An optimal scheduling method of an electricity-heat multi-energy flow system based on a heat supply phasor model is provided. The method considers a mutual influence of the electricity-heat system, establishes a constraint equation of a heat supply system in a phasor form, considers dynamic characteristics of the heat supply system, and realizes an optimal scheduling of the electricity-heat multi-energy flow system.

A controller is configured to control a system by generating a control input to an actuator changing a state of the system in accordance with the control input. The controller includes an interface configured to receive data indicative of dynamic response of the actuator and a tuner configured to determine the maximum rate of change of the control input during a control cycle using the received data indicative of dynamic response of the actuator. The controller also includes a receiver configured to receive measurements of the state of the system and a solver configured to determine a current value of the control input for controlling the controlled system based on the state of the controlled system subject to constraints on operation of the system and a constraint on the maximum rate of change of the control input, and to cause the actuator to change the state of the system according to the current value of the control input.

Computer systems attempt to manage resource pools of a dynamic number of similar resources and work tasks in order to optimize system performance. Work requests are received into the resource pool having a dynamic number of resources instances. An instance-throughput curve is determined that relates a number of resource instances in the resource pool to throughput of the work requests. A slope of a point on the instance-throughput curve is estimated with stochastic gradient approximation. The number of resource instances for the resource pool is selected when the estimated slope of the instance-throughput curve is zero.

The present disclosure discloses a system and a method for controlling an operation of a machine including at least one actuator. The method comprises obtaining a time period of an operation of the at least one actuator, collecting an energy level of the at least one actuator, and determining one or more hyperparameters of a time bound function such that a value of the time bound function is greater than or equal to the time period of the operation of the at least one actuator. The method further comprises solving an optimal control problem optimizing a cost function of the operation of the at least one actuator using an adaptive gradient descent method that is initialized with the collected energy level and a constant defined based on the one or more hyperparameters and controlling the at least one actuator based on a solution of the optimal control problem.

An optimal scheduling method of an electricity-heat multi-energy flow system based on a heat supply phasor model is provided. The method considers a mutual influence of the electricity-heat system, establishes a constraint equation of a heat supply system in a phasor form, considers dynamic characteristics of the heat supply system, and realizes an optimal scheduling of the electricity-heat multi-energy flow system.