Abstract: A method reduces the computational complexity for determining optimal run-curves for a specific travel time of a vehicle along a route between two locations, when travel time and speed limit requirements are subject to change. The determination is partitioned into preprocessing and real-time steps. A set of weights are generated, and run-curves for the weights are obtained and stored during the preprocessing. A state transition matrix is generated in the preprocessing step and updated partially in the real-time step only for a subspace of velocities and locations constrained by speed limits. The optimal weight for solving an objective function to obtain an optimal run-curve can be obtained by searching with an initial estimation of multiple weights, and interpolating from the relation between the travel time and the initial weights to obtain the optimal weight.

Abstract: A method reduces the computational complexity for determining optimal run-curves for a specific travel time Iola vehicle along a route between two locations, when travel time and speed limit requirements are subject to change. The determination is partitioned into preprocessing and real-time steps. A set of weights are generated, and run-curves for the weights are obtained and stored during the preprocessingA state transition matrix is generated in the preprocessing step and updated partially in the real-time step only for a subspace of velocities and locations constrained by speed limits. The optimal weight for solving an objective function to obtain an optimal run-curve can be obtained by searching with an initial estimation of multiple weights, and interpolating from the relation between the travel time and the initial weights to obtain the optimal weight.

Abstract: A method reduces the computation time for determining optimal run-curves for a specific travel time of a vehicle along a route between two locations. The computation is partitioned between pre-processing and real-time steps. A set of weights ? are generated, and run-curves for the weights are obtained and stored during the pre-processing. State transition matrices can also be determined and stored during the pre-processing. During real-time, a specific travel time is obtained. The travel time is used to interpolate the weight ? for the specific travel time from the stored weights. The memory can be updated for each solution for a specific travel time to dramatically reduce the time to optimize the run-curves.

Abstract: A method determines a run-curve of a motion of a vehicle as a function of at least a speed of the vehicle and a position of the vehicle in a continuous space. First, the method determines Markov decision process (MDP) with respect to a set of anchor states selected from the continuous space, such that a control moving the vehicle to a state transitions the MDP to an anchor state with a probability determined as a function of a distance between the anchor state and the state in the continuous space, and solves the MDP subject to constraints to determine an MDP policy optimizing a cost function representing a cost of the motion of the vehicle. Next, the method determines the run-curve based on the MDP policy.

Abstract: A method controls a heating, ventilation, air conditioning (HVAC) system by determining a travel time from a mobile site to a fixed site, and determining a conditioning time for a HVAC system at the fixed site. The HVAC is maintained in an ON state if the travel time is less than the conditioning time, and otherwise maintaining the HVAC in an OFF state, and wherein the conditioning time is determined using a building thermal model.

Abstract: An optimal conditional operational schedule for a set of power generators is determined by constructing states and transitions of a factored Markov decision process (fMDP) from a target electrical demand and generator variables. A cost function for the fMDP is constructed based on the electrical demand, the generator variables, and a risk coefficient. Then, the fMDP is solved to obtain the optimal conditional operational schedule.

Abstract: A method controls a heating, ventilation, air conditioning (HVAC) system by determining a travel time from a mobile site to a fixed site, and determining a conditioning time for a HVAC system at the fixed site. The HVAC is maintained in an ON state if the travel time is less than the conditioning time, and otherwise maintaining the HVAC in an OFF state, and wherein the conditioning time is determined using a building thermal model.

Abstract: A gray-box model of a system is constructed by specifying constraints for the system and applying subspace system identification to inputs and outputs of the system to determine system matrices and system state sequences for the system. A transformation matrix that satisfy the constraints from the system matrices and the system state sequences is determined, wherein the transformation matrix defines parameters of the gray-box model.

Abstract: A method and system recommend a product to a consumer. A purchasing history of a consumer is represented by an adjacency lattice stored in a memory. Training examples are extracted from the adjacency lattice, and a decision tree is constructed using the training examples. A size of the decision tree is reduced, and the reduced size decision tree is searched for a recommendation of a product to the consumer.

Abstract: A method schedules cars of an elevator system, the elevator system including a set of cars, and a set of hall calls. For each car, a waiting time is determined independently if the hall call is the only hall call assigned to the car. For each car, a mutual delay ?W(h|g) is determined for each possible pair of unassigned hall calls h and assigned hall calls g. The waiting time and mutual delays are summed. Then, the assignments are made to the set of cars so that the sum is a minimum.

Abstract: A method schedules cars of an elevator system. Each possible assignment of a set of hall calls to a set of cars is represented by a solution vector maintained as a node in a search tree. Each solution vector is evaluated using an ESA-DP process according to an immediate policy to determine initially a best solution. A branch-and-bound process is applied to each solution vector using the initial best solution and the search tree to determine a globally optimal solution for scheduling the cars according to a reassignment policy.

Abstract: A marketing system and method for a retail environment periodically reads RFID tags attached to products to produce a list of product identifications. Consumer recommendation rules are updated according to each list, and recommendations are generated according to the updated consumer recommendation rules. Then, content can be displayed in the retail environment based on the recommendations.