A tool to analyze robust stability for constrained nonlinear MPC

Santos, Lino O.; Biegler, Lorenz T.; Castro, José Almiro A. M.

doi:10.1016/j.jprocont.2007.10.004

Cited by 12 publications

(12 citation statements)

References 11 publications

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“…This formulation comprises two types of constraints as described in [50] to enforce the nominal stability of the NMPC controller, the terminal cost term in (28) and the terminal state constraint (31c). At this point we are not considering any additional bounds and/or constraints on the problem solution.…”

Section: Model Predictive Control Problem Statementmentioning

confidence: 99%

“…Regarding the developments of the robust stability analysis in the next sections it is essential to list here the main assumptions on which that analysis is based [49,50]. …”

Section: Assumptionsmentioning

confidence: 99%

“…In order to ensure stability of MPC under mismatch we essentially will follow the arguments given by [49,50]. The outcome of the approach will be a criterion on the objective function value of problem (31) which when satisfied it will ensure its decrease along the computed trajectories and therefore stability of the closed-loop system.…”

Section: Mismatch Casementioning

confidence: 99%

“…In this work a sufficient condition for robust stability of nominal MPC with modeling error similar to the one proposed in [49,50] will be extended to the application of MPC of dissipative distributed process systems. It will be employed to select a reduced order model of the plant among a sequence of possible approximations so that the stabilizing properties of MPC are preserved despite uncertainties and disturbances.…”

Section: Introductionmentioning

confidence: 99%

“…It will be employed to select a reduced order model of the plant among a sequence of possible approximations so that the stabilizing properties of MPC are preserved despite uncertainties and disturbances. The authors in [49,50] address the question of how much mismatch a given MPC algorithm can tolerate and how it can be assessed for stability of the MPC controller. Then an off-line procedure is developed to evaluate constants which determine sufficient conditions for robust stability.…”

Section: Introductionmentioning

confidence: 99%

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A robust multi-model predictive controller for distributed parameter systems

García

Vilas²,

Santos

et al. 2012

Journal of Process Control

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Section: Model Predictive Control Problem Statementmentioning

confidence: 99%

“…Regarding the developments of the robust stability analysis in the next sections it is essential to list here the main assumptions on which that analysis is based [49,50]. …”

Section: Assumptionsmentioning

confidence: 99%

Section: Mismatch Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A robust multi-model predictive controller for distributed parameter systems

García

Vilas²,

Santos

et al. 2012

Journal of Process Control

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Dynamic Modeling and Simulation for Robust Control of Distributed Processes and Bioprocesses

Alonso¹,

García²,

Vilas³

2010

Process Systems Engineering

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370 11 Dynamic Modeling and Simulation for Robust Control dimensional space of particle positions and velocities into a reduced order formulation which usually takes the form of the Boltzmann equation. Finally, coarse graining methods will zoom out the view point of the system and take the description back to the mesoscopic and macroscopic world of continuum [29].One conclusion to be drawn from this picture is that for any given time and length scales there will be a number of states dynamically active, coupled with others either relaxed (those states active at shorter scales) or frozen (as they are associated with much slower dynamics). Mathematically, such description translates into a highly coupled stiff system obeying a nonlinear set of algebraic, partial, and ordinary differential equations, which is usually difficult to solve. In this way, the stiffness of the resulting problem is the effect of the diversity of time scales coexisting in the system. From a control point of view or even from the more general perspective of "decision making," stiffness must be avoided, what calls for model reduction methods able to provide the simplest robust dynamic description representative of the system at the scales of interest.The application to process control should be considered not just in the restricted sense of a PID regulator or any other such device equipped with a "compensation" rule which responds to deviations between the prescribed operation condition and the current one. From a broader perspective a controller consists of a virtual representation of the system one wants to operate (the plant), and a sort of agent which at regular time instants inspects the current state of the process and employs the system representation to screen future scenarios by asking whether a given decision should be made or not. Once the best possible action is found, the agent implements it in the real plant and waits for the response given by the sensors to initiate further corrective actions. This logic, properly repeated during the process operation, is what is known as a feedback control scheme. In its simple version a PID contains one such representation of the linear dynamic range, which in this case is explicitly inverted in some smart way as the internal model control (IMC) theory clearly highlights [39].More sophisticated control algorithms will also share the same construction logic, namely a virtual representation of the system dynamics, an agent devising future operation, and a comparison rule which evaluates the real effect of the control actions on the process. Such control methods would include adaptive control [41], feedback linearization control [34], slide mode control [48], or model predictive control (MPC) in all its flavors (linear, nonlinear, constrained, etc.) [23,32,42].In constructing a reliable dynamic representation for the system to be controlled, and depending on the class of description employed, there are a wide variety of methods at hand. However, they all rely on the very same basic principle, n...

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Optimal control applications and methods literature survey (No. 6)

2008

Optim Control Appl Methods

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A tool to analyze robust stability for constrained nonlinear MPC

Cited by 12 publications

References 11 publications

A robust multi-model predictive controller for distributed parameter systems

A robust multi-model predictive controller for distributed parameter systems

Dynamic Modeling and Simulation for Robust Control of Distributed Processes and Bioprocesses

Optimal control applications and methods literature survey (No. 6)

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