Abstract: A predictive controller controls a system under uncertainty subject to constraints on state and control variables of the system. At each control step, the predictive controller solves an inequality constrained nonlinear dynamic optimization problem including probabilistic chance constraints representing the uncertainty to produce a control command, and controls an operation of the system using the control command. The predictive controller solves the dynamic optimization problem based on a two-level optimization that alternates, until a termination condition is met, propagation of covariance matrices of the probabilistic chance constraints within the prediction horizon for fixed values of the state and control variables with optimization of the state and control variables within the prediction horizon for fixed values of the covariance matrices.

Abstract: A system is controlled by solving a mixed-integer optimal control optimization problem using branch-and-bound (B&B) optimization that searches for a global optimal solution within a search space. The B&B optimization iteratively partitions the search space into a nested tree of regions, and prunes at least one region from the nested tree of regions before finding a local optimal solution for each region when a dual objective value of a projection of a sub-optimal dual solution estimate for each region into a dual feasible space is greater than an upper bound or lesser than a lower bound of the global optimal solution maintained by the B&B optimization.

Abstract: A system control a vehicle using a friction function describing a friction between a type of surface of the road and a tire of the vehicle as a function of a slip of a wheel of the vehicle. The parameters of each friction function include an initial slope of the friction function defining a stiffness of the tire and one or combination of a peak friction, a shape factor and a curvature factor of the friction function. Upon estimating a slip and a stiffness of the tire, the system selects from the memory parameters of the friction function corresponding to the current stiffness of the tire, determines a control command using a value of the friction corresponding to the slip of the tire according to the friction function defined by the selected parameters, and submits the control command to an actuator of the vehicle.

Abstract: A predictive controller controls a system under uncertainty subject to constraints on state and control variables of the system. At each control step, the predictive controller solves an inequality constrained nonlinear dynamic optimization problem including probabilistic chance constraints representing the uncertainty to produce a control command, and controls an operation of the system using the control command. The predictive controller solves the dynamic optimization problem based on a two-level optimization that alternates, until a termination condition is met, propagation of covariance matrices of the probabilistic chance constraints within the prediction horizon for fixed values of the state and control variables with optimization of the state and control variables within the prediction horizon for fixed values of the covariance matrices.

Abstract: Methods and systems including processor configured to receive a transition indication to switch a semi-autonomous vehicle from a driving mode to another driving mode while a driver is driving the vehicle on a roadway. Wherein the driving modes include an autonomous lane keeping mode, an autonomous lane change mode and a manual mode. In response to receiving the request, use protocol data to assess a status of the vehicle's environment, a vehicle state and systems of the vehicle. Select, a set of conditions corresponding to the vehicle's state, based on one or more of the assessments. Determine, whether a switch between driving modes is initiated by the driver, by verifying if the vehicle's state satisfies the set of conditions, in order to validate if the driver actuated the vehicle into or out of a safety region.

Abstract: A control system for controlling an operation of a machine subject to constraints including equality and inequality constraints on state and control variables of the system iteratively solves an optimal control structured optimization problem (OCP), such that each iteration outputs primal variables and dual variables with respect to the equality constraints and dual variables and slack variables with respect to the inequality constraints. For a current iteration, the system classifies each of the inequality constraints as an active, an inactive or an undecided constraint based on a ratio of a slack variable to a dual variable of the corresponding inequality constraint determined by a previous iteration, finds an approximate solution to the set of relaxed optimality conditions subject to the equality constraints and the active and undecided inequality constraints, and update the primal, dual, and slack variables for each of the equality and inequality constraint.

Abstract: A control system for controlling a motion of a vehicle to a target driving goal uses a decision-maker configured to determine a sequence of intermediate goals leading to the next target goal by optimizing the motion of the vehicle subject to a first model and tightened driving constraints formed by tightening driving constraints by a safety margin, and uses a motion planner configured to determine a motion trajectory of the vehicle tracking the sequence of intermediate goals by optimizing the motion of the vehicle subject to the second model. The driving constraints include mixed logical inequalities of temporal logic formulae specified by traffic rules to define an area where the temporal logic formulae are satisfied, while the tightened driving constraints shrink the area by the safety margin, which is a function of a difference between the second model and the first model approximating the second model.

Abstract: A control system for controlling an operation of a machine subject to constraints including equality and inequality constraints on state and control variables of the system iteratively solves an optimal control structured optimization problem (OCP), such that each iteration outputs primal variables and dual variables with respect to the equality constraints and dual variables and slack variables with respect to the inequality constraints. For a current iteration, the system classifies each of the inequality constraints as an active, an inactive or an undecided constraint based on a ratio of a slack variable to a dual variable of the corresponding inequality constraint determined by a previous iteration, finds an approximate solution to the set of relaxed optimality conditions subject to the equality constraints and the active and undecided inequality constraints, and update the primal, dual, and slack variables for each of the equality and inequality constraint.

Abstract: A machine subject to state and control input constraints is control, while the control policy is learned from data collected during an operation of the machine. To ensure satisfaction of the constraints, the state of machine is maintained within a constraint admissible invariant set (CAIS) satisfying the constraints and the machine is controlled with corresponding control policy mapping a state of the system within the CAIS to a control input satisfying the control input constraints. The machine is controlled using a constrained policy iteration, in which a constrained policy evaluation updates CAIS and value function and a constrained policy improvement updates control policy that improves the cost function of operation according to the updated CAIS and the corresponding updated value function.

Abstract: A control system controls a vehicle using a probabilistic motion planner and an adaptive predictive controller. The probabilistic motion planner produces a sequence of parametric probability distributions over a sequence of target states for the vehicle with parameters defining a first and higher order moments. The adaptive predictive controller optimizes a cost function over a prediction horizon to produce a sequence of control commands to one or multiple actuators of the vehicle. The cost function balances a cost of tracking of different state variables in the sequence of the target states defined by the first moments. The balancing is performed by weighting different state variables using one or multiple of the higher order moments of the probability distribution.

Abstract: A controller for controlling a system with continuous and discrete elements of operation accepts measurements of a current state of the system, solves a mixed-integer model predictive control (MI-MPC) problem subject to state constraints on the state of the system to produce control inputs to the system, and submits the control inputs to the system thereby changing the state of the system. To solve the MI-MPC, the controller transforms the state constraints into state-invariant control constraints on the control inputs to the system, such that any combination of values for the control inputs, resulting in a sequence of values for the state variables that satisfy the state constraints, also satisfy the state-invariant control constraints, and solve the MI-MPC problem subject to the state constraints and the state-invariant control constraints.

Abstract: A predictive controller controls a vehicle subject to equality and inequality constraints on state and control variables of the vehicle and solves a matrix equation of necessary optimality conditions to produce control inputs to control the vehicle. The controller represents the state variables as a function of the control variables using discrete-time dynamics and determines the control inputs iteratively using two levels of iterations. The first level of iterations selects active inequality constraints, updates a constraint Jacobian matrix with a low-rank update for a change in the set of active inequality constraints to include the active inequality constraints, and updates a preconditioning matrix with a low-rank factorization update, in response to the low-rank update of the constraint Jacobian matrix. The second level of iterations, nested in the first level, solves the matrix equation with the updated constraint Jacobian matrix using the updated preconditioning matrix to produce the control inputs.

Abstract: Methods and systems including processor configured to receive a transition indication to switch a semi-autonomous vehicle from a driving mode to another driving mode while a driver is driving the vehicle on a roadway. Wherein the driving modes include an autonomous lane keeping mode, an autonomous lane change mode and a manual mode. In response to receiving the request, use protocol data to assess a status of the vehicle's environment, a vehicle state and systems of the vehicle. Select, a set of conditions corresponding to the vehicle's state, based on one or more of the assessments. Determine, whether a switch between driving modes is initiated by the driver, by verifying if the vehicle's state satisfies the set of conditions, in order to validate if the driver actuated the vehicle into or out of a safety region.

Abstract: A controller for controlling a system with continuous and discrete elements of operation accepts measurements of a current state of the system, solves a mixed-integer model predictive control (MI-MPC) problem subject to state constraints on the state of the system to produce control inputs to the system, and submits the control inputs to the system thereby changing the state of the system. To solve the MI-MPC, the controller transforms the state constraints into state-invariant control constraints on the control inputs to the system, such that any combination of values for the control inputs, resulting in a sequence of values for the state variables that satisfy the state constraints, also satisfy the state-invariant control constraints, and solve the MI-MPC problem subject to the state constraints and the state-invariant control constraints.

Abstract: A system control a vehicle using a friction function describing a friction between a type of surface of the road and a tire of the vehicle as a function of a slip of a wheel of the vehicle. The parameters of each friction function include an initial slope of the friction function defining a stiffness of the tire and one or combination of a peak friction, a shape factor and a curvature factor of the friction function. Upon estimating a slip and a stiffness of the tire, the system selects from the memory parameters of the friction function corresponding to the current stiffness of the tire, determines a control command using a value of the friction corresponding to the slip of the tire according to the friction function defined by the selected parameters, and submits the control command to an actuator of the vehicle.

Abstract: A machine subject to state and control input constraints is control, while the control policy is learned from data collected during an operation of the machine. To ensure satisfaction of the constraints, the state of machine is maintained within a constraint admissible invariant set (CAIS) satisfying the constraints and the machine is controlled with corresponding control policy mapping a state of the system within the CAIS to a control input satisfying the control input constraints. The machine is controlled using a constrained policy iteration, in which a constrained policy evaluation updates CAIS and value function and a constrained policy improvement updates control policy that improves the cost function of operation according to the updated CAIS and the corresponding updated value function.

Abstract: A predictive controller for controlling a system subject to constraints including equality and inequality constraints on state and control variables of the system, includes an estimator to estimate a current state of the system using measurements of outputs of the system and a controller to solve, at each control step, a matrix equation of necessary optimality conditions to produce a control solution and to control the system using the control solution to change a state of the system. The matrix equation includes a block-structured matrix having a constraint Jacobian matrix of the equality constraints of the system.

Abstract: A predictive controller controls a vehicle subject to equality and inequality constraints on state and control variables of the vehicle and solves a matrix equation of necessary optimality conditions to produce control inputs to control the vehicle. The controller represents the state variables as a function of the control variables using discrete-time dynamics and determines the control inputs iteratively using two levels of iterations. The first level of iterations selects active inequality constraints, updates a constraint Jacobian matrix with a low-rank update for a change in the set of active inequality constraints to include the active inequality constraints, and updates a preconditioning matrix with a low-rank factorization update, in response to the low-rank update of the constraint Jacobian matrix. The second level of iterations, nested in the first level, solves the matrix equation with the updated constraint Jacobian matrix using the updated preconditioning matrix to produce the control inputs.

Abstract: A control system for controlling an operation of a system with continuous-time nonlinear dynamics subject to constraints including equality and inequality constraints on state and control variables of the system, including an estimator to estimate a current state of the system using measurements of the operation of the system and a controller to iteratively solve, at each control time step, an approximation of a constrained nonlinear optimization problem to produce a control solution, wherein the approximation includes a linearization of the nonlinear dynamics of the system discretized by time intervals in the control horizon and represented using an approximation of the constraint Jacobian matrix for each time interval of the control horizon.

Abstract: A control system for controlling an operation of a system with continuous-time nonlinear dynamics subject to constraints including equality and inequality constraints on state and control variables of the system, including an estimator to estimate a current state of the system using measurements of the operation of the system and a controller to iteratively solve, at each control time step, an approximation of a constrained nonlinear optimization problem to produce a control solution, wherein the approximation includes a linearization of the nonlinear dynamics of the system discretized by time intervals in the control horizon and represented using an approximation of the constraint Jacobian matrix for each time interval of the control horizon.