Reachability for piecewise affine systems is known to be undecidable, starting from dimension 2. In this paper we investigate the exact complexity of several decidable variants of reachability and control questions for piecewise affine systems. We show in particular that the region to region bounded time versions leads to NP -complete or co-NP -complete problems, starting from dimension 2.

The theory of differential inclusions provides certain sufficient conditons for the uniqueness of Filippov solutions such as one-sided Lipschitzian property or maximal monotone condition. When applied to piecewise affine dynamical systems, these conditions impose rather strong conditions. In this paper, we provide less restrictive conditions for uniqueness of Filippov solutions for the bimodal ...

In this paper we present a novel approach to the design of reference tracking controllers for constrained, discrete-time piecewise affine systems and apply it to a vehicle yaw control problem. The paper is divided in two parts. In the first part, we present a methodology for designing reference tracking controllers for constrained, discrete-time piecewise affine systems. The approach follows th...

Piecewise affine (PWA) systems is an important class of systems. In this paper we consider optimal control of constrained, discontinuous, discrete-time, piecewise affine systems with state and input dependent disturbances. We seek to pre-compute, via dynamic programming, an explicit control law for these systems when a piecewise affine cost function is utilized. The main difficulty with this pr...

Explicit MPC of constrained linear systems is known to result in a piecewise affine controller and therefore also piecewise affine closed loop dynamics. The complexity of such analytic formulations of the control law can grow exponentially with the prediction horizon. The suboptimal solutions offer a trade-off in terms of complexity and several approaches can be found in the literature for the ...

We consider the problem of designing piecewise affine policies for two-stage adjustable robust linear optimization problems under right-hand side uncertainty. It is well known that a piecewise affine policy is optimal although the number of pieces can be exponentially large. A significant challenge in designing a practical piecewise affine policy is constructing good pieces of the uncertainty s...

– We discuss a class of control problems for continuous time dynamical systems featuring synthesis of controllers to meet certain logic specifications. Such problems fall in the area of hybrid systems. Hybrid systems have been studied for some time; unfortunately the area has not delivered all that it promised: a theory of control synthesis has remained elusive. Some work has been done at the h...

This paper studies problems such as: given a discrete time dynamical system of the form x(t + 1) = f(x(t)) where f : R → R is a (possibly discontinuous) piecewise affine function, decide whether all trajectories converge to 0. We show in our main theorem (Theorem 2) that this Attractivity Problem is undecidable as soon as n ≥ 2. The same is true of two related problems: Stability (is the dynami...