method.