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In this paper we consider optimal control of constrained, discontinuous, discrete-time, piecewise affine systems with state and input dependent disturbances. We seek to precompute, via dynamic programming, an explicit control law for these systems when a piecewise affine cost function is utilized. The main difficulty with this problem class is that, even for initial states for which the value function...
A method for obtaining continuous solutions to convex quadratic and linear programs with parameters in the linear part of the objective function and right-hand side of the constraints is presented. For parameter values for which the problem has nonunique solutions, the optimizer with the least Euclidean norm is selected. The normal cone optimality condition is utilized to obtain a unique polyhedral...
Recent results in parametric mathematical programming established that the explicit piecewise affine solution to some optimal control problems can be defined on a partition of the state space. An optimal feedback control law is associated with each member of the state space partition. Instead of solving an optimization problem online at every time instant, the recent, so-called explicit, MPC schemes...
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