A control problem for affine dynamical systems on a full-dimensional simplex

Given an affine system on a simplex, the problem of reaching a particular facet of the simplex, using affine state feedback is studied. Necessary and sufficient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the vertices of the simplex. If these conditions are met, a constructive procedure yields an affine feedback control law, that solves this reachability problem

Design of Wideband Fractional-Order Differentiator Using Interlaced Sampling Method

[[abstract]]In this paper, the design of a wideband digital fractional-order differentiator (FOD) is investigated. First, conventional FOD designs are reviewed, and the reconstruction formula of the interlaced sampling method is used to design the proposed wideband FOD by index substitution and the Gr?nwald–Letnikov fractional derivative. Because a closed-form window design is obtained, the filter coefficients are easily computed. Then, the weighted least squares and convex optimization methods are applied to design non-sparse digital FODs that are optimal in the least squares or min–max sense. Next, the iterative hard thresholding and orthogonal matching pursuit methods are used to design sparse digital FODs to reduce the implementation complexity. Finally, several numerical examples are presented to show that the proposed FODs have smaller design errors in the high-frequency band than conventional digital FODs that do not use the auxiliary interlaced sampling signal

Control of Piecewise-Affine Hybrid Systems - Extended abstract

The character of this paper is an extended abstract of the approach developed by the authors for control of piecewise-affine hybrid systems. Control of hybrid systems is a wide ranging research topic with many theoretical problems. The authors have therefore decided early on to restrict attention to piecewise-affine hybrid systems on polytopes. The approach developed includes for affine systems on polytopes sufficient conditions for the problems (1) leaving the polytope in finite time through a prespecified set of facets; (2) remaining inside a particular polytope forever; and (3) converging to a fixed state inside a particular polytope. For piecewise-affine hybrid system on polytopes a procedure for reachability and control synthesis is proposed consisting of (1) for each discrete state the computation of all possible exit facets and exit events; (2) abstraction of the continuous dynamics to an automaton; and (3) the search of a path in the automaton from an initial discrete state to a target discrete state. Open research issues for control of hybrid systems are stated