Abstract: A hybrid quantum-classical computer solves systems of equations and eigenvalue problems utilizing non-unitary transformations on the quantum computer. The method may be applied, for example, to principal component analysis, least squares fitting, regression, spectral embedding and clustering, vibrations in mechanics, fluids and quantum chemistry, material sciences, electromagnetism, signal processing, image segmentation and data mining.

Abstract: A hybrid quantum-classical computing method for solving optimization problems though applications of non-unitary transformations. An initial state is prepared, a transformation is applied, and the state is updated to provide an improved answer. This update procedure is iterated until convergence to an approximately optimal solution.

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 hybrid quantum-classical computer solves systems of equations and eigenvalue problems utilizing non-unitary transformations on the quantum computer. The method may be applied, for example, to principal component analysis, least squares fitting, regression, spectral embedding and clustering, vibrations in mechanics, fluids and quantum chemistry, material sciences, electromagnetism, signal processing, image segmentation and data mining.

Abstract: A hybrid quantum-classical computing method for solving optimization problems though applications of non-unitary transformations. An initial state is prepared, a transformation is applied, and the state is updated to provide an improved answer. This update procedure is iterated until convergence to an approximately optimal solution.

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 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 method for a model predictive control (MPC) of a system determines entries of an approximate coefficient matrix only at locations identified in a map of locations as significant. The map of locations identifies each location of an entry in the approximate coefficient matrix as either significant or insignificant. The entries are determined using one or combination of an approximate coefficient function and an exact coefficient function. Next, the method determines a preconditioner using the approximate coefficient matrix and determines a solution vector by solving a matrix equation of the MPC with a coefficient matrix defined by an exact coefficient function at a current time step of a control using an iterative method with the preconditioner. The method generates a control signal for controlling the system using the solution vector.

Abstract: A model predictive control (MPC) system for controlling an operation of a machine according to a model of the machine dynamics optimizes a cost function over a time-horizon subject to constraints to produce a sequence of control inputs to control the state of the machine over the time horizon. The machine is control using the first control input in the sequence. The cost function includes a first term defined by an objective of the MPC and a second term penalizing deviation of a state of the machine from a value satisfying an equation of dynamics of the machine.

Abstract: Anomalies in real time series are detected by first determining a similarity matrix of pairwise similarities between pairs of normal time series data. A spectral clustering procedure is applied to the similarity matrix to partition variables representing dimensions of the time series data into mutually exclusive groups. A model of normal behavior is estimated for each group. Then, for the real time series data, an anomaly score is determined, using the model for each group, and the anomaly score is compared to a predetermined threshold to signal the anomaly.

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 analyzes traps in a semiconductor device by determining a first-order derivative of a signal representing an operation of the semiconductor device over time to produce a signal rate change. The traps in the semiconductor device are analyzed based on lifetimes corresponding to peaks of the signal rate change.

Abstract: A method for a model predictive control (MPC) of a system determines entries of an approximate coefficient matrix only at locations identified in a map of locations as significant. The map of locations identifies each location of an entry in the approximate coefficient matrix as either significant or insignificant. The entries are determined using one or combination of an approximate coefficient function and an exact coefficient function. Next, the method determines a preconditioner using the approximate coefficient matrix and determines a solution vector by solving a matrix equation of the MPC with a coefficient matrix defined by an exact coefficient function at a current time step of a control using an iterative method with the preconditioner. The method generates a control signal for controlling the system using the solution vector.

Abstract: A method processes a signal by first constructing a graph from the signal, and then determining a graph matrix from the graph and the signal. A Krylov-based subspace is determined based on the graph matrix and the signal. A filter for the Krylov subspace is determined. The filter transforms the signal to produce a filtered signal, which is output.

Abstract: A method for a continuation model predictive control (CMPC) of a system determines at least a part of a preconditioner using an approximate coefficient function and determines a solution vector by solving a matrix equation of the CMPC with a coefficient matrix defined by an exact coefficient function at a current time step of a control using an iterative method with the preconditioner. The approximate coefficient function applied to a vector approximates a result of an application of the exact coefficient function to the vector. A control signal for controlling the system is generated using the solution vector.

Abstract: A method reconstructs a signal by sampling the signal using a sampling procedure to obtain an input signal. A consistent set is determined from the input signal including the first elements such that applying the sampling procedure to the first elements results in the input signal. According to the type of the signal, a guiding set is determined including second elements disjoint from the first elements. A reconstruction set including third elements is generated so that the third elements minimize a sum of a first similarity measure of the third elements to the second elements and a second similarity measure of the third elements to the first elements. A transformed signal that minimizes a function on the reconstruction set is determined. A reconstructed signal is rendered so that a third similarity measure of the reconstructed signal to the transformed signal is smaller than a tolerance.

Abstract: A navigation system includes a first navigation module for determining a first position and a second navigation module for determining a second position. The first and the second navigation modules are mechanically connected, such that the first position is dependent on the second position. Also, the first and the second navigation modules are communicatively connected to exchange information including at least one of the first and the second positions. At an instant of time during an operation of the navigation system, the first navigation module receives the second position from the second navigation module and determines the first position based on the second position.

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 navigation system includes a first navigation module for determining a first position and a second navigation module for determining a second position. The first and the second navigation modules are mechanically connected, such that the first position is dependent on the second position. Also, the first and the second navigation modules are communicatively connected to exchange information including at least one of the first and the second positions. At an instant of time during an operation of the navigation system, the first navigation module receives the second position from the second navigation module and determines the first position based on the second position.