Recent developments in the control of constrained hybrid systems

Morari, Manfred; Barić, Miroslav

doi:10.1016/j.compchemeng.2006.05.041

Cited by 59 publications

(19 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Then, the maximal robust stabilizable set ( ) X ∞ Ω can be computed through the iterative solution to (3) and is summarized in the following algorithm:…”

Section: Computation Of Maximal Robust Stabilizable Setmentioning

confidence: 99%

See 1 more Smart Citation

Robust low complexity predictive control of constrained piecewise affine systems with bounded disturbances

2010

Int. J. Control Autom. Syst.

View full text Add to dashboard Cite

A robust low complexity model predictive control (MPC) scheme, referred to as robust onestep control, is proposed for constrained piecewise affine (PWA) systems with bounded disturbances. First, the maximal robust stabilizable set is added into the MPC formulation to guarantee the robust feasibility and low complexity. Second, the robust stability is analyzed via linear matrix inequalities (LMI). Extensive numerical examples illustrate the low complexity of the proposed robust one-step control.

show abstract

“…Then, the maximal robust stabilizable set ( ) X ∞ Ω can be computed through the iterative solution to (3) and is summarized in the following algorithm:…”

Section: Computation Of Maximal Robust Stabilizable Setmentioning

confidence: 99%

“…Model predictive control, based on optimal control and receding horizon control (RHC) policy, of piecewise affine (PWA) systems have received considerable attention in the research community, since this system can approximate non-linear systems and because of their equivalence to many classes of hybrid systems [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

Robust low complexity predictive control of constrained piecewise affine systems with bounded disturbances

2010

Int. J. Control Autom. Syst.

View full text Add to dashboard Cite

show abstract

“…An example of such a system is MPC with a mixed logical dynamical (MLD) prediction model, that consists of linear dynamic equations that are subject to mixed-integer (continuous and integer) inequalities (Morari and Barić, 2006;Zabiri and Samyudia, 2006). Mixed integer programming methods are less efficient in terms of computational effort compared to continuous optimization problems.…”

Section: Hybrid Mpc Methodsmentioning

confidence: 99%

Gradient-based hybrid model predictive control using Time Instant Optimization for Dutch regional water systems

Dekens¹

2014

2014 European Control Conference (ECC)

View full text Add to dashboard Cite

Many areas in the Netherlands can be characterized as low-lying polder systems. In order to keep our feet dry, a lot of effort is put into ensuring the safety of the physical structures that protect us from flooding, such as dams and dikes. To control the water quantity and quality within the polders, hydraulic structures such as pumps and gates are in place. These can be operated to meet different requirements. Some of these structures are operated manually, but often the control has been automated. The operation of such structures is in many cases done by rule-based (if-then) operators, which base their control actions on a comparison of the current state (e.g. water levels) with the desired state. The field of operational water management aims at optimizing the control of these automated structures.Model Predictive Control (MPC) is an anticipatory control technique that originated in the process industries, and found its way into water management over the last one or two decades. This methodology uses a mathematical model of the controlled process and forecasts of future process states and external disturbances to determine the optimal sequence of control actions over a finite prediction horizon. The trade-off between different, often conflicting objectives of a controller is described mathematically in an objective function. At every time step, an optimization problem has to be solved by minimizing the objective function subject to constraints. Only the first control step is implemented, and the optimization starts again with updated measurements and predictions at the new time step.This thesis focusses on Dutch regional water systems. These systems are often low-lying polder-belt canal systems, where many pumps are needed to meet different requirements regarding water quantity and quality. The control of a complex water system, consisting of continuous dynamics (evolution of water flow and levels) and discrete elements (e.g. barriers and pumps that are operated on or off) can be optimized using a so-called hybrid Model Predictive Controller. However, particularly the optimization of the combination of discrete and continuous elements requires extensive computational effort. Even with the ongoing increase in computational power, computational time remains an issue for the optimization of large hybrid systems in real-time control applications.Time Instant Optimization MPC has been proposed in literature as an alternative to the computationally more demanding Mixed Logical Dynamical models. TIO-MPC involves the Master of Science ThesisBart Dekens ii optimization of a (a priori determined) number of time instants, which are the moments that a discrete variable changes its state. The rationale behind this approach is that in many cases, it is undesirable to have too many switching of controllers. This significantly reduces the amount of optimization variables, as the controller does not have to decide at every time step whether or not to switch the state of discrete variables. The latter would normally l...

show abstract

“…Bemporad and Morari (1999); Morari and Baric (2006)). Especially when combined with a model-predictive control (MPC) strategy, the MLD framework provides a powerful tool for a wide range of modeling and control tasks.…”

Section: Introductionmentioning

confidence: 99%

Predictive Control for Multi-Robot Observation of Multiple Moving Targets Based on Discrete-Continuous Linear Models

Kühn

Reinl

Stryk

2011

IFAC Proceedings Volumes

View full text Add to dashboard Cite

The observation of multiple moving targets by cooperating mobile robots is a key problem in many security, surveillance and service applications. In essence, this problem is characterized by a tight coupling of target allocation and continuous trajectory planning. Optimal control of the multi-robot system generally neither permits to neglect physical motion dynamics nor to decouple or successively process target assignment and trajectory planning. In this paper, a numerically robust and stable model-predictive control strategy for solving the problem in the case of discrete-time double-integrator dynamics is presented. Optimization based on linear mixed logical dynamical system models allows for a flexible weighting of different aspects and optimal control inputs for settings of moderate size can be computed in real-time. By simulating sets of randomly generated situations, one can determine a maximum problem size solvable in real-time in terms of the number of considered robots, targets, and length of the prediction horizon. Based on this information, a decentralized control approach is proposed.

show abstract

Recent developments in the control of constrained hybrid systems

Cited by 59 publications

References 36 publications

Robust low complexity predictive control of constrained piecewise affine systems with bounded disturbances

Robust low complexity predictive control of constrained piecewise affine systems with bounded disturbances

Gradient-based hybrid model predictive control using Time Instant Optimization for Dutch regional water systems

Predictive Control for Multi-Robot Observation of Multiple Moving Targets Based on Discrete-Continuous Linear Models

Contact Info

Product

Resources

About