Kok Lay Teo

Control parametrization: a unified approach to optimal control problems with general constraints

Abstract In this paper, we consider a class of optimal control problems with general constraints. The aim is to provide a unified approach to the numerical solution of this general class of optimal control problems by using the control parametrization technique, where different types of constraints are shown to be equivalent to essentially the same functional form as the cost functional. Some convergence properties of this proposed method are also investigated.

Guidance Laws with Finite Time Convergence

Conventional guidance laws are designed based on Lyapunov theorems on asymptotic stability or exponential stability. They will guide the line-of-sight angular rate to converge to zero or its small neighborhood, however, only as time approaches infinity. In this paper, new guidance laws with finite convergent time are proposed. The guidance laws are obtained based on new sufficient conditions derived in this paper for the finite time convergence of the line-of-sight angular rate. It is proved that, with the guidance laws, the line-of-sight angular rate will converge to zero or a small neighborhood of zero before the final time of the guidance process. Furthermore, such guidance laws will ensure finite time convergence and finite time stability in both the planar and three-dimensional environments. Simulation results show that the guidance laws are highly effective.

A new computational algorithm for functional inequality constrained optimization problems

Abstract In this note, a computational algorithm is devised for solving a class of functional inequality constrained optimization problems, based on a penalty function. For illustration, a numerical example is solved.

Optimal control of drug administration in cancer chemotherapy

Basic concepts optimal control - theory and applications multiple characteristic time (MCT) constraints minimize the final tumour size parameter uncertainty forced decrease of tumour size drug resistance I drug resistance II summary and conclusions list of notation and symbols appendix: elements of mathematical analysis.

Kalman filtering for multiple time-delay systems

This paper is to study the linear minimum variance estimation for discrete-time systems with instantaneous and l-time delayed measurements by using re-organized innovation analysis. A simple approach to the problem is presented in this paper. It is shown that the derived estimator involves solving l+1 different standard Kalman filtering with the same dimension as the original system.

THE CONTROL PARAMETERIZATION ENHANCING TRANSFORM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS

Consider a general class of constrained optimal control problems in canonical form. Using the classical control parameterization technique, the time (planning) horizon is partitioned into several subintervals. The control functions are approximated by piecewise constant or piecewise linear functions with pre-fixed switching times. However, if the optimal control functions to be obtained are piecewise continuous, the accuracy of this approximation process greatly depends on how fine the partition is. On the other hand, the performance of any optimization algorithm used is limited by the number of decision variables of the problem. Thus, the time horizon cannot be partitioned into arbitrarily many subintervals to reach the desired accuracy. To overcome this difficulty, the switching points should also be taken as decision variables. This is the main motivation of the paper. A novel transform, to be referred to as the control parameterization enhancing transform, is introduced to convert approximate optimal control problems with variable switching times into equivalent standard optimal control problems involving piecewise constant or piecewise linear control functions with pre-fixed switching times. The transformed problems are essentially optimal parameter selection problems and hence are solvable by various existing algorithms. For illustration, two non-trivial numerical examples are solved using the proposed method.

Exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays

This paper considers the problems of global exponential stability and exponential convergence rate for impulsive high-order Hopfield-type neural networks with time-varying delays. By using the method of Lyapunov functions, some sufficient conditions for ensuring global exponential stability of these networks are derived, and the estimated exponential convergence rate is also obtained. As an illustration, an numerical example is worked out using the results obtained.

Brief paper: Optimal control problems with a continuous inequality constraint on the state and the control

We consider an optimal control problem with a nonlinear continuous inequality constraint. Both the state and the control are allowed to appear explicitly in this constraint. By discretizing the control space and applying a novel transformation, a corresponding class of semi-infinite programming problems is derived. A solution of each problem in this class furnishes a suboptimal control for the original problem. Furthermore, we show that such a solution can be computed efficiently using a penalty function method. On the basis of these two ideas, an algorithm that computes a sequence of suboptimal controls for the original problem is proposed. Our main result shows that the cost of these suboptimal controls converges to the minimum cost. For illustration, an example problem is solved.

Optimal insulin infusion resulting from a mathematical model of blood glucose dynamics

The application of mathematical optimization techniques to a simplified mathematical model of blood glucose dynamics to derive insulin infusion programs for the control of blood glucose levels in diabetic individuals is discussed. Two particular cases are discussed: first, that of the insulin infusion program which results in an initially high blood glucose level being reduced to acceptable levels; secondly, that of the control of blood glucose levels following a meal, prior to which blood glucose and net blood-glycemic hormone were at their fasting levels.<<ETX>>

Solution semicontinuity of parametric generalized vector equilibrium problems

In this paper, the lower semicontinuity and continuity of the solution mapping to a parametric generalized vector equilibrium problem involving set-valued mappings are established by using a new proof method which is different from the ones used in the literature.