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This dissertation is concerned with constrained control problems and two types of problems are addressed: control problems with smooth state constraints and control problems with state constraints and smooth input constraints. For the control problems with state constraints, the dynamical system with state constraints is converted into another dynamical system of higher dimension with equality constraints on the initial states. For dynamical systems with multiple constraints and/or multiple inputs, the slack variable method is extended to address this case. It is shown that by proper choice of the slack variables, the resulting dynamical system can be reduced to its original order. Also, the application of feedback linearization for the systems which result from applying the slack variable method is examined. It was found that by input-output feedback linearization the order of the resulting dynamical system is reduced to at least its original order. For control problems with state and input constraints, necessary conditions for the existence of a solution are derived. In this case, the smoothness of the state constraint is relaxed. A solution for the minimum time control problem for a second order system in Brunovsky form subject to state and input constraints is presented. Moreover, some collision a voidance problems for robotic manipulators are formulated in the context of a control problem with state and input constraints. |
