Robust optimal feedback for terminal linear-quadratic control problems under disturbances

We consider a linear dynamic system in the presence of an unknown but bounded perturbation and study how to control the system in order to get into a prescribed neighborhood of a zero at a given final moment. The quality of a control is estimated by the quadratic functional. We define optimal guaranteed program controls as controls that are allowed to be corrected at one intermediate time moment. We show that an infinite dimensional problem of constructing such controls is equivalent to a special bilevel problem of mathematical programming which can be solved explicitely. An easy implementable algorithm for solving the bilevel optimization problem is derived. Based on this algorithm we propose an algorithm of constructing a guaranteed feedback control with one correction moment. We describe the rules of computing feedback which can be implemented in real time mode. The results of illustrative tests are given.     

Anticipating synchronization through optimal feedback control

In this paper, we investigate the anticipating synchronization of a class of coupled chaotic systems through discontinuous feedback control. The stability criteria for the involved error dynamical system are obtained by means of model transformation incorporated with Lyapunov functional and linear matrix inequality. Also, we discuss the optimal designed controller based on the obtained criteria. The numerical simulation is presented to demonstrate the theoretical results.     

Examples of nonclassical feedback control problems

We consider a control system with “nonclassical” dynamics: ? = f(t, x, u, D _x u), where the right hand side depends also on the first order partial derivatives of the feedback control function. Given a probability distribution on the initial data, we seek a feedback u = u(t, x) which minimizes the expected value of a cost functional. Various relaxed formulations of this problem are introduced. In particular, three specific examples are studied, showing the equivalence or non-equivalence of these approximations.     

Sparse Dirichlet optimal control problems

Computational Optimization and Applications - In this paper, we analyze optimal control problems governed by an elliptic partial differential equation, in which the control acts as the Dirichlet...     

Dual formulations of optimal control problems

First-order necessary conditions are obtained for a dual formulation, in terms of a class of direction fields, of an optimal control problem of Hestenes. The control functions do not appear. A maximum principle for a boundary arc of a class of admissible arcs is stated in a similar dual formulation.This research is part of a dissertation submitted in partial satisfaction of the requirements for the Ph.D. degree in mathematics at the University of California at Los Angeles. The author would like to express his appreciation to Dr. M. R. Hestenes for his guidance.     

Proper relaxation of optimal control problems

In a recent paper, we proposed different relaxation procedures for optimal control problems involving time delays in the control functions. We introduced a notion of proper relaxation, applicable to problems without side constraints, where we required the minimum cost of the relaxed problem to coincide with the infimum cost of the original one. In this paper, a new and appropriate notion of relaxation for problems with side constraints is introduced. As examples of proper extensions, in the new sense, we describe in detail the standard procedure for delay-free problems and the procedure for one-delay systems which we recently proposed.     

Reduction of delayed optimal control problems to nondelayed problems

Typographical errors are corrected in Ref. 1.     

Reduction of delayed optimal control problems to nondelayed problems

A method is exhibited which transforms a large class of optimal control problems with fixed delays to nondelayed problems, thus permitting classical results to be used in their analysis.     

Nonlinearly constrained time-delayed optimal control problems

A computational algorithm for solving a class of optimal control problems involving terminal and continuous state constraints of inequality type was developed in Ref. 1. In this paper, we extend the results of Ref. 1 to a more general class of constrained time-delayed optimal control problems, which involves terminal state equality constraints as well as terminal state inequality constraints and continuous state constraints. Two examples have been solved to illustrate the efficiency of the method.     

Differential stability in optimal control problems

This paper deals with optimal control problems subject to differentiable perturbations in the objective function and constraints. The results of [9] are applied to obtain upper and lower bounds for the directional derivative of the extremal value function as well as necessary and sufficient conditions for the existence of the directional derivative. In particular, the results show the close connection between the multipliers of the Minimum Principle and the sensitivity of the optimal value with respect to perturbations.Partially supported by the Deutsche Forschungsgemeinschaft under No. Ma 691/2     

Singular manifolds in optimal control problems

We propose a method of solving an optimal control problem with constraints on the control. The method is applied to find an upper bound of the Hamilton-Pontryagin function and is based on the construction of a system of differential equations containing the constraints available in the problem as singular manifolds. Bibliography: 2 titles. Translated fromProblemy Matematicheskoi Fiziki, 1998, pp. 214–216.     

Averaging in optimal switching control problems

Abstract. The averaging in optimal switching control problems is considered under the following two cases: the switching cost does not depend on e and the switching cost vanishes as e tends to zero. The value function of the original fast problem converges locally uniformly to the value function of the averaged problem under both cases. The ways of averaging turn out to be different between both cases.     

On sensitivity in optimal control problems

Two types of interpretations of multipliers in both static and dynamic optimization problems are described. It is snown that the Lagrange multipliers encountered in mathematical programming problems and the auxiliary functions arising in Pontryagintype optimal control problems sometimes have highly analogous interpretations as rates of change of the optimal attainable value of an objective function, or in some cases as bounds on average rates of change.