Abstract: The present disclosure discloses a system and a method for controlling an operation of a machine according to a task. The method comprises formulating an original quadratic program (QP) for optimizing an objective function subject to equality constraints and inequality constraints, lifting the equality constraints and the inequality constraints into a lifted space by a lifting operation introducing an additional non-negative variable, and transforming the objective function of the original QP into a quadratic objective function. The quadratic objective function subject to the lifted equality and inequality constraints forms a homogeneous QP in the lifted space. The method further comprises solving the homogeneous QP to produce a solution in the lifted space and controlling the machine according to an infeasibility protocol when a value of the additional non-negative variable in the solution in the lifted space equals zero.

Abstract: A controller for controlling an operation of a robot to execute a task is provided. The controller comprises a memory configured to store a set of dynamic movement primitives (DMPs) associated with the task. The set of DMPs comprise a set of at least two dynamical systems: a function representing point attractor dynamics and a forcing function corresponding to a learned demonstration of the task. The controller comprises a processor configured to transform the set of DMPs to a set of constrained DMPs (CDMPs) by determining a perturbation function associated with the forcing function. The perturbation function is associated with a set of operational constraints. The processor is further configured to solve, a non-linear optimization problem for the set of CDMPs based on the set of operational constraints and generate, a control input for controlling the robot for executing the task, based on the solution.

Abstract: A controller controls a motion of an object performing a task for changing a state of the object from a start state to an end state while avoiding collision of the object with an obstacle according to an optimal trajectory determined by solving an optimization problem of the dynamics of the object producing an optimal trajectory for performing the task subject to constraints on a solution of first-order stationary conditions modeling a minimum distance between the convex hull of the object and the convex hull of the obstacle using complementarity constraints.

Abstract: A device for controlling an operation of a system performing a task determines a current control input based on the feedback signal by solving a polynomial optimization of a polynomial function with a reformulation derived by introducing additional variables reducing the degree of the polynomial function till a target degree subject to constraints on a structure of the additional variables. The device solves a mixed-integer optimization problem to find a subset of encodings among all possible encodings of factorizations of the polynomial function that reduce the degree of the polynomial function to the target degree with a predetermined minimum number of additional variables and selects an optimal encoding from the subset of encodings with an optimal relaxation bound.

Abstract: A device for controlling an operation of a system performing a task is disclosed. The device submits a sequence of control inputs to the system thereby changing states of the system according to the task and receives a feedback signal. The device determines a current control input for controlling the system based on the feedback signal including a current measurement of a current state of the system by solving a polynomial optimization of a polynomial function with a reformulation derived by introducing additional variables reducing a degree of the polynomial function till a target degree subject to constraints on a structure of the additional variables. The device solves a mixed-integer optimization problem to find an optimal solution among all possible encodings of factorizations of the polynomial function that reduces the degree of the polynomial function till the target degree with a minimum number of additional variables.

Abstract: A manipulation controller is provided for reorienting an object by a manipulator of a robotic system. The manipulation controller includes an interface controller configured to acquire measurement data from sensors arranged on the robotic system, at least one processor, and a memory configured to store a computer-implemented method.

Abstract: A robotic system for manipulating an object with a robotic manipulator is provided. The robotic system is configured to collect a digital representation of a task for manipulating the object; solve a robust control problem to optimize a sequence of control forces to be applied by the robotic manipulator to change a state of the object, where an evolution of the state of the object is governed by a stochastic complementarity system modeling the task with a predefined probability. The robust control problem optimizes a cost function to generate the sequence of control forces performing the task subject to joint chance constraints including a first chance constraint on the state of the object being manipulated and a second chance constraint on stochastic complementarily constraints modeling manipulation of the object. The robotic system is further configured to control the manipulation of the object based on the sequence of control forces.

Abstract: A system for designing a circuitry configuration of heat-exchanger units includes an interface to acquire design parameters the heat-exchanger units, a memory to store computer-executable programs including a relaxed decision diagram formation module, and a processor, in connection with the memory, configured to perform the computer-executable programs. The computer-executable programs include steps of providing a configuration of the heat-exchanger units, providing the design parameters of the heat-exchanger units acquired via the interface, generating a relaxed decision diagram based on the design parameters, creating constraints with respect to connections of the heat-exchanger units according to the relaxed decision diagram, and generating feasible configurations of the heat-exchanger units by a mixed-integer-programing method using the constraints.

Abstract: A computer-implemented learning method for optimizing a control policy controlling a system is provided. The method includes receiving states of the system being operated for a specific task, initializing the control policy as a function approximator including neural networks, collecting state transition and reward data using a current control policy, estimating an advantage function and a state visitation frequency based on the current control policy, updating the current control policy using the second-order approximation of the objective function, a second-order approximation of the KL-divergence constraint on the permissible change in the policy using a quasi-newton trust region policy optimization, and determining an optimal control policy, for controlling the system, based on the average reward accumulated using the updated current control policy.

Abstract: A train trip controller system is provided. The train trip controller system may collect operational data for the train, the operational data comprising at least: an itinerary information for a trip the train, constraints on capacity of the train and on ratio between number of passenger cars and number of seats in a particular type of passenger car for different types of passenger cars, an operational cost factor for adding and removing passenger cars, sales horizon condition, and a congestion factor. Based on the operational data, the train trip controller system is configured to determine an upper bound of a stochastic cost function, using a mean of arrival rate of passengers over the sales horizon condition, for each of a different type passenger car. The computation of the upper bound is then used to determine a ticket price and capacity to be used for the train. The determined ticket price and capacity are in turn used to achieve an optimization objective for the train trip controller system.

Abstract: A device for controlling an operation of a system performing a task is disclosed. The device submits a sequence of control inputs to the system thereby changing states of the system according to the task and receives a feedback signal. The device determines a current control input for controlling the system based on the feedback signal including a current measurement of a current state of the system by solving a polynomial optimization of a polynomial function with a reformulation derived by introducing additional variables reducing a degree of the polynomial function till a target degree subject to constraints on a structure of the additional variables. The device solves a mixed-integer optimization problem to find an optimal solution among all possible encodings of factorizations of the polynomial function that reduces the degree of the polynomial function till the target degree with a minimum number of additional variables.

Abstract: A controller controls a motion of an object performing a task for changing a state of the object from a start state to an end state while avoiding collision of the object with an obstacle according to an optimal trajectory determined by solving an optimization problem of the dynamics of the object producing an optimal trajectory for performing the task subject to constraints on a solution of first-order stationary conditions modeling a minimum distance between the convex hull of the object and the convex hull of the obstacle using complementarity constraints.

Abstract: Systems and methods for scheduling early riders (ERs) and late riders (LRs) to vehicles in a multi-modal transportation network (MTN). Stored instructions, when executed, cause a processor to perform acts of forecasting a finite set of scenarios, each scenario having a possible set of forecast LRs (FLRs) itinerary requests. Iteratively, generate ER groups and FLR groups for each scenario, based on a desired time of arrival at a destination. Assign a commuter vehicle (CV) for each ER and FLR group in each scenario. Iteratively, determine for each ER and FLR group a start time and an arrival time at the destination in the corresponding CV, for which, the ER and FLR group are assigned. The iterations continue until a joint schedule for the ERs and the FLRs form each scenario that minimizes an objective function. Formulate assignment information, and transmit the assignment information to the ERs and the assigned CVs.

Abstract: A controller for optimizing a local control policy of a system for trajectory-centric reinforcement learning is provided. The controller includes performing steps of learning a stochastic predictive model for the system using a set of data collected during trial and error experiments performed using an initial random control policy, estimating mean prediction and uncertainty associated, determining a local set of deviations of the system using the learned stochastic system model, from a nominal system state upon use of a control input at a current time-step, determining a system state with a worst-case deviation, determining a gradient of the robustness constraint, providing and solving a robust policy optimization problem using non-linear programming to obtain system trajectory and stabilizing local policy simultaneously, updating the control data according to the solved optimization problem, and output the updated control data via the interface.

Abstract: A computer-implemented learning method for optimizing a control policy controlling a system is provided. The method includes receiving states of the system being operated for a specific task, initializing the control policy as a function approximator including neural networks, collecting state transition and reward data using a current control policy, estimating an advantage function and a state visitation frequency based on the current control policy, updating the current control policy using the second-order approximation of the objective function, a second-order approximation of the KL-divergence constraint on the permissible change in the policy using a quasi-newton trust region policy optimization, and determining an optimal control policy, for controlling the system, based on the average reward accumulated using the updated current control policy.

Abstract: A power generation planning system for controlling on/off sequence of generators according to operational parameters includes an interface to receive the operational parameters including a power demand, state-data of the generators and operational histories of the generators from a power control system, a memory to store an objective function, a mixed-integer programming solver, generator parameters of each the generators and planning modules including a state-space representation module, a variable assignment module, a network flow module and a tight constraint module, a processor to perform the planning modules based on the operational parameters received by the interface.

Abstract: System and methods for controlling a movement of elevator cars of an elevator system. Determine, for each elevator car, an individual waiting time of accommodating each hall call. Determine, for each pair of hall calls assigned to each elevator car, a pairwise delay over the individual waiting time of each hall call in the pair caused by a joint assignment of the elevator car to accommodate the pair of the hall calls. Approximate a cumulative waiting time of an assignment of the elevator cars. Determine the assignment of the elevator cars using a branch and bound algorithm using spectral relaxations based on a generalized eigenvalue and spectral branching that assigns the plurality of hall calls to the elevator cars to minimize the approximated cumulative waiting time. Use a controller for controlling the movement of the elevator cars according to the assignment.

Abstract: A power generation planning system for controlling on/off sequence of generators according to operational parameters includes an interface to receive the operational parameters including a power demand, state-data of the generators and operational histories of the generators from a power control system, a memory to store an objective function, a mixed-integer programming solver, generator parameters of each the generators and planning modules including a state-space representation module, a variable assignment module, a network flow module and a tight constraint module, a processor to perform the planning modules based on the operational parameters received by the interface.

Abstract: A system for designing a circuitry configuration of heat-exchanger units includes an interface to acquire design parameters the heat-exchanger units, a memory to store computer-executable programs including a relaxed decision diagram formation module, and a processor, in connection with the memory, configured to perform the computer-executable programs. The computer-executable programs include steps of providing a configuration of the heat-exchanger units, providing the design parameters of the heat-exchanger units acquired via the interface, generating a relaxed decision diagram based on the design parameters, creating constraints with respect to connections of the heat-exchanger units according to the relaxed decision diagram, and generating feasible configurations of the heat-exchanger units by a mixed-integer-programing method using the constraints.

Abstract: Systems and methods for scheduling early riders (ERs) and late riders (LRs) to vehicles in a multi-modal transportation network (MTN). Stored instructions, when executed, cause a processor to perform acts of forecasting a finite set of scenarios, each scenario having a possible set of forecast LRs (FLRs) itinerary requests. Iteratively, generate ER groups and FLR groups for each scenario, based on a desired time of arrival at a destination. Assign a commuter vehicle (CV) for each ER and FLR group in each scenario. Iteratively, determine for each ER and FLR group a start time and an arrival time at the destination in the corresponding CV, for which, the ER and FLR group are assigned. The iterations continue until a joint schedule for the ERs and the FLRs form each scenario that minimizes an objective function. Formulate assignment information, and transmit the assignment information to the ERs and the assigned CVs.