A control system is configured to operate a plant to achieve an optimal value for a performance variable of the plant. The system comprise a feedforward controller configured to receive a measurable disturbance to the plant and generate a feedforward contribution to a control input to the plant using the measurable disturbance. The system also comprises an extremum-seeking controller configured to receive the performance variable from the plant and generate an extremum-seeking contribution to the control input to drive the performance variable to the optimal value. The system further comprises a control input element configured to generate the control input by combining the extremum-seeking contribution and the feedforward contribution and provide the control input to the plant.

A method for a direct current (DC) islanding detection based on positive feedback of a bus voltage at a specific frequency, essentially including three steps: extraction of a specific frequency component of the bus voltage, injection of a disturbance component of the specific frequency, and determination of DC islanding. The extraction of the specific frequency component of the bus voltage and the injection of the disturbance component of the specific frequency constitute a positive feedback mechanism in a power management unit control loop. In a grid-connected mode of a DC grid, the positive feedback mechanism fails due to a control action of a voltage management unit on a bus, and the bus voltage remains stable. In an islanding mode of the DC grid, under an action of the positive feedback mechanism, the power management unit allows the bus voltage to generate a self-excited oscillation at the specific frequency.

A self-configuring extremum-seeking controller includes a dither signal generator, a communications interface, a phase delay estimator, and a bandwidth estimator. The dither signal generator identifies a stored dither frequency, generates a dither signal having the stored dither frequency, and uses the dither signal to perturb a control input for a plant. The communications interface provides the perturbed control input to the plant and receives an output signal from the plant resulting from the perturbed control input. The phase delay estimator estimates a phase delay between the output signal and the dither signal. The bandwidth estimator estimates a bandwidth of the plant based on the estimated phase delay. The dither signal generator updates the stored dither frequency based on the estimated bandwidth.

The present invention discloses a model-free online recursive optimization method for a batch process based on variable period decomposition. Variable operation data closely related to product quality is acquired, optimization action on each subset is integrated on the basis of time domain variable division on the process by utilizing a data driving method and a global optimization strategy is formed, based on which an online recursive error correction optimization strategy is implemented. According to the method, the online optimization strategy is formed completely based on the operation data of the batch process without needing prior knowledge or a model of a process mechanism. Meanwhile, the optimized operation locus line has better adaptability by using the online recursive correction strategy, and thus the anti-interference requirement of the actual industrial production is better met.

A non-transitory, computer-readable recording medium stores a program of reinforcement learning by a state-value function. The program causes a computer to execute a process including calculating a TD error based on an estimated state-value function, the TD error being calculated by giving a perturbation to each component of a feedback coefficient matrix that provides a policy; calculating based on the TD error and the perturbation, an estimated gradient function matrix acquired by estimating a gradient function matrix of the state-value function with respect to the feedback coefficient matrix for a state of a controlled object, when state variation of the controlled object in the reinforcement learning is described by a linear difference equation and an immediate cost or an immediate reward of the controlled object is described in a quadratic form of the state and an input; and updating the feedback coefficient matrix using the estimated gradient function matrix.

A self-configuring extremum-seeking controller includes a dither signal generator, a communications interface, a phase delay estimator, and a bandwidth estimator. The dither signal generator identifies a stored dither frequency, generates a dither signal having the stored dither frequency, and uses the dither signal to perturb a control input for a plant. The communications interface provides the perturbed control input to the plant and receives an output signal from the plant resulting from the perturbed control input. The phase delay estimator estimates a phase delay between the output signal and the dither signal. The bandwidth estimator estimates a bandwidth of the plant based on the estimated phase delay. The dither signal generator updates the stored dither frequency based on the estimated bandwidth.

A method determines the topology of a DERs system having a plurality of assets, where at least one of the assets is a controllable asset. The method injects a power signal at a given frequency from a controllable asset into the DERs system. The voltage at each of the plurality of assets is measured, and the magnitude of perturbation of the voltage at the given frequency is determined for each of the plurality of assets. The method then constructs the topology of the DERs system as a function of the differences of the magnitude of perturbations of each of the plurality of assets.

Techniques for controlling a bottom hole assembly (BHA) include determining a first candidate BHA control signal; generating an input to a BHA control, the input comprising a perturbation signal superimposed on the first candidate BHA control signal; controlling the BHA using the input to the BHA control; determining a change in an objective value as a function of the perturbation signal, based on a received downhole sensor measurement; and generating, based on the change in the objective value, a second candidate BHA control signal.

An extremum-seeking control system includes a plant operable to affect a variable state or condition of a building and an extremum-seeking controller. The extremum-seeking controller is configured to provide a control input to a plant and receive a performance variable as a first feedback from the plant. The plant uses the control input to affect the performance variable. The extremum-seeking controller is configured to receive a constrained variable as a second feedback from the plant and calculate a performance penalty by applying a penalty function to the constrained variable. The extremum-seeking controller is further configured to modify the performance variable with the performance penalty to generate a modified cost function, estimate a gradient of the modified cost function with respect to the control input, and drive the gradient of the modified cost function toward zero by modulating the control input.

A control system is configured to operate a plant to achieve an optimal value for a performance variable of the plant. The system comprise a feedforward controller configured to receive a measurable disturbance to the plant and generate a feedforward contribution to a control input to the plant using the measurable disturbance. The system also comprises an extremum-seeking controller configured to receive the performance variable from the plant and generate an extremum-seeking contribution to the control input to drive the performance variable to the optimal value. The system further comprises a control input element configured to generate the control input by combining the extremum-seeking contribution and the feedforward contribution and provide the control input to the plant.