Computer-implemented method for designing a state controller with stochastic optimization

A computer system configured to design a state controller, the computer system configured to:

• receive a state space model for describing a system to be controlled, wherein:
• the state space model includes a system matrix, a state vector that contains one or more state variables, an input matrix, and an input variable vector;
• the input variable vector is based on the state vector;
• and
• each of at least one of the state variables is associated with a respective probability distribution that characterizes uncertainty in a respective system state to which the respective state variable corresponds;
• formulate a stochastic optimization problem that includes a cost function that is based on the probability distributions and is calculated using the system matrix, a feedback matrix that describes a state controller, an initial state, and the input matrix, wherein the cost function is formed by (a) a first contribution corresponding to respective expected values of the one or more state variables and (b) a second contribution corresponding to one or more variances of the one or more state variables;
• solve the stochastic optimization problem to determine entries of the feedback matrix;
• and
• design the state controller based on the feedback matrix whose entries are determined from the solving of the stochastic optimization problem, wherein:
• the state vector represents system states of the system to be controlled during operation of the system;
• the input variable vector represents control inputs applied to the system to be controlled during the operation of the system;
• the feedback matrix defines a state-feedback relationship by which, during the operation of the system to be controlled using the state controller, the input variable vector is determined from the state vector;
• and
• incorporation of the feedback matrix having the determined entries into the state controller provides reduced variability of the one or more state variables of the state vector such that fluctuations of the state variables of the state vector, during operation of the system using the state controller to produce control inputs from the input variable vector, are attenuated under the characterized uncertainty as a result of the variance contribution of the cost function, thereby stabilizing operation of the system to be controlled.

A non-transitory computer-readable medium on which is stored a computer program that is executable by a computer system and that, when executed by the computer system, causes the computer system to perform the following steps:

• receiving a state space model for describing a system to be controlled, wherein the state space model includes a system matrix, a state vector which contains one or more state variables, an input matrix, and an input variable vector, wherein the input variable vector is based on the state vector;
• modeling each of at least one of the state variables as a respective random variable having an associated probability distribution that characterizes uncertainty in a respective system state to which the respective state variable corresponds;
• formulating a stochastic optimization problem that includes a cost function which is calculated at least using the system matrix, a feedback matrix that describes the state controller, an initial state, and the input matrix, wherein (a) the cost function includes at least an expected value component that is based on the probability distribution, and (b) the feedback matrix defines a state feedback by which the input variable vector is determined based on the state vector;
• solving the stochastic optimization problem to determine entries of the feedback matrix based on the modeled probability distribution of the at least one state variable, such that the cost function is minimized with respect to the feedback matrix;
• and
• generating a state controller of a vehicle incorporating the feedback matrix, the state controller being configured to control a drive operation of the vehicle according to the input variable vector obtained using the feedback matrix, wherein:
• the state vector represents system states of the system to be controlled during operation of the system;
• the input variable vector represents control inputs applied to the system to be controlled during the operation of the system;
• the feedback matrix defines a state-feedback relationship by which, during the operation of the system to be controlled using the state controller, the input variable vector is determined from the state vector;
• and
• incorporation of the feedback matrix having the determined entries into the state controller provides reduced variability of the one or more state variables of the state vector such that fluctuations of the state variables of the state vector, during operation of the system using the state controller to produce control inputs from the input variable vector, are attenuated under the characterized uncertainty as a result of the variance contribution of the cost function, thereby stabilizing operation of the system to be controlled.

A computer-implemented method comprising the following steps:

• receiving a state space model for describing a system to be controlled, wherein the state space model includes a system matrix, a state vector which contains one or more state variables, an input matrix, and an input variable vector, wherein the input variable vector is based on the state vector, and a feedback matrix which describes the state controller, and the one or more state variables are described based on one or more probability distributions;
• describing an optimization problem that includes a cost function which is calculated at least using the system matrix, the feedback matrix, an initial state, and the input matrix;
• solving the optimization problem to determine entries of the feedback matrix;
• and
• generating a state controller of a vehicle incorporating the feedback matrix, the state controller being configured to control a drive operation of the vehicle according to the input variable vector obtained using the feedback matrix;
• wherein:
• (I) the describing includes determining one or more expected values and one or more variances of the one or more state variables of the state vector, the cost function being formed by (a) a first contribution that corresponds to the one or more expected values of the one or more state variables of the state vector, and (b) a second contribution that corresponds to the one or more variances of the one or more state variables of the state vector;
• (II) the describing includes performing one or more series developments based on the one or more probability distributions to describe the one or more state variables;
• and/or
• (III) the one or more probability distributions are represented by one or more polynomial bases;
• and
• wherein:
• the state vector represents system states of the system to be controlled during operation of the system;
• the input variable vector represents control inputs applied to the system to be controlled during the operation of the system;
• the feedback matrix defines a state-feedback relationship by which, during the operation of the system to be controlled using the state controller, the input variable vector is determined from the state vector;
• and
• incorporation of the feedback matrix having the determined entries into the state controller provides reduced variability of the one or more state variables of the state vector such that fluctuations of the state variables of the state vector, during operation of the system using the state controller to produce control inputs from the input variable vector, are attenuated under the characterized uncertainty as a result of the variance contribution of the cost function, thereby stabilizing operation of the system to be controlled.

A computer-implemented method comprising the following steps:

• receiving a state space model for describing a vehicle to be controlled, wherein:
• the state space model includes a system matrix, a state vector that contains one or more state variables, an input matrix, and an input variable vector;
• the input variable vector is based on the state vector;
• and
• each of at least one of the state variables is associated with a respective probability distribution that characterizes uncertainty in a respective system state to which the respective state variable corresponds;
• formulating a stochastic optimization problem that includes a cost function that is based on the probability distributions and is calculated using the system matrix, a feedback matrix that describes a state controller, an initial state, and the input matrix, wherein the cost function is formed by (a) a first contribution corresponding to respective expected values of the one or more state variables and (b) a second contribution corresponding to one or more variances of the one or more state variables;
• solving the stochastic optimization problem to determine entries of the feedback matrix;
• designing the state controller based on the feedback matrix whose entries are determined from the solving of the stochastic optimization problem;
• and
• during operation of the vehicle, controlling at least one of transverse guidance or longitudinal guidance of the vehicle by:
• determining, using the state controller, the input variable vector from the state vector in accordance with the feedback matrix;
• and
• applying the determined input variable vector as control inputs to a system of the vehicle to influence movement of the vehicle.