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In this paper we consider piecewise affine differential equations modeling gene networks. We work with arbitrary decay rates, and under a local hypothesis expressed as an alignment condition of successive focal points. The interaction graph…
We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables…
We present a method for representing the closed-loop dynamics of piecewise affine (PWA) systems with bounded additive disturbances and neural network-based controllers as mixed-integer (MI) linear constraints. We show that such…
Piecewise affine (PWA) systems are widely applied in many practical cases such as the control of nonlinear systems and hybrid dynamics. However, most of the existing PWA control methods have poor scalability with respect to the number of…
Piecewise affine (PWA) systems are widely used to model highly nonlinear behaviors such as contact dynamics in robot locomotion and manipulation. Existing control techniques for PWA systems have computational drawbacks, both in offline…
We propose a piecewise learning framework for controlling nonlinear systems with unknown dynamics. While model-based reinforcement learning techniques in terms of some basis functions are well known in the literature, when it comes to more…
Neural networks (NN) have been successfully applied to approximate various types of complex control laws, resulting in low-complexity NN-based controllers that are fast to evaluate. However, when approximating control laws using NN,…
This paper presents a novel approach for distributed model predictive control (MPC) for piecewise affine (PWA) systems. Existing approaches rely on solving mixed-integer optimization problems, requiring significant computation power or…
Constrained model predictive control (MPC) is a widely used control strategy, which employs moving horizon-based on-line optimisation to compute the optimum path of the manipulated variables. Nonlinear MPC can utilize detailed models but it…
Symbolic models have been recently used as a sound mathematical formalism for the formal verification and control design of purely continuous and hybrid systems. In this paper we propose a sequence of symbolic models that approximates a…
PieceWise Affine (PWA) approximations for nonlinear functions have been extensively used for tractable, computationally efficient control of nonlinear systems. However, reaching a desired approximation accuracy without prior information…
Model inversion is a fundamental technique in feedforward control. Unstable inverse models present a challenge in that useful feedforward control trajectories cannot be generated by directly propagating them. Stable inversion is a process…
Online model predictive control (MPC) for piecewise affine (PWA) systems requires the online solution to an optimization problem that implicitly optimizes over the switching sequence of PWA regions, for which the computational burden can be…
This paper presents a novel approach to ensure the safety of continuous-time linear dynamical systems controlled by a neural network (NN) based state-feedback. Our method capitalizes on the use of continuous piece-wise affine (PWA)…
The switch-like character of gene regulation has motivated the use of hybrid, discrete-continuous models of genetic regulatory networks. While powerful techniques for the analysis, verification, and control of hybrid systems have been…
To promote the widespread use of mobile robots in diverse fields, the performance of trajectory tracking must be ensured. To address the constraints and nonlinear features associated with mobile robot systems, we apply nonlinear model…
We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced…
Hybrid systems have steadily grown in popularity over the last few decades because they ease the task of modeling complicated nonlinear systems. Legged locomotion, robotic manipulation, and additive manufacturing are representative examples…
In the context of studying periodic processes, this paper investigates first under which conditions switching affine systems in the plane generate stable limit cycles. Based on these conditions, a design methodology is proposed by which the…
The fundamental problem of stabilizing a general nonaffine continuous-time nonlinear system is investigated via piecewise affine linear models (PALMs) in this article. A novel integral sliding-mode parallel control (ISMPC) approach is…