Nonlinear Hybrid Dynamical Systems: Modeling, Optimal Control, and Applications

Abstract

Abstract. Nonlinear hybrid dynamical systems are the main focus of this paper. A modeling framework is proposed, feedback control strategies and numerical solution methods for optimal control problems in this setting are introduced, and their implementation with various illustrative applications are presented. Hybrid dynamical systems are characterized by discrete event and continuous dynamics which have an interconnected structure and can thus represent an extremely wide range of systems of practical interest. Consequently, many modeling and control methods have surfaced for these problems. This work is particularly focused on systems for which the degree of discrete/continuous interconnection is comparatively strong and the continuous portion of the dynamics may be highly nonlinear and of high dimension. The hybrid optimal control problem is defined and two solution techniques for obtaining suboptimal solutions are presented (both based on numerical direct collocation for continuous dynamic optimization): one fixes interior point constraints on a grid, another uses branch-and-bound. These are applied to a robotic multi-arm transport task, an underactuated robot arm, and a benchmark motorized traveling salesman problem.

Behaviour Prediction Framework in System Architecture Development

“…Two domains are usually considered as separate issues: structural complexity management models cannot describe the system's behaviour and dynamical system modelling methods cannot be applied to large scale or complex systems as it requires detailed and expensive process to acquire information about all interactions. One of the recent approaches to combine two domains is presented in work of Diepold et al [6] as a Multi-Dynamic Mapping framework (see Figure 1) between MultipleDomain Matrices [5] and Generalized Hybrid State Model [7]. Figure 1.…”

“…All parameters from equations (1)(2)(3)(4)(5)(6)(7)(8), depend on the properties of fluids (air and water), material (for air heaters), and on air heater design (dimensions of the case plate for air heater and moisturizer). With presented set of equations (1)(2)(3)(4)(5)(6)(7)(8) the mathematical model of the subsystems in state space is defined to be used for behaviour simulation in order to check performance stability.…”

Hybrid system identification using a structural approach and its model based control: An experimental validation

“…We motivate our method by considering the following switched nonlinear hybrid system [20], If the partition of the hybrid system is predetermined, as considered here, the identification problem reduces to estimating the 2 ns models of the PWA system. We assume that a linear affine model adequately describes the continuous state dynamics in each location.…”

“…(18)- (20). Repeating the procedure for all non-basis δ i , will yield the discrete-time models for all non-basis locations from the ns+1 basis models.…”

Optimal Task Allocation and Dynamic Trajectory Planning for Multi-Vehicle Systems Using Nonlinear Hybrid Optimal Control

“…The numerical solution approach consists of a decomposition of MBOCP in coupled discrete and dynamic optimization problems at outer and inner levels (see Buss et al (2002); von Stryk and Glocker (2001) for details). At the inner optimization level dynamic optimization problems are considered of which the nonlinear state dynamics is defined on multiple phases (Fig.…”