System and method for training a support vector machine (SVM) with process constraints. A model (primal or dual formulation) implemented with an SVM and representing a plant or process with one or more known attributes is provided. One or more process constraints that correspond to the one or more known attributes are specified, and the model trained subject to the one or more process constraints. The model includes one or more inputs and one or more outputs, as well as one or more gains, each a respective partial derivative of an output with respect to a respective input. The process constraints may include any of: one or more gain constraints, each corresponding to a respective gain; one or more Nth order gain constraints; one or more input constraints; and/or one or more output constraints. The trained model may then be used to control or manage the plant or process.