This document presents methods by which system parameters are tracked online. For adjusting the values of the system parameters, the presented methods take advantage of the data that become available during the system's operation. The values of the parameters can be used for estimating the system state and controlling the system. This document includes methods comprising constructing a cost function based on the data collected during the system operation as a function system parameters and running a memetic algorithm that reduces the cost function value. A memetic algorithm combines an evolutionary or a population-based algorithm with a procedure for local improvement (local search, refinements) of candidate solutions. This document includes methods by which the rotor speed, the rotor flux, and the stator currents of the induction motor can be estimated from electrical measurements while covariance matrices of noise are adjusted online.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method for online estimating one or a plurality of parameters of a system having an input-state-output mathematical model in which the input signal value at each time is determined based on a reference signal and estimated values of state variables, the method comprising at each time of estimating one or a plurality of parameters: constructing a cost function based on the reference signal, the input signal, and the estimated values of the state variables at time instants in a subset of the union of the training period and the system operation period as a function of a vector comprising one or a plurality of components representing said one or a plurality of parameters; Determining an estimated value of the vector comprising one or a plurality of components representing said one or a plurality of parameters with a memetic algorithm reducing the cost function. 2. The method of claim 1, wherein the memetic algorithm comprises: obtaining an initial set of candidate solutions, a candidate solution being defined as a possible value of the vector comprising one or a plurality components representing said one or a plurality of parameters, making the initial set of candidate solutions a current candidate solution set, and generating additional candidate solution sets by performing steps of: a) determining the fitness of each candidate solution in the current candidate solution set by using the cost function; b) selecting one or a plurality of candidate solutions from the current candidate solution set; c) from each candidate solution selected in said step b), successively generating one or a plurality of candidate solutions by searching along descent directions associated with the cost function; d) making the union of the current candidate solution set and a subset of the candidate solutions generated in said step c) the current candidate solution set; e) Creating a new current candidate solution set according to an evolutionary algorithm; and iterating steps a) through e) until a termination condition is satisfied. 3. The method of claim 2, wherein said successively generating one or a plurality of candidate solutions by searching along descent directions associated with the cost function comprises initializing a vector variable, μc to said each candidate solution selected in said step b); generating additional vector values by steps of: c1) finding a descent direction vector associated with the cost function from the current value of the vector variable, μc; c2) determining a scalar step size; c3) performing multiplication of the scalar step size in said step c2) and the descent direction vector in said step c1); c4) performing vector addition of the current value of the vector variable, μc and the result of scalar-vector multiplication in said step c3) and updating the value of the vector variable, μc to the result of said vector addition; and iterating steps c1) through c4) until a termination condition is satisfied. 4. The method of claim 3, wherein said evolutionary algorithm comprises at least one of a genetic algorithm, a particle swarm optimization algorithm, an ant colony optimization algorithm, an artificial bee colony algorithm, a biogeography-based optimization algorithm, a quantum-inspired evolutionary algorithm, an immune quantum-inspired evolutionary algorithm, an estimation-of-distribution algorithm, a fireworks algorithm, differential evolution algorithms, and evolution strategy algorithms. 5. The method of claim 3, wherein said finding a descent direction vector associated with the cost function from the current value of the vector variable, μc in said step c1) comprises: Computing a gradient of the cost function at the current value of the vector variable, μc; and Finding a vector whose inner product with said gradient is negative. 6. The method of claim 4, wherein said finding a descent direction vector associated with the cost function from the current value of the vector variable, μc in step c1) comprises computing a negative gradient of the cost function at the current value of the vector variable, μc. 7. The method of claim 3, wherein the cost function is based on at least one of a mean square of a difference between the reference signal data and the estimated state data, a mean square of a difference between the reference signal data and the output data, and a mean square of a difference between output data corresponding to the estimated state data and the output data. 8. The method of claim 7, wherein said evolutionary algorithm comprises at least one of a genetic algorithm, a particle swarm optimization algorithm, an ant colony optimization algorithm, an artificial bee colony algorithm, a biogeography-based optimization algorithm, a quantum-inspired evolutionary algorithm, an immune quantum-inspired evolutionary algorithm, an estimation-of-distribution algorithm, a fireworks algorithm, differential evolution algorithms, and evolution strategy algorithms. 9. The method of claim 8, wherein said estimated values of state variables represent computational results of a circuit implementing an estimation according to at least one of a Kalman filter, an extended Kalman filter, an unscented Kalman filter, a particle filter. 10. The method of claim 1, wherein the memetic algorithm comprises: obtaining an initial set of candidate solutions, a candidate solution being defined as a possible value of the vector comprising one or a plurality components representing said one or a plurality of parameters, making the initial set of candidate solutions a current candidate solution set, and generating additional candidate solution sets by performing steps of: a) determining the fitness of each candidate solution in the current candidate solution set by using the cost function; b) selecting one or a plurality of candidate solutions from the current candidate solution set; c) from each candidate solution selected in said step b), successively generating one or a plurality of candidate solutions by performing at least one of a gradient algorithm and a gradient projection algorithm with the cost function; d) making the union of the current candidate solution set and a subset of the candidate solutions generated in said step c) the current candidate solution set; e) Creating a new current candidate solution set according to an evolutionary algorithm; and iterating steps a) through e) until a termination condition is satisfied. 11. The method of claim 10, wherein the system having an input-state-output mathematical model comprises an induction motor; the output signal comprises stator currents; and the input signal comprises stator voltage. 12. The method of claim 11, wherein said estimated values of state variables represent computational results of a circuit implementing an estimation according to at least one of a Kalman filter, an extended Kalman filter, an unscented Kalman filter, a particle filter. 13. The method of claim 12, wherein the cost function is based on at least one of a mean square of a difference between the reference signal data and the estimated state data, a mean square of a difference between the reference signal data and the output data, and a mean square of a difference between output data corresponding to the estimated state data and the output data. 14. The method of claim 13, wherein said evolutionary algorithm comprises at least one of a genetic algorithm, a particle swarm optimization algorithm, an ant colony optimization algorithm, an artificial bee colony algorithm, a biogeography-based optimization algorithm, a quantum-inspired evolutionary algorithm, an immune quantum-inspired evolutionary algorithm, an estimation-of-distribution algorithm, a fireworks algorithm, differential evolution algorithms, and evolution strategy algorithms 15. The method of claim 14, wherein said one or a plurality of parameters of a system comprises at least one of the entries of covariance matrices of process noise and measurement noise. 16. A method for online adjusting parameters representing a covariance matrix of measurement noise of a system having an input-state-output mathematical model in which the state at each time t is represented by a column vector, denoted by x(t), comprising state variables at time t, and the output at time t is represented by a column vector, denoted by y(t), and the state vector x(t) at time t and the output vector y(t) at time t are mathematically related by y(t)=C(t)x(t)+Z(t), where C(t) is a measurement matrix at time t, C(t)x(t) denotes pre-multiplying x(t) by C(t), and Z(t) represents the measurement noise at time t, the method comprising: installing an online estimator circuit that estimates state variables of the system, estimates covariance matrices of state variables of the system, and maintains in said circuit's memory a subset of estimated values of the state variables, estimated values of the states' covariance matrices, and measured output variables associated with one or a plurality of time instants; for each time instant, s that is in a subset, T, of time instants associated with which said estimated values of the state variables, said estimated values of the states' covariance matrices, and said measured output variables are in said circuit's memory, performing steps of: a) pre-multiplying the estimated value of the state vector x(s) at time s by the matrix C(s); b) from measurement vector, y(s), at time s, subtract the column vector resulting from step a); c) transposing the column vector resulting from step b) to a row vector; d) post-multiplying the column vector resulting from step b) with the row vector resulting from step c); e) pre-multiplying the estimated value of the covariance matrix of x(s) by the C(s), the measurement matrix at time s; f) post-multiplying the matrix resulting from step e) by the transpose of the matrix C(s); g) subtracting the matrix resulting from step f) from the matrix resulting from step d); Computing a weighted average of matrices resulting from step e) at time instants in said subset denoted by T. 17. A method for online adjusting parameters representing a covariance matrix, denoted by Q, of process noise of a system having a discrete-time input-state-output mathematical model in which discrete times are represented by a sequence of integers; the state at each time t is represented by a column vector, denoted by x(t), comprising state variables at time t; the output at time t is represented by a column vector, denoted by y(t); the input at time t is represented by a column vector, denoted by u(t); the state vector x(t) at time t and the state vector x(t+1) at time t+1 are mathematically related by x(t+1)=h(x(t),u(t))+W(t), where h(,) is a known mapping and W(t) represents the process noise at time t, the method comprising: at each discrete time N at which said parameters are adjusted, installing an online estimator circuit that estimates at each discrete time t the state vector x(t−1) and state vector x(t) on the basis of available output data y(0), y(1), . . . , y(t) and maintains in the circuit's memory the estimate of x(s−1) made at time s, {circumflex over (x)}[s−1|s], and the estimate of x(s) made at time s, {circumflex over (x)}[s|s] for each of s=t−K,t−K+1, . . . ,t−1,t for a predetermined finite integer K; at each discrete time t at which said parameters are adjusted, comprising steps of: a) computing {circumflex over (x)}[s|s]−h({circumflex over (x)}[s−1|s],u[s−1]) for s=t−K,t−K+1, . . . ,t−1,t; b) transposing {circumflex over (x)}[s|s]−h({circumflex over (x)}[s−1|s],u[s−1]) to a row vector {{circumflex over (x)}[s|s]−h({circumflex over (x)}[s−1|s],u[s−1])}T for s=t−K,t−K+1, . . . ,t−1,t c) performing matrix multiplication {{circumflex over (x)}[s|s]−h({circumflex over (x)}[s−1|s],u[s−1])}{{circumflex over (x)}[s|s]−h({circumflex over (x)}[s−1|s],u[s−1])}T for s=t−K,t−K+1, . . . ,t−1,t; computing a weighted average of the results in step c) over s=t−K,t−K+1, . . . ,t−1,t 18. The method of claim 17, wherein said estimator circuit performs at least one of of a Kalman filter, an extended Kalman filter, an unscented Kalman filter, a particle filter.