Abstract: An LPV/MPC engine control system is disclosed that includes an engine control unit connected to multiple sensors. The engine control unit receives, from the sensors, signals indicative of desired engine torque and engine torque output, and determines, from these signals, optimal engine control commands using a piecewise LPV/MPC routine. This routine includes: determining a nonlinear and a linear system model for the engine assembly, minimizing a control cost function in a receding horizon for the linear system model, determining system responses for the nonlinear and linear system models, determining if a norm of an error function between the system responses is smaller than a calibrated threshold, and if the norm is smaller than the predetermined threshold, applying the linearized system model in a next sampling time for a next receding horizon to determine the optimal control command. Once determined, the optimal control command is output to the engine assembly.

Abstract: A system according to the principles of the present disclosure includes a model predictive control (MPC) module and an actuator module. The MPC module generates a set of possible target values for an actuator of an engine and predicts an operating parameter of the engine for each of the possible target values. The MPC module determines a weighting value associated with each of the target values based on a corresponding iteration number and determines a cost for the set of possible target values based on the predicted operating parameters and the weighting values. The MPC module selects the set of possible target values from multiple sets of possible target values based on the cost and sets target values to the possible target values of the selected set. The actuator module controls an actuator of an engine based on at least one of the target values.

Abstract: A requesting module generates a first torque request for an engine based on driver input. A conversion module converts the first torque request into a second torque request. A model predictive control (MPC) module determines a current set of target values based on the second torque request, a model of the engine, a tableau matrix, and a basic solution matrix. The MPC module: initializes the basic solution matrix to a predetermined matrix that is dual feasible; selectively iteratively updates the basic solution matrix and columns of the tableau matrix; determines changes for the target values, respectively, based on entries of the basic solution matrix resulting from the selective iterative updating; and determines the current set of target values by summing the changes with a last set of target values, respectively. An actuator module controls an engine actuator based on a first one of the current set of target values.

Abstract: A system according to the principles of the present disclosure includes a model predictive control (MPC) module and an actuator module. The MPC module generates a set of possible target values for an actuator of an engine and predicts an operating parameter of the engine for each of the possible target values. The MPC module determines a weighting value associated with each of the target values based on a corresponding iteration number and determines a cost for the set of possible target values based on the predicted operating parameters and the weighting values. The MPC module selects the set of possible target values from multiple sets of possible target values based on the cost and sets target values to the possible target values of the selected set. The actuator module controls an actuator of an engine based on at least one of the target values.

Abstract: A model predictive control (MPC) module performs multiple iterations to determine a current set of target values for an engine based on a torque request, a model of the engine, a tableau matrix, and a basic solution matrix. Each of the iterations includes: determining whether the basic solution matrix is not in standard form; when the basic solution matrix is not in standard form, identifying a first column of the tableau matrix based on a first entry position of the primal variable of the non-basic pair; when the basic solution matrix is in standard form and one or more primal variables of the basic solution matrix are negative, identifying the first column of the tableau matrix based on a second entry position of a dual variable of the basic pair; and selectively updating the basic solution matrix based on the first column of the tableau matrix.

Abstract: A torque requesting module generates a first torque request for a spark ignition engine based on driver input. A torque conversion module converts the first torque request into a second torque request. A model predictive control (MPC) module determines a set of target values based on the second torque request, a model of the engine, and a matrix having dimensions of (m+n) by (m+n). n is an integer greater than zero that is equal to a number of lower boundary constraints used in the determination of the set of target values. m is an integer greater than zero that is equal to a number of constraints used in the determination of the set of target values other than the lower boundary constraints. An actuator module controls opening of an engine actuator based on a first one of the target values.

Abstract: A prediction module generates predicted engine operating parameters for a set of possible target values based on a plurality of values indicative of states of the engine and a first set of predetermined values set based on characteristics of the engine. A parameter estimation module determines one or more estimated operating parameters of the vehicle based on the plurality of values indicative of states of the engine and a second set of predetermined values. A cost module determines a cost for the set of possible target values based on the predicted engine operating parameters. A selection module, based on the cost, selects the set of possible target values from a group including the set of possible target values and N other sets of possible target values, wherein N is an integer greater than zero, and sets target values based on the selected set of possible target values.

Abstract: A requesting module generates a first torque request for an engine based on driver input. A conversion module converts the first torque request into a second torque request. A model predictive control (MPC) module determines a current set of target values based on the second torque request, a model of the engine, a tableau matrix, and a basic solution matrix. The MPC module: initializes the basic solution matrix to a predetermined matrix that is dual feasible; selectively iteratively updates the basic solution matrix and columns of the tableau matrix; determines changes for the target values, respectively, based on entries of the basic solution matrix resulting from the selective iterative updating; and determines the current set of target values by summing the changes with a last set of target values, respectively. An actuator module controls an engine actuator based on a first one of the current set of target values.

Abstract: A model predictive control (MPC) module performs multiple iterations to determine a current set of target values for an engine based on a torque request, a model of the engine, a tableau matrix, and a basic solution matrix. Each of the iterations includes: determining whether the basic solution matrix is not in standard form; when the basic solution matrix is not in standard form, identifying a first column of the tableau matrix based on a first entry position of the primal variable of the non-basic pair; when the basic solution matrix is in standard form and one or more primal variables of the basic solution matrix are negative, identifying the first column of the tableau matrix based on a second entry position of a dual variable of the basic pair; and selectively updating the basic solution matrix based on the first column of the tableau matrix.

Abstract: An engine control method includes: generating a first predicted engine output torque and a first predicted mass of air per cylinder (APC) based on a model of the spark ignition engine and a first set of possible target values determined based on an engine torque request; generating a second predicted engine output torque and a second predicted mass of APC based on the model of the spark ignition engine and a second set of possible target values determined based on the engine torque request; determining a first cost for the first set of possible target values; determining a second cost for the second set of possible target values; selecting one of the first and second sets based on the first and second costs; and setting target values based on the possible target values of the selected one of the first and second sets.

Abstract: An engine control method includes: generating a first predicted engine output torque and a first predicted mass of air per cylinder (APC) based on a model of the spark ignition engine and a first set of possible target values determined based on an engine torque request; generating a second predicted engine output torque and a second predicted mass of APC based on the model of the spark ignition engine and a second set of possible target values determined based on the engine torque request; determining a first cost for the first set of possible target values; determining a second cost for the second set of possible target values; selecting one of the first and second sets based on the first and second costs; and setting target values based on the possible target values of the selected one of the first and second sets.

Abstract: A torque requesting module generates a first torque request for a spark ignition engine based on driver input. A torque conversion module converts the first torque request into a second torque request. A model predictive control (MPC) module determines a set of target values based on the second torque request, a model of the engine, and a matrix having dimensions of (m+n) by (m+n). n is an integer greater than zero that is equal to a number of lower boundary constraints used in the determination of the set of target values. m is an integer greater than zero that is equal to a number of constraints used in the determination of the set of target values other than the lower boundary constraints. An actuator module controls opening of an engine actuator based on a first one of the target values.

Abstract: A prediction module generates predicted engine operating parameters for a set of possible target values based on a plurality of values indicative of states of the engine and a first set of predetermined values set based on characteristics of the engine. A parameter estimation module determines one or more estimated operating parameters of the vehicle based on the plurality of values indicative of states of the engine and a second set of predetermined values. A cost module determines a cost for the set of possible target values based on the predicted engine operating parameters. A selection module, based on the cost, selects the set of possible target values from a group including the set of possible target values and N other sets of possible target values, wherein N is an integer greater than zero, and sets target values based on the selected set of possible target values.