Methods and systems for backlash compensation. Restrictive assumptions on the backlash nonlinearity (e.g. the same slopes of the lines, etc.) are not required. The compensator scheme has dynamic inversion structure, with a neural network in the feedforward path that approximates the backlash inversi
Methods and systems for backlash compensation. Restrictive assumptions on the backlash nonlinearity (e.g. the same slopes of the lines, etc.) are not required. The compensator scheme has dynamic inversion structure, with a neural network in the feedforward path that approximates the backlash inversion error plus filter dynamics needed for backstepping design. The neural network controller does not require preliminary off-line training. Neural network tuning is based on a modified Hebbian tuning law, which requires less computation than backpropagation. The backstepping controller uses a practical filtered derivative, unlike the usual differentiation required by earlier backstepping routines. Rigorous stability proofs are given using Lyapunov theory. Simulation results show that the proposed compensation scheme is an efficient way of improving the tracking performance of a vast array of nonlinear systems with backlash.
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Methods and systems for backlash compensation. Restrictive assumptions on the backlash nonlinearity (e.g. the same slopes of the lines, etc.) are not required. The compensator scheme has dynamic inversion structure, with a neural network in the feedforward path that approximates the backlash inversi
Methods and systems for backlash compensation. Restrictive assumptions on the backlash nonlinearity (e.g. the same slopes of the lines, etc.) are not required. The compensator scheme has dynamic inversion structure, with a neural network in the feedforward path that approximates the backlash inversion error plus filter dynamics needed for backstepping design. The neural network controller does not require preliminary off-line training. Neural network tuning is based on a modified Hebbian tuning law, which requires less computation than backpropagation. The backstepping controller uses a practical filtered derivative, unlike the usual differentiation required by earlier backstepping routines. Rigorous stability proofs are given using Lyapunov theory. Simulation results show that the proposed compensation scheme is an efficient way of improving the tracking performance of a vast array of nonlinear systems with backlash. ed in claim 2, wherein the shopper identification data include data selected from the group consisting of name, street address, city, state, zip code, country, phone number, e-mail address, social security number, driver's license number, store registration name, and store registration password. 4. A computer system for using one or more virtual wish lists of one or more shoppers over one or more networks, as recited in claim 2, wherein the shopper demographic data are selected from the group consisting of gender, marital status, number of member in household, household income, residence ownership, monthly rent or mortgage, education level, employer, number of years with the current employer, race, religion, computer ownership, Internet-accessibility, and online shopping experience. 5. A computer system for using one or more virtual wish lists of one or more shoppers over one or more networks, as recited in claim 1, wherein said observation by said virtual wish list retrieval process comprises product identity, store identity, a time of the first visit to a Web page presenting the product, a time of a most recent visit to the Web page presenting the product, a total number of visits to the Web page presenting the product, and an interest level. 6. A computer system for using one or more virtual wish lists of one or more shoppers over one or more networks, as recited in claim 5, wherein the interest level of a shopper for a product is calculated by taking into account factors selected from the group consisting of a time of a first visit to the Web page presenting the product, a time of a most recent visit to the Web page presenting the product, a total number of visits to the Web page product, and which shopping steps the shopper reached for the product. 7. A computer system for using one or more virtual wish lists of one or more shoppers over one or more networks, as recited in claim 6, wherein the shopping steps of a product in one or more online stores comprise an impression of the product where the shopper sees a link to a product Web page, a click through where the shopper clicks on the link and examines the product Web page, a shopping cart placement where the shopper inserts one or more units of the product into the shopper's online shopping cart, and a purchase step where the shopper completes one or more transactions for purchasing the product. 8. A computer system for using one or more virtual wish lists of one or more shoppers over one or more networks, as recited in claim 1, wherein the online address book of a shopper comprises one or more address records for one or more people, each address record including any one or more of the following the person's name, title, affiliation, street address, city, state, zip code, state, country, phone number, and e-mail address. 9. A computer system for using one or more virtual wish lists of one or more shoppers over one or more networks, as recited in claim 1, wherein the recipient list of a shopper is a list of people for whom the shopper wants to purchase one or more products, and comprises recipients' identification information including their name and addresses and one or more shopping constraints. 10. A computer system for using one or more virtual wish lists of one or more shoppers over one or more networks, as recited in claim 1, wherein an actual wish list of a shopper comprises a shopper's identification information including one or more of the shopper's name, addresses, user name and password, and one or more records of products of interest, each record specifying a product with its identity, the time when the record was created, the occasion for the purchase of this product, if any, and one or more attributes of this product including price, size, color and brand. 11. A computer system for using one or more virtual wish lists of one or more shoppers over one or more networks, as recited in claim 1, wherein a merchandising effort of an online store includes cross-se
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