Methods and systems for multi-objective optimization and/or wireless power delivery

1. A method for wireless power transmission from a transmitter to a plurality of receivers, the method comprising:

evaluating a set of points in a transmission parameter space based on a set of objective functions that map from the transmission parameter space to an objective space associated with the plurality of receivers, wherein each point in the transmission parameter space corresponds to a respective transmission configuration of the transmitter, wherein evaluating the set of points comprises, for each point of the set:

at the transmitter, wirelessly transmitting power while configured substantially in a respective transmission configuration corresponding to the point;

at the plurality of receivers, receiving power while the transmitter is configured substantially in the respective transmission configuration;

at the plurality of receivers, based on the power received while the transmitter is configured substantially in the respective transmission configuration, determining a respective set of power reception metrics associated with the point; and

based on the respective set of power reception metrics, evaluating the set of objective functions at the point;

determining a subset of dominant points within the transmission parameter space, wherein:

the set of points comprises the subset of dominant points;

for each dominant point of the subset, no point of the set of points is Pareto dominant, with respect to the objective space, over the dominant point;

selecting a first point from the subset of dominant points, wherein the first point corresponds to a first transmission configuration; and

in response to selecting the first point, at the transmitter, wirelessly transmitting power to the plurality of receivers while configured substantially in the first transmission configuration.

2. The method of claim 1 , wherein:

the objective space defines a Pareto front in the objective space, wherein each point on the Pareto front is Pareto-optimal with respect to the set of objective functions; and

each dominant point of the subset is substantially on the Pareto front.

3. The method of claim 1 , wherein each receiver of the plurality is associated with a different objective function of the set.

4. The method of claim 3 , wherein each objective function of the set is indicative of a respective power reception metric of the receiver associated with the objective function.

5. The method of claim 4 , wherein each respective power reception metric is indicative of power transmission efficiency from the transmitter to the receiver associated with the objective function.

6. The method of claim 1 , wherein:

the transmitter comprises a plurality of transmission elements; and

for each transmission element of the plurality, the transmission parameter space comprises a respective parameter.

7. The method of claim 6 , wherein:

the plurality of transmission elements defines a phased array; and

for each transmission element of the plurality, the respective parameter is a respective phase parameter.

8. The method of claim 7 , wherein, for each transmission element of the plurality, the transmission parameter space further comprises a respective amplitude parameter.

9. The method of claim 1 , wherein determining the subset of dominant points comprises:

based on an initial point of the set of points, determining a set of ascent vectors extending from the initial point in the transmission parameter space;

determining a total ascent direction based on a linear combination of the ascent vectors;

selecting an updated point along the total ascent direction, wherein the updated point is Pareto dominant, with respect to the objective space, over the initial point; and

determining a dominant point of the subset based on the updated point.

10. The method of claim 9 , wherein determining the dominant point comprises:

based on the updated point, determining an updated set of ascent vectors extending from the updated point in the transmission parameter space;

determining an updated total ascent direction based on a linear combination of the ascent vectors of the updated set; and

selecting the dominant point along the updated total ascent direction, wherein the dominant point is Pareto dominant, with respect to the objective space, over the updated point.

11. The method of claim 9 , wherein each ascent vector of the set of ascent vectors is associated with a respective objective function of the set of objective functions.

12. The method of claim 11 , wherein determining the set of ascent vectors comprises, for each ascent vector of the set, determining the ascent vector based on a local optimum search with respect to the associated objective function.

13. The method of claim 12 , wherein, for each ascent vector of the set, the local optimum search is performed beginning substantially at the initial point.

14. The method of claim 12 , wherein each ascent vector extends from the initial point to a respective convergence point of the associated local optimum search.

15. The method of claim 12 , wherein, for each ascent vector of the set, the local optimum search comprises a gradient-free search.

16. A system for wireless power transmission, the system comprising:

a transmitter associated with a transmission parameter space, wherein each point in the transmission parameter space corresponds to a respective transmission configuration of the transmitter; and

a plurality of receivers;

wherein:

a set of objective functions map from the transmission parameter space to an objective space associated with the plurality of receivers;

for each point of a set of points in the transmission parameter space:

the transmitter wirelessly transmits power while configured substantially in a respective transmission configuration corresponding to the point;

based on power received while the transmitter is configured substantially in the respective transmission configuration, the plurality of receivers determine a respective set of power reception metrics associated with the point; and

based on the respective set of power reception metrics, the system evaluates the set of objective functions at the point;

the system determines a subset of dominant points within the transmission parameter space, wherein:

the set of points comprises the subset of dominant points; and

for each dominant point of the subset, no point of the set of points is Pareto dominant, with respect to the objective space, over the dominant point;

the system selects a first point from the subset of dominant points, wherein the first point corresponds to a first transmission configuration; and

in response to selecting the first point, the transmitter wirelessly transmits power to the plurality of receivers while configured substantially in the first transmission configuration.

17. The system of claim 1 , wherein:

the system further selects a second point from the subset of dominant points, wherein the second point corresponds to a second transmission configuration;

based on the evaluations of the set of objective functions at the first and second points, the system determines a charging plan comprising:

a first duty cycle associated with the first point; and

a second duty cycle associated with the second point; and

the transmitter wirelessly transmits power to the plurality of receivers while switching between the first and second transmission configurations based on the charging plan.

18. The system of claim 16 , wherein:

each receiver of the plurality is associated with a different objective function of the set; and

for each point of the set of points, each receiver of the plurality:

receives power transmitted by the transmitter; and

determines a respective power reception metric associated with the point, wherein the objective function associated with the receiver is evaluated based on the respective power reception metric.

19. The system of claim 16 , wherein:

the transmitter comprises a plurality of transmission elements defining a phased array; and

for each transmission element of the plurality, the transmission parameter space comprises a respective phase parameter.

20. The system of claim 16 , wherein:

the objective space defines a Pareto front in the objective space, wherein each point on the Pareto front is Pareto-optimal with respect to the set of objective functions; and

each dominant point of the subset is substantially on the Pareto front.