A control method for controlling an operation of 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 steps of the method, comprising:
- acquiring measurements from at least one sensor sensing an environment surrounding the machine based on a state of the machine and sensing instructions controlling an operation of the at least one sensor;
- processing the measurements to acquire information of the environment;
- processing the acquired information of the environment to estimate a state of the environment and uncertainty of the state of the environment, wherein the state of the environment includes one or more state variables related to the environment;
- solving a multivariable constrained optimization of a model of dynamics of the machine, subject to probabilistic constraints on i.) first values of the states of the environment and the machine and ii.) a sequence of control inputs to the machine to determine jointly i.) the sequence of control inputs to the machine, wherein the sequence of control inputs define a state trajectory of the machine and ii.) desired information of the environment, wherein the model of dynamics of the machine relates the state trajectory with the sequence of the control inputs wherein the probabilistic constraints on the first values of the states of the environment and the machine and the control inputs are defined based on the state of the environment and the uncertainty of the state of the environment,
- wherein the multivariable constrained optimization optimizes a cost function including:
- a stage cost of the operation of the machine controlled by optimized control inputs taken along a prediction horizon, and
- a terminal cost associated with terminal conditions at end of the prediction horizon,
- wherein each of the stage cost and the terminal cost includes a performance term related to a performance of the operation of the machine relative to a control objective to be satisfied and an environment term related to the uncertainty of the state of the environment, where balancing between the performance term and the environment term is obtained by weights of each of the performance term and the environment term, and
- wherein satisfaction of the control objective is guaranteed based on:
- the environment term of the stage cost for a current time step being less than the environment term for the terminal cost at a previous time step,
- the environment term of the terminal cost for the current time step being less than the environment term for the terminal cost at the previous time step,
- the performance term of the stage cost for the current time step being less than or equal to the performance term of terminal cost for the previous time step, and
- the performance term of terminal cost for the current time step being less than or equal to the performance term of terminal cost for the previous time step;
- controlling the machine based on the sequence of the control inputs to change the state of the machine;
- and
- submitting the updated sensing instructions to the sensor.