Abstract: A method solves a stochastic quadratic program (StQP) for a convex set with a set of general linear equalities and inequalities by an alternating direction method of multipliers (ADMM). The method determines an optimal solution, or certifies that no solution exists. The method optimizes a step size ? for the ADMM. The method is accelerated using a conjugate gradient (CG) method. The StMPC problem is decomposed into two blocks. The first block corresponds to an equality constrained QP, and the second block corresponds to a projection onto the StMPC inequalities and anticipativity constraints. The StMPC problem can be decomposed into a set of time step problems, and then iterated between the time step problems to solve the decoupled problems until convergence.

Abstract: A method solves a convex quadratic program (QP) for a convex set. Constrains of the QP include sets of linear equalities and linear inequalities. The solving uses an Alternating Direction Method of Multipliers (ADMM). Variables of the convex QP include a linear subspace constrained variable vector and a set constrained variable vector. The method solves the linear subspace constrained variable vector while keeping the set constrained variable vector fixed using an optimal step size and a Lagrangian multiplier, and solves the set of constrained variable vector while keeping linear subspace constrained variable vector fixed using the optimal step size and the Lagrangian multiplier. Then, the Lagrangian multiplier is updated. A feasible solution is outputted if a termination condition for the feasible solution is satisfied, and an infeasible solution is signaled if a termination condition for the satisfied for the infeasible solution is satisfied. Otherwise, the steps are repeated.

Abstract: An operation of a processing machine with redundant actuators is controlled according to a reference trajectory by selecting, from a set of points forming a segment of the reference trajectory to be processed for a period of time, a subset of points corresponding to a fraction of the period of time. The subset of points is selected such that the redundant actuators are capable to position the worktool at each point in the subset within the period of time and are capable to maintain the worktool at the last point of the subset after the period of time while satisfying constraints on motion of the redundant actuators. The segment of the reference trajectory is modified in the time domain and the control inputs for controlling the motion of the redundant actuators are determined using the modified segment of the reference trajectory.

Abstract: A method computes reference signals for a machine with redundant positioning by first generating a reference trajectory according to an ordered list of points. Then, using a filter or by choosing the value of the reference at each sampling time, a reference trajectory for the slow subsystem is produced. Next, determine whether the reference trajectory and the slow subsystem reference trajectory violate feasibility constraints, and if true, slowing down the reference trajectory and repeating with the generation of the slow subsystem reference trajectory. The slow subsystem reference trajectory is sent, via a model predictive control block, to a slow positioning subsystem controller, and a combination of the slow subsystem reference trajectory and the reference trajectory is sent to a fast positioning subsystem controller.

Abstract: A method controls an operation of a spacecraft according to a model of the spacecraft. The method determines control inputs for controlling concurrently thrusters of the spacecraft and momentum exchange devices of the spacecraft using an optimization of a cost function over a receding horizon subject to constraints on a pose of the spacecraft and constraints on inputs to the thrusters. The cost function includes components for controlling the pose of the spacecraft and a momentum stored by the momentum exchange devices. The method generates a command to control concurrently the thrusters and the momentum exchange devices according to at least a portion of the control inputs.

Abstract: A method for controlling an operation of a vapor compression system (VCS) determines values of measured outputs of the operation of the VCS that include performance and constrained outputs. The method determines states of the VCS using an estimator model of the VCS defining a relationship between the states of the VCS, control inputs and controlled outputs, such that a difference between outputs predicted using the estimator model and the measured outputs asymptotically approaches zero. The states of the VCS include a main state representing the operation of the VCS and an auxiliary state representing the effect of unknown disturbances on each measured output of the VCS. The control inputs for controlling the operation of the VCS are determined using a prediction model, such that the constrained output satisfies the constraints, and a difference between the performance output and the value of the setpoint asymptotically approaches zero.

Abstract: A method controls an operation of a machine using a model predictive control (MPC). The method determine, in response to receiving a state of the operation of the machine, a dual solution of a dual parametric problem of a parametric form of the MPC using a parallel quadratic programming (PQP) rescaling iteratively a candidate dual solution of the dual parametric problem. The coefficients of the dual parametric problem include data representing dynamics of the machine and constraints on the operation of the machine. A parameter of the dual parametric problem includes the state of the operation of the machine. The method determines a primal solution of a primal problem of the MPC using the dual solution of the dual parametric problem.

Abstract: A method controls a motion of a vehicle using a model of the motion of the vehicle that includes an uncertainty. The method samples a control space of possible control inputs to the model of the motion of the vehicle to produce a set of sampled control inputs and determines a probability of each sampled control input to move the vehicle into state satisfying constraints on the motion of the vehicle. The method determines, using the probabilities of the sampled control inputs, a control input having the probability to move the vehicle in the state above a threshold. The control input is mapped to a control command to at least one actuator of the vehicle to control the motion of the vehicle.

Abstract: A multi-zone vapor compression system (MZ-VCS) includes a compressor connected to a set of heat exchangers controlling environments in a set of zones, a supervisory controller determining a set of control inputs for controlling a vapor compression cycle of the MZ-VCS, and a set of capacity controllers. The supervisory controller is a model predictive controller (MPC) determining the set of control inputs using a model of the MZ-VCS including a linear relationship between thermal capacities of each heat exchanger and temperatures in a corresponding zone controlled by the heat exchanger. Each capacity controller enforces the linear relationship between the thermal capacity and the temperature in the corresponding zone.

Abstract: A method for controlling a semi-autonomous vehicle modifies a current path for the vehicle desired by a driver of the vehicle. The current path starts at a current position of the vehicle and ends in a target position of the vehicle and the method modifies the current path while preserving the current position and the target position of the vehicle in the modified path. The method overrides the actions of the driver to control a movement of the vehicle according to the modified path.

Abstract: An operation of the machine is iteratively controlled with control inputs determined from an optimization of a cost function along a prediction horizon subject to constraints on the control inputs. The optimization is performed according to the model and the cost function includes at least one parameter of the model. During at least some iterations of the control, the parameter of the model is updated resulting in updating the cost function.

Abstract: A method for stopping a train at a range of predetermined positions, first acquires a measured state of the trains, and then updates, in a parameter estimator, estimates of unknown parameters and a reliability of the unknown parameters, based on a comparison of a predicted state of the train with the measured state of the train. An excitation input sequence reference generator acquires dynamics of the train to determine a sequence of excitation inputs based on a current estimate of system parameters, the measured state of the train, and a set of constraints on an operation of the train. A model predictive controller (MPC) receives a control-oriented cost function, a set of constraints, the sequence of excitation inputs, the estimate of the unknown parameters and the reliability of the estimate of the unknown parameters to determine an input command for a traction-brake actuator of the train.

Abstract: A method of controlling a line pressure in a transmission is provided. Line pressure in a transmission is set to a pressure value including a first term that is proportional to an input torque value. The first term has a coefficient of proportionality that is increased in response to a signal indicating clutch slippage. The input torque value is a measured input torque value in a steady-state condition. The input torque value may be a maximum of the measured input torque value and a driver demand torque value in a transient condition.

Abstract: An operation of a processing machine with redundant actuators is controlled according to a reference trajectory by selecting, from a set of points forming a segment of the reference trajectory to be processed for a period of time, a subset of points corresponding to a fraction of the period of time. The subset of points is selected such that the redundant actuators are capable to position the worktool at each point in the subset within the period of time and are capable to maintain the worktool at the last point of the subset after the period of time while satisfying constraints on motion of the redundant actuators. The segment of the reference trajectory is modified in the time domain and the control inputs for controlling the motion of the redundant actuators are determined using the modified segment of the reference trajectory.

Abstract: A method controls a movement of a train to a stop at a stopping position between a first position and a second position. The method determines constraints of a velocity of the train with respect to a position of the train forming a feasible area for a state of the train during the movement, such that an upper curve bounding the feasible area has a zero velocity only at the second position, and a lower curve bounding the feasible region has a zero velocity only at the first position. Next, the method controls the movement of the train subject to the constraints.

Abstract: A controller for controlling a system includes a non-transitory computer-readable memory storing data for an operation and a control of the system and at least one processor operatively connected to the memory for determining a control signal transitioning a state of the system from a current state to a next state. At least two instances of the data are stored in the memory with different precisions defined by numbers of bits storing the instance in the memory. The processor determines the control signal using the instances of the data with the different precisions.

Abstract: A method for controlling an operation of a machine according to a model of the machine having uncertainties determines a set of triples of data points representing the operation of the machine over a period of time. Each triple of data points in the set includes two subsequent states of the machine and corresponding control input causing a transition of the machine between the subsequent states. Next, the method determines a current model of the machine based on the set of triples of data points, such that the current model is within a feasible space of models of the machine corresponding to a polytope with vertices defined by base models representing extreme values of different parameters of the model.

Abstract: A method for stopping a train at a range of predetermined positions, first acquires a measured state of the trains, and then updates, in a parameter estimator, estimates of unknown parameters and a reliability of the unknown parameters, based on a comparison of a predicted state of the train with the measured state of the train. An excitation input sequence reference generator acquires dynamics of the train to determine a sequence of excitation inputs based on a current estimate of system parameters, the measured state of the train, and a set of constraints on an operation of the train. A model predictive controller (MPC) receives a control-oriented cost function, a set of constraints, the sequence of excitation inputs, the estimate of the unknown parameters and the reliability of the estimate of the unknown parameters to determine an input command for a traction-brake actuator of the train.

Abstract: A method controls a movement of a train to a stop at a stopping position between a first position and a second position. The method determines constraints of a velocity of the train with respect to a position of the train forming a feasible area for a state of the train during the movement, such that an upper curve bounding the feasible area has a zero velocity only at the second position, and a lower curve bounding the feasible region has a zero velocity only at the first position. Next, the method controls the movement of the train subject to the constraints.

Abstract: A method controls an operation of a spacecraft according to a model of the spacecraft. The method determines control inputs for controlling concurrently thrusters of the spacecraft and momentum exchange devices of the spacecraft using an optimization of a cost function over a receding horizon subject to constraints on a pose of the spacecraft and constraints on inputs to the thrusters. The cost function includes components for controlling the pose of the spacecraft and a momentum stored by the momentum exchange devices. The method generates a command to control concurrently the thrusters and the momentum exchange devices according to at least a portion of the control inputs.