Abstract: An extremum seeking control system and a method for controlling a system is provided. The method comprises receiving a tracking error, consecutive measurements of a system output, and consecutive measurements of a cost function of the system, and estimating a gradient based on the tracking error, the consecutive measurements of the system output, and the consecutive measurements of the cost function of the system. The method further comprises determining a step-size based on a ratio of a covariance of the gradient to the gradient, and determining a set-point optimizing performance of the system, based on the gradient and the step-size. The method further comprises controlling the system based on the set-point optimizing performance of the system.

Abstract: A controller and a method for controlling motion of a vehicle is provided. The method comprises acquiring motion information including a current state of the vehicle and a desired state of the vehicle, determining a combination of a steering angle of the wheels and motor forces for moving the vehicle from the current state into the desired state by using a first model of the motion of the vehicle and a second model of the motion of the chassis of the vehicle, determining a cost function of the motion of the vehicle, optimizing the cost function of the motion of the vehicle to compute a command signal for controlling the steering wheel and the plurality of electric motors, and controlling the steering angle of the wheels and the motor forces based on the command signal.

Abstract: A controller and a method for controlling motion of a vehicle is provided. The method comprises acquiring motion information including a current state of the vehicle and a desired state of the vehicle, determining a combination of a steering angle of the wheels and motor forces for moving the vehicle from the current state into the desired state by using a first model of the motion of the vehicle and a second model of the motion of the chassis of the vehicle, determining a cost function of the motion of the vehicle, optimizing the cost function of the motion of the vehicle to compute a command signal for controlling the steering wheel and the plurality of electric motors, and controlling the steering angle of the wheels and the motor forces based on the command signal.

Abstract: A control system for wheel-slip prevention in a railway vehicle with a pneumatic brake is provided. The control system comprises an input interface configured to accept a deceleration reference for controlling the pneumatic brake, and a memory configured to store a reference governor providing executable instructions for modifying the deceleration reference upon its violation of a wheel-slip constraint, and configured to store a controller providing executable instructions for mapping the modified deceleration reference to a sequence of control commands for controlling pressure applied by the pneumatic brake. The control system further comprises a processor configured to execute the reference governor to modify the deceleration reference and configured to execute the controller to map the modified deceleration reference to the sequence of control commands. Further, an output interface of the control system is configured to output the sequence of control commands to control the pneumatic brake.

Abstract: A control system for controlling a set of actuators of a system. The control system comprising a switcher configured to select a subset of setpoints from a set of setpoints that control the corresponding set of actuators. An extremum-seeking controller (ESC) configured to perturb a subset of setpoints at each iteration based on a probabilistic distribution of partial gradients of a cost function relating values of the subset of setpoints to a cost of operation of the system. A stochastic gradient estimator is configured to estimate a full gradient of the cost function and update the estimation of the full gradient based on the probabilistic distribution of the partial gradients generated at each ESC iteration. A feedback controller is configured to drive a state of the subset of actuators of the system towards the corresponding perturbed subset of setpoints.

Abstract: A control system for controlling a set of actuators of a system. The control system comprising a switcher configured to select a subset of setpoints from a set of setpoints that control the corresponding set of actuators. An extremum-seeking controller (ESC) configured to perturb a subset of setpoints at each iteration based on a probabilistic distribution of partial gradients of a cost function relating values of the subset of setpoints to a cost of operation of the system. A stochastic gradient estimator is configured to estimate a full gradient of the cost function and update the estimation of the full gradient based on the probabilistic distribution of the partial gradients generated at each ESC iteration. A feedback controller is configured to drive a state of the subset of actuators of the system towards the corresponding perturbed subset of setpoints.

Abstract: An extremum seeking control system and a method for controlling a system is provided. The method comprises receiving a tracking error, consecutive measurements of a system output, and consecutive measurements of a cost function of the system, and estimating a gradient based on the tracking error, the consecutive measurements of the system output, and the consecutive measurements of the cost function of the system. The method further comprises determining a step-size based on a ratio of a covariance of the gradient to the gradient, and determining a set-point optimizing performance of the system, based on the gradient and the step-size. The method further comprises controlling the system based on the set-point optimizing performance of the system.

Abstract: A computing system for generating optimal tracking control (TC) policies for controlling a machine to track a given time-varying reference (GTVR) trajectory. An updated augmented state of the machine is obtained. Stored in memory is the GTVR trajectory, a constraint-admissible invariant set (CAIS) of machine states satisfying machine state constraints and a corresponding TC policy mapping a machine state within the CAIS to a control input satisfying control input rate constraints. A processor jointly controls the computing system to control the operation to drive an augmented state of the machine to zero, and update the CAIS and TC policy. Joint control includes using a sequence of control inputs and a sequence of augmented machine states within CAIS corresponding to the sequence of tracking control inputs. Execute a constrained tracking approximate dynamic programming (TADP) using the received data to update the value function, update the CAIS and the corresponding TC policy.

Abstract: A computing system for generating optimal tracking control (TC) policies for controlling a machine to track a given time-varying reference (GTVR) trajectory. An updated augmented state of the machine is obtained. Stored in memory is the GTVR trajectory, a constraint-admissible invariant set (CAIS) of machine states satisfying machine state constraints and a corresponding TC policy mapping a machine state within the CAIS to a control input satisfying control input rate constraints. A processor jointly controls the computing system to control the operation to drive an augmented state of the machine to zero, and update the CAIS and TC policy. Joint control includes using a sequence of control inputs and a sequence of augmented machine states within CAIS corresponding to the sequence of tracking control inputs. Execute a constrained tracking approximate dynamic programming (TADP) using the received data to update the value function, update the CAIS and the corresponding TC policy.

Abstract: A receding horizon state estimator estimates state of a vehicle such as to reduce total communication cost of acquiring external measurements over a prediction horizon, in which state estimation accuracy for a time step is a function of state estimation accuracy for a previous time step. For each time step of the prediction horizon, estimator selects a subset of external sensors with external measurements sufficient to estimate the state with accuracy satisfying the constraint on state estimation accuracy for the corresponding time step while reducing a total communication cost of acquiring the external measurements over the prediction horizon. The estimator requests the external measurements from the subset of external sensors determined for a current time step and estimates the state of the vehicle using the internal and the requested external measurements.

Abstract: A control system for controlling motions of a vehicle having wheels is provided. The control system includes suspension units configured to support the wheels respectively driven by motors controlled by throttles, a set of sensors configured to detect the motions of the vehicle, wherein the motions are represented by lift, pitch, and roll values of the vehicle, an allocation module configured, in connected with the sensors, to generate and transmit allocated throttle signals to the throttles to minimize the motion by solving an optimization problem related to the motion, and a motor control unit configured to drive each of the motors via the throttles according to the allocated throttle signals.

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 of a vehicle for controlling motion of the vehicle traveling on a road shared with a set of moving objects include a memory to store a set of regions of states of lateral dynamic of the vehicle corresponding to a set of equilibrium points. Each region defines a control invariant set of the states of the lateral dynamic determined for different speeds of the vehicle, such that the vehicle having a state within a region determined for a speed is capable to maintain its states within the region while moving with the speed. Each region includes a corresponding equilibrium point and intersects with at least one adjacent region. Each equilibrium point is associated with one or multiple regions determined for different speeds.

Abstract: A control system for wheel-slip prevention in a railway vehicle with a pneumatic brake is provided. The control system comprises an input interface configured to accept a deceleration reference for controlling the pneumatic brake, and a memory configured to store a reference governor providing executable instructions for modifying the deceleration reference upon its violation of a wheel-slip constraint, and configured to store a controller providing executable instructions for mapping the modified deceleration reference to a sequence of control commands for controlling pressure applied by the pneumatic brake. The control system further comprises a processor configured to execute the reference governor to modify the deceleration reference and configured to execute the controller to map the modified deceleration reference to the sequence of control commands. Further, an output interface of the control system is configured to output the sequence of control commands to control the pneumatic brake.

Abstract: A control system uses a set of regions of states of lateral dynamic of the vehicle corresponding to a set of equilibrium points to control a vehicle. Each region defines a control invariant set of the states of the lateral dynamic determined such that the vehicle having a state within a region is capable to maintain its states within the region. Each region includes a corresponding equilibrium point and intersects with at least one adjacent region. The control system identifies collision-free regions at different time steps of control to produce a collision free sequence of regions forming a union of regions in space and time connecting a region including an initial displacement with a region including a target displacement. The control system produces a trajectory within the union connecting the initial displacement with the target displacement and control the vehicle according to the trajectory.

Abstract: A receding horizon state estimator estimates state of a vehicle such as to reduce total communication cost of acquiring external measurements over a prediction horizon, in which state estimation accuracy for a time step is a function of state estimation accuracy for a previous time step. For each time step of the prediction horizon, estimator selects a subset of external sensors with external measurements sufficient to estimate the state with accuracy satisfying the constraint on state estimation accuracy for the corresponding time step while reducing a total communication cost of acquiring the external measurements over the prediction horizon. The estimator requests the external measurements from the subset of external sensors determined for a current time step and estimates the state of the vehicle using the internal and the requested external measurements.

Abstract: A method for controlling an operation of a machine exhibiting symmetries in dynamics of the machine, a cost of the operation of the machine, and constraints on the operation of the machine performs iteratively a control optimization until a termination condition is met to produce an optimal control input and controls the machine according to the optimal control input.

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 method for controlling an operation of a machine exhibiting symmetries in dynamics of the machine, a cost of the operation of the machine, and constraints on the operation of the machine performs iteratively a control optimization until a termination condition is met to produce an optimal control input and controls the machine according to the optimal control input.

Abstract: A control system of a vehicle for controlling motion of the vehicle traveling on a road shared with a set of moving objects include a memory to store a set of regions of states of lateral dynamic of the vehicle corresponding to a set of equilibrium points. Each region defines a control invariant set of the states of the lateral dynamic determined for different speeds of the vehicle, such that the vehicle having a state within a region determined for a speed is capable to maintain its states within the region while moving with the speed. Each region includes a corresponding equilibrium point and intersects with at least one adjacent region. Each equilibrium point is associated with one or multiple regions determined for different speeds.