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This paper deals with the problem of parametric piecewise quadratic programming (in which the cost is a piecewise quadratic function of both the decision variable and a parameter) and the problem of parametric piecewise affine quadratic programming (in which both the cost and the constraint depend on a piecewise affine function of the decision variable and a parameter). Parametric programming seeks...
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...
Synthesis methods for the construction of invariant sets for delay difference equations (DDEs) suffer either from computational complexity, i.e., those based on the Krasovskii approach, or come with considerable conservatism, i.e., those based on the Razumikhin approach. This paper utilizes the concepts of vector Lyapunov functions and set-dynamics in order to introduce a novel notion of invariance...
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