System and method for data-driven control with partially unknown feedback

A control method for controlling a machine, wherein the method uses a processor coupled with stored instructions implementing the method, wherein the instructions, when executed by the processor carry out at least some steps of the method, comprising:

• controlling a machine according to a control policy parameterized on a lifted state space of the machine having an unknown onto mapping to a state space of the machine, wherein a state of the machine is an instance in the state space that uniquely defines the machine at a time instance, wherein a lifted state of the machine is an instance in the lifted state space that defines the machine at the time instance, such that the lifted state at the time instance has the unknown onto mapping to the state of the machine at the time instance;
• accepting a sequence of measurements of state variables measured over a sequence of time instances, the state variables measured for the time instance form a portion of the state of the machine at the time instance;
• determining, for the time instance, a derivative of at least one measured state variable using values of the state variable measured for multiple time instances, wherein a combination of the measured state variables and the derivative of the at least one measured state variable defines the lifted state for the time instance;
• and
• updating the control policy by evaluating a value function of the control policy using the lifted states, such that the controller determines a control input to the machine using the lifted state and the updated control policy.

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

• controlling a machine according to a control policy parameterized on a lifted state space of the machine having an unknown onto mapping to a state space of the machine, wherein a state of the machine is an instance in the state space that uniquely defines the machine at a time instance, wherein a lifted state of the machine is an instance in the lifted state space that defines the machine at the time instance, such that the lifted state at the time instance has the unknown onto mapping to the state of the machine at the time instance;
• accepting a sequence of measurements of state variables measured over a sequence of time instances, the state variables measured for the time instance form a portion of the state of the machine at the time instance;
• determining, for the time instance, a derivative of at least one measured state variable using values of the state variable measured for multiple time instances, wherein a combination of the measured state variables and the derivative of the at least one measured state variable defines the lifted state for the time instance;
• and
• updating the control policy by evaluating a value function of the control policy using the lifted states, such that the controller determines a control input to the machine using the lifted state and the updated control policy.