Model-based control under uncertainty

A method for controlling a system, wherein the method uses a processor coupled with stored instructions implementing the method, wherein the instructions, when executed by the processor carry steps of the method, comprising:

• retrieving a model of the system including a motion model of the system subject to process noise and a measurement model of the system subject to measurement noise, such that one or combination of the process noise and the measurement noise forms an uncertainty of the model of the system with unknown probabilistic parameters, wherein the uncertainty of the model of the system causes a state uncertainty of the system with unknown probabilistic parameters;
• receiving a sequence of measurements indicative of a state of the system;
• estimating, using at least one or combination of the motion model, the measurement model, and the measurements of the state of the system, a first Student-t distribution representing the uncertainties of the model and a second Student-t distribution representing the state uncertainty of the system, wherein the estimating is performed iteratively until a termination condition is met;
• fitting a Gaussian distribution representing the state uncertainty into the second Student-t distribution;
• determining a control input to the system using the model of the system with state uncertainty represented by the Gaussian distribution;
• and
• controlling the system according to the control input, wherein performing an iteration of the joint estimate of the first and the second Student-t distributions comprises:
• estimating, using the motion model, the state of the system, current values of the first Student-t distribution, and current values of the second Student-t distribution based on a previous estimation of the state of the system, previous values of the first Student-t distribution, and previous values of the second Student-t distribution;
• and
• updating, using the measurements and the measurement model in response to receiving current values of the measurements, the current estimation of the state of the system, the current values of the first Student-t distribution, and the current values of the second Student-t distribution.

A non-transitory computer readable storage medium embodied thereon a program executable by a processor for performing a method, the method comprising:

• retrieving a model of the system including a motion model of the system subject to process noise and a measurement model of the system subject to measurement noise, such that one or combination of the process noise and the measurement noise forms an uncertainty of the model of the system with unknown probabilistic parameters, wherein the uncertainty of the model of the system causes a state uncertainty of the system with unknown probabilistic parameters;
• receiving a sequence of measurements indicative of a state of the system;
• estimating, using at least one or combination of the motion model, the measurement model, and the measurements of the state of the system, a first Student-t distribution representing the uncertainties of the model and a second Student-t distribution representing the state uncertainty of the system, wherein the estimating is performed iteratively until a termination condition is met;
• fitting a Gaussian distribution representing the state uncertainty into the second Student-t distribution;
• determining a control input to the system using the model of the system with state uncertainty represented by the Gaussian distribution;
• and
• controlling the system according to the control input, wherein performing an iteration of the joint estimate of the first and the second Student-t distributions comprises:
• estimating, using the motion model, the state of the system, current values of the first Student-t distribution, and current values of the second Student-t distribution based on a previous estimation of the state of the system, previous values of the first Student-t distribution, and previous values of the second Student-t distribution;
• and
• updating, using the measurements and the measurement model in response to receiving current values of the measurements, the current estimation of the state of the system, the current values of the first Student-t distribution, and the current values of the second Student-t distribution.