In robust control theory, an uncertain dynamical system is described by a set of models rather than a single model. For example, a system with an unknown parameter generates a set of models, one for each possible value of the parameter; likewise for a system with an unknown disturbance (which can be a function of time as well as state variables and control inputs). As a result, any map one might define for a single model becomes a set-valued map. Such is the case with an input/output map, a map from initial states to final states, or a map from disturbances to values of cost functionals. It is therefore natural that, in our study of robust nonlinear control, we use the language and mathematical apparatus of set-valued maps. In doing so, we follow the tradition started in the optimal control literature in the early sixties [27, 153] and continued in the control-related fields of nonsmooth analysis, game theory, differential inclusions, and viability theory [21, 127, 128, 5, 79].
KeywordsNeighborhood Versus Continuity Property Steiner Point Closed Unit Ball Selection Theorem
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