The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
We consider an optimal control problem described by ordinary differential equations, with control and state constraints. The state equation is first discretized by a general explicit Runge-Kutta scheme and the controls are approximated by piecewise polynomial functions. We then propose approximate gradient and gradient projection methods, and their penalized versions, that construct sequences of discrete...
A nonlinear anaerobic digester model of wastewater treatment plants is considered. The stabilizability of the dynamic system is studied and a continuous stabilizing feedback, depending only on an on-line measurable variable, is proposed. Computer simulations are carried out in Maple to illustrate the theoretical results.
We investigate approximation in W1,2 topology of the solution set of a differential inclusion with Kamke Lipschitz right-hand side. The results are then applied to Bolza optimal control problem in form of differential inclusions. Namely it is shown that the optimal solution is the limit of optimal solution of appropriately defined finite dimensional nonlinear programming problems.
The properties of set-valued solutions (trajectory tubes) for measure driven (impulsive) differential control systems are considered. Numerical simulation results related to the procedures of set-valued approximations of trajectory tubes of linear impulsive systems are also given.
We study the limit behavior of reachable sets for time-invariant linear control systems under two types of the control bounds: the geometric bounds, and the bound for the total impulse. Our main results consist in the description of the arising (as time tends to ∞) attractors in the space of shapes of the reachable sets, shape being the totality of sets obtained from a fixed one by an invertible...
Starting from states near to a closed set S we want to steer S and to stay always close to S. Unfortunately, open-loop controls are very sensitive to disturbances and can lead to very bad practical results. For that reason, we propose an approach for constructing a discontinuous feedback control law that asymptotically stabilizes the system in a neighborhood of the set S.
In this paper, we investigate the existence of controls which allow to reach a given target through trajectories of a nonlinear control system in the case of a non exactly known initial state. For doing this, we use the key concept of weakly invariant tubes and we give a new compactness property for weakly invariant tubes with values in a prescribed collection of sets. We give some consequences of...
An overview of numerical methods for solving optimal control problems described by ODE and integral equations is presented. We consider direct and indirect methods. The finer indirect methods use necessary optimality conditions. Direct methods transform the control problem after discretization to an optimization problem. The nonlinear optimization problem can be solved by means of SQP–methods or gradient...
The paper presents a class of time-discretization schemes for terminal optimal control problems for linear systems. An error estimate is obtained for the optimal control and for the optimal performance, although the optimal control is typically discontinuous, and neither Lipschitz nor structurally stable with respect to perturbations.
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.