Modeling and Control of Hybrid Systems: A Survey

Labinaz, G.; Bayoumi, M.M.; Rudie, Karen

doi:10.1016/s1474-6670(17)58427-x

Cited by 61 publications

(53 citation statements)

References 31 publications

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“…Systems with purely discrete state dynamics are often modeled by a finite state automaton or a Petri-Net. Interconnections of these very different system descriptions are denoted as hybrid dynamical systems and a variety of modeling paradigms have been proposed for which we refer to [14,23,30,35,39]. The hybrid modeling approach presented here is rooted in the theory of continuous dynamical systems and includes discrete system elements such as discontinuous nonlinearities and switching actions as extensions to these systems.…”

Section: Fig 1 Hybrid Dynamical System (Hds) With Continuous Variabmentioning

confidence: 99%

“…The investigation of hybrid systems attempts to effectively unite these two formalisms in order to model, investigate, and design these systems with analytical and numerical tools. The attempt to provide a unified hybrid modeling scheme well-suited to the study of hybrid dynamical systems has inspired many researchers [4,14,16,23,30,35,36,40], including the hybrid modeling approach presented here which is based on previous work in [18]. The characteristic behavior of hybrid systems is discussed and illustrated using this modeling scheme.…”

Section: Introductionmentioning

confidence: 99%

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

Buss

Glocker

Hardt

et al. 2002

Modelling, Analysis, and Design of Hybrid Systems

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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.

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Section: Fig 1 Hybrid Dynamical System (Hds) With Continuous Variabmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Buss

Glocker

Hardt

et al. 2002

Modelling, Analysis, and Design of Hybrid Systems

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“…The discrete state dynamics may be modeled, e.g., by a finite state automaton or a Petri-net. For some modeling paradigms of hybrid dynamical systems see, e.g., [4,10,17,21,26].…”

Section: Hybrid Optimal Controlmentioning

confidence: 99%

Towards Hybrid Optimal Control

Buss¹,

Stryk²,

Bulirsch³

et al. 2000

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In this article a general class of hybrid optimal control problems with continuous and discrete state variables and control inputs is defined. After a brief review of conventional optimal control, major novel challenges resulting from the hybrid nature are discussed. Some application problems are comparatively easy to solve because of the fixed or known sequence of discrete events; however, if the number and the sequence of discrete phases is not known a priori, the solution must then be found among a combinatorial number of possible sequence candidates. The article presents several preliminary approaches to the (numerical) solution of hybrid optimal control problems by hybrid dynamic programming, by decomposition using branch-and-bound, or fixing transversality conditions to obtain suboptimal solutions. The last two methods rely on the capabilities of the direct collocation method DIRCOL to solving multi-phase optimal control problems robustly and efficiently. Results obtained by the proposed methods are presented in two examples: an underactuated robotic system with a holding brake as the discrete component, and a hybrid, motorized traveling salesman problem.

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“…Hybrid systems have attracted the interest of many researchers, because they can capture in a single model the interaction between continuous and discrete-valued dynamics. Various models for hybrid system have been proposed (Labinaz et al, 1997), (Lygeros et al, 1999), and the research focused on the investigation of basic properties such as stability (Branicky, 1998), controllability and observability (Bemporad et al, 2000), and the development of control (Bemporad and Morari, 1999) (Lygeros et al, 1999), state estimation (FerrariTrecate et al, 2002a) and verification (Alur et al, 1996) schemes. We will use discrete-time hybrid systems in the Mixed Logical Dynamical (MLD) form (Bemporad and Morari, 1999) for two reasons: first, they provide a general framework for modelling many discrete features of CCPPs, including the coordination and prioritization between different devices; second, they are suitable to be used in on-line optimization schemes.…”

Section: Introductionmentioning

confidence: 99%

Modelling and Control of Co-Generation Power Plants Under Consideration of Lifetime Consumption: A Hybrid System Approach

Ferrari-Trecate

Gallestey

Stothert

et al. 2002

IFAC Proceedings Volumes

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In this paper the load optimization of a combined cycle power plant under consideration of the real cost of lifetime usage is accomplished by exploiting hybrid systems, i.e., systems evolving according to continuous dynamics, discrete dynamics, and logic rules. The possibility of turning on/off the gas and steam turbines, the operating constraints (minimum up and down times) and the different types of start up of the turbines characterize the hybrid behavior of a combined cycle power plant. In order to model both the continuous/discrete dynamics and the switching between different operating conditions we use the framework of Mixed Logic Dynamical systems. Next, we recast the economic optimization problem as a Model Predictive Control (MPC) problem, that allows us to optimize the plant operations by taking into account the time variability of both prices and electricity/steam demands. Because of the presence of integer variables, the MPC scheme is formulated as a mixed integer linear program that can be solved in an efficient way by using commercial solvers.

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Modeling and Control of Hybrid Systems: A Survey

Cited by 61 publications

References 31 publications

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

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

Towards Hybrid Optimal Control

Modelling and Control of Co-Generation Power Plants Under Consideration of Lifetime Consumption: A Hybrid System Approach

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