Optimal Switching for Hybrid Semilinear Evolutions

We consider the optimization of a dynamical system by switching at discrete time points between abstract evolution equations composed by nonlinearly perturbed strongly continuous semigroups, nonlinear state reset maps at mode transition times and Lagrange-type cost functions including switching costs. In particular, for a fixed sequence of modes, we derive necessary optimality conditions using an adjoint equation based representation for the gradient of the costs with respect to the switching times. For optimization with respect to the mode sequence, we discuss a mode-insertion gradient. The theory unifies and generalizes similar approaches for evolutions governed by ordinary and delay differential equations. More importantly, it also applies to systems governed by semilinear partial differential equations including switching the principle part. Examples from each of these system classes are discussed

The control parametrization enhancing transform for constrained time--delayed optimal control problems

The Control Parametrization Enhancing Technique (CPET), is extended to a general class of constrained time-delayed optimal control problems. A model transformation approach is used to convert the time-delayed problem to an optimal control problem involving mixed boundary conditions, but without time-delayed arguments. The CPET is then used to solve this non delayed problem. Two test examples have been solved to illustrate the efficiencies of the CPET for time delayed problems

Modeling a PV- diesel-battery power system: An optimal control approach

The optimal design and operation of hybrid power systems used in remote area electri-fication are difficult tasks due to a large variety of location specific factors.Several mathematical models have been proposed in literature, aiming to capture the behavior of hybrid power system and optimize its overall operating cost.In this paper, we review an existing optimal control model of a PV-diesel-battery hybrid power system.We then compare the characteristics of the model with several generic computer simulation tools.Finally, we identify the limitations of the model and propose several improvements for future development

Control parametrization enhancing technique for optimal discrete-valued control problems

In this paper, we consider a class of optimal discrete-valued control problems. Since the range set of the control function is a discrete set and hence not convex. These problems are, in fact, nonlinear combinatorial optimization problems. Using the novel idea of the control parametrization enhancing technique, it is shown that optimal discrete-valued control problems are equivalent to optimal control problems involving a new control function which is piecewise constant with pre-fixed switching points. The transformed problems are essentially optimal parameter selection problems and can hence be readily solved by various existing algorithms. A practical numerical example is solved using the proposed method. (C) 1999 Elsevier Science Ltd. All rights reserved