Automatic control software synthesis for quantized discrete time hybrid systems

Abstract

Many Embedded Systems are indeed Software Based Control Systems, that is control systems whose controller consists of control software running on a microcontroller device. This motivates investigation on Formal Model Based Design approaches for automatic synthesis of embedded systems control software. This paper addresses control software synthesis for discrete time nonlinear systems. We present a methodology to overapproximate the dynamics of a discrete time nonlinear hybrid system H by means of a discrete time linear hybrid system L H , in such a way that controllers for L H are guaranteed to be controllers for H. We present experimental results on the inverted pendulum, a challenging and meaningful benchmark in nonlinear Hybrid Systems control.

A Map-Reduce Parallel Approach to Automatic Synthesis of Control Software

“…Such transition relation is not linear, as it contains the function sin x 1 . A linear model can be found by under-and over-approximating the non-linear function sin x on different intervals for x. Namely, we may proceed as follows [13]. First of all, in order to exploit sinus periodicity, we consider the equation x 1 = 2πy k + y α , where y k represents the period in which x 1 lies and y α ∈ [−π, π] 1 represents the actual x 1 inside a given period.…”

On-the-Fly Control Software Synthesis

“…Control software synthesis from formal system level specifications for Discrete Time (possibly non Linear) Hybrid Systems has been investigated in [25,26,3,2]. The on-the-fly algorithm presented here improves on the one in [25,26] by reducing of about 99% the time to terminate when it cannot find a controller, possibly at a price of a 25% time penalty when it can find one.…”

“…The inverted pendulum (see Fig. 2) is a classical, hard control problem [22] whose DTLHS formulation is far from trivial [2]. The inverted pendulum is modeled by taking the angle θ and the angular velocityθ as state variables and the torquing force u · F as the system input.…”

“…4.1, where the state variables bounds are fixed as follows: c x1 = −1.1π radiants, d x1 = 1.1π radiants, c x2 = −4 radiants per second, d x2 = 4 radiants per second. As for pendulum parameters, we set F = 0.5 N and, as in [22,2,3], we set l and m in such a way that g l = 1 (i.e. l = g) and 1 ml 2 = 1 (i.e.…”

Patient-specific models from inter-patient biological models and clinical records

“…In a discrete time setting this problem has been addressed, for piecewise affine systems and safety properties, in [30], [2], [1], [31], [4], [3], [32], [8].…”