Abstract-In this paper, we study the problem of optimal balancing of traffic density distributions. The optimization is carried out over the sets of equilibrium points for the Cell Transmission Traffic Model. The goal is to find the optimal balanced density distribution that maximizes the Total Travel Distance. The optimization is executed in two steps. At the first step, we consider a nonlinear problem to find a uniform density distribution that maximizes the Total Travel Distance. The second step is to solve the constrained quadratic problem to find the near balanced optimal equilibrium point. At both steps, we use decomposition methods. The quadratic optimization problem is solved by using the Dual Problem. The computational algorithms associated to such a problem are given.
In this paper, we study the problem of optimal balancing of vehicle density in the freeway traffic. The optimization is performed in a distributed manner by utilizing the controllability properties of the freeway network represented by the Cell Transmission Model. By using these properties, we identify the subsystems to be controlled by local ramp meters. The optimization problem is then formulated as a noncooperative Nash game that is solved by decomposing it into a set of two-players hierarchical and competitive games. The process of optimization employs the communication channels matching the switching structure of system interconnectivity. By defining the internal model for the boundary flows, local optimal control problems are efficiently solved by utilizing the method of Linear Quadratic Regulator. The developed control strategy is tested via numerical simulations in two scenarios for uniformly congested and transient traffic.
This paper presents a new method for the semi-active control of the span system of linear guideways subjected to a travelling load. Two elastic beams are coupled by a set of controlled dampers. The relative velocity of the spans provides an opportunity for efficient control via semi-active suspension. The magnitude of the moving force is assumed to be constant by neglecting inertial forces. The response of the system is solved in modal space. The full analytical solution is based on the power series method and can be given over an arbitrary time interval. The control strategy is formulated by using bilinear optimal control theory. As a result, bang-bang controls are taken into account. The final solution is obtained as a numerical mean value. Several examples demonstrate the efficiency of the proposed method. The controlled system outperforms passive solutions over a wide range. Due to the simplicity of its design, the presented solution should be interesting to engineers.
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