Approach to the Solution of the Optimum Control Problem of the Water Supply System

This paper considers the problem of optimal control of branched water supply systems. To control the system, the problem of optimal distribution of products is delivered whereas non-linear programming problems are applied. We consider a system for providing products, consisting of magistral and distribution pipelines, taking products from the magistral pipeline. Each distribution line has many warehouses. Products are taken into the system using the main intake facility and transferred between the warehouses using intermediate distribution facilities. To eliminate the deficiencies in management, tasks are set to determine the necessary intensities of product supply in the facilities, allowing timely provision of consumers with the necessary volume of products, to minimize losses, product discharges of facilities in the system during a certain control period.

A Problem With the LQ Control of Overhead Cranes

The control of an overhead crane is a classic optimum control problem, and its solution can be found in most textbooks on the subject of automatic controls. However, there is a design issue with respect to the relative mass of the cart and the suspended payload. If this problem is ignored, then the results of an analysis can be misleading and the response can be unstable. Based on a stability analysis, a design recommendation for optimal asymptotic linear quadratic (LQ) controllers with fixed gains is presented to avoid this problem. The results are validated by both simulation and experiment.

A small parameter method to improve optimum control via the linearization technique

SUMMARYA method that has been proposed for the design of a control system of a muti-link arm is the optimum approach applied to the system linearized around its nominal trajectory, i.e. the dynamic trajectory that the manipulator should follow. This method works, in as much as the initial deviation from the reference trajectory is small enough. When such is not the case, it is necessary to take into account the quadratic term in the approximation, and the paper proposes a small parameter technique to solve the corresponding optimum control problem which otherwise involves cumbersome calculations.

Coordination Concepts in Multilevel Hierarchical Differential Games

This paper presents possible extensions of the usual differential game theory to the case where the players, say the supremal players do not completely govern the plant, but control it only via infimal players who have their own pay-off functions. One assumes that the internal structure of the game is given in the sense that the supremal players cannot define arbitrary decompositions for the system. One further assumes that these supremal players have given programming terminal objectives which they desire to attain. In this framework, the supremal players can only select suitable functions, which are the coordination controls, to coordinate the system for the best. It follows that the problem so defined is simultaneously an optimum control problem and a programming one. The direct coordination mode, the open-loop indirect coordination mode and the closed-loop indirect coordination mode are defined and are mainly based upon a direct reference to the overall system, together with a two-level optimization process. The explicit equations are given in the important case where the comparison criterion is defined in the form of an Euclidean norm, and an illustrative example is solved. This approach would be interesting to apply to the problem of learning and self-learning in optimum control systems for instance, via gradient techniques.