Invariant sets for constrained nonlinear discrete-time systems with application to feasibility in model predictive control

Kerrigan, Eric C.; Maciejowski, Jan M.

doi:10.1109/cdc.2001.914717

Cited by 137 publications

(100 citation statements)

References 15 publications

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“…In control theory, invariant sets are used to prove stability of model predictive control (also called receding horizon control), as shown in [3]. In [4] a nonlinear model predictive control framework is presented that guarantees nominal feasibility using invariant sets by providing necessary and sufficient conditions on the control horizon, the prediction horizon and the constraint set. Receding horizon control for UAVs based on mixed integer linear programming is presented in [5].…”

Section: Related Workmentioning

confidence: 99%

Online safety verification of trajectories for unmanned flight with offline computed robust invariant sets

Althoff

Scherer

2015

2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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Abstract-We address the problem of verifying motion plans for aerial robots in uncertain and partially-known environments. Thereby, the initial state of the robot is uncertain due to errors from the state estimation and the motion is uncertain due to wind disturbances and control errors caused by sensor noise. Since the environment is perceived at runtime, the verification of partial motion plans must be performed online (i.e. during operation) to ensure safety within the planning horizon and beyond. This is achieved by efficiently generating robust control invariant sets based on so-called loiter circles, where the position of the aerial robot follows a circular pattern. Verification of aerial robots is challenging due to the nonlinearity of their dynamics, the high dimensionality of their state space, and their potentially high velocities.We use novel techniques from reachability analysis to overcome those challenges. In order to ensure that the robot never finds itself in a situation for which no safe maneuver exists, we provide a technique that ensures safety of aerial robots beyond the planning horizon. Our method is applicable to all kinds of robotic systems that follow reference trajectories, such as bipedal robotic walking, robotic manipulators, automated vehicles, and the like. We evaluate our method by simulations of high speed helicopter flights.

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Section: Related Workmentioning

confidence: 99%

Online safety verification of trajectories for unmanned flight with offline computed robust invariant sets

Althoff

Scherer

2015

2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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“…Un enfoque diferente mediante el cual es posible analizar la Controlabilidad de Estado es por medio de los Mé-todos en Teoría de Conjuntos en Control (MTCC), la cual en los últimos años se ha venido utilizando en diferentes aplicaciones de control [13], [14], [15], [16]. Los MTCC son equivalentes a la controlabilidad de estado, tal como se demuestra en [17]; no obstante, los MTCC permiten no sólo determinar si la controlabilidad de estado se verifica o no, sino que además indica que tan controlable es el sistema dinámico y permite incluir las restricciones en los estados y en la acción de control de una manera natural [14].…”

Section: Controlabilidad De Estadosunclassified

“…En los últimos años, los métodos de teoría de conjuntos aplicados a control se han venido aplicando con éxito, especialmente en el diseño de controladores predictivos basados en modelos [13,14,15,16,17]. Los conjuntos permiten no sólo verificar que se cumpla o no la propiedad de controlabilidad, sino que además brinda una medida cuantitativa que permite estimar que tan controlable es el proceso, aportando por tanto mayores elementos de juicio a la hora de diseñar un sistema de control.…”

Section: Introductionunclassified

Diseño Simultáneo de Procesos y su control usando Teoría de Conjuntos

Alzate¹

2015

prospect

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RESUMENEn el diseño simultáneo de proceso se diseña al mismo tiempo el proceso y su sistema de control. En este artículo se presenta una metodología para el diseño simultáneo, basada en los Métodos de Teoría de Conjuntos en Control. En estos métodos además de verificar que la propiedad de controlabilidad se cumpla, es posible cuantificar la controlabilidad y por tanto, complementa el tratamiento clásico para la verificación de la propiedad de controlabilidad. La metodología propuesta se aplica con éxito al conocido problema de referencia (benchmark) del CSTR, y se observa que después de aplicada la metodología, se debe disminuir el volumen del reactor, con el fin de tener un mejor valor del indicador de controlabilidad, que se evidencia en un mejor desempeño del lazo cerrado.Palabras Clave: Diseño Simultáneo; Modelo Semifísico de Base Fenomenológica; Métodos de Teoría de Conjuntos en Control, Problema de referencia CSTR. ABSTRACTIn simultaneous design of process both the process and its control system at the same time are designed, but process' controllability in a binary way is evaluated. This paper introduces a methodology for simultaneous design, based on Set-Theoretic Methods in Control. In the given methods there is a different approach of understanding the process' state controllability, which is complementary to the classical look, because it is possible to quantify controllability. The proposed methodology is successfully applied to a CSTR's benchmark, and it is observed that after the methodology is applied, the reactor volume must be decreased, in order to get a best value of controllability's indicator, which it is evidenced in an improved performance of the closed loop.Key words: Simultaneous design; Phenomenological based semiphysical model; Set-Theoretic Methods in Control; CSTR Benchmark. INTRODUCCIÓNEl diseño de procesos y su control es un área de investigación que emerge debido a las altas exigencias del mercado en términos de consumo energético y de calidad. Estas exigencias, junto con la alta interacción dinámica de los procesos complejiza, no sólo el diseño mismo del proceso, sino también su control. Lo anterior ha ocasionado que la forma tradicional de diseñar procesos químicos y su control; esto es, de manera secuencial [1], [2], metodología en la cual primero se diseña el proceso de tal forma que se garanticen un criterio económico en el estado estacionario y luego se

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“…We apply this latter definition of S j . Methods to compute controlled invariant sets for LTI systems can be found in for instance [10]. Remark 1.…”

Section: Problem Descriptionmentioning

confidence: 99%

An exact penalty-function approach to proactive fault-tolerant economic MPC

Knudsen

Brusevold

Foss

2016

2016 European Control Conference (ECC)

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Abstract-This paper presents a fault-tolerant economic model predictive control scheme for proactive handling of incipient actuator faults. The scheme applies an 1 exact penalty function with a set of switching rules in order to steer the system by a minimum-time approach inside a controlled invariant set where stability of the system can be preserved during loss of actuation from the faulty actuator. We consider the approach for linear control systems, thereby allowing computation of a lower bound for the penalty parameter to ensure exactness of the penalty function. We prove nominal asymptotic stability of the modes of the proposed model predictive control scheme, and illustrate the approach by a numerical example.

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Invariant sets for constrained nonlinear discrete-time systems with application to feasibility in model predictive control

Cited by 137 publications

References 15 publications

Online safety verification of trajectories for unmanned flight with offline computed robust invariant sets

Online safety verification of trajectories for unmanned flight with offline computed robust invariant sets

Diseño Simultáneo de Procesos y su control usando Teoría de Conjuntos

An exact penalty-function approach to proactive fault-tolerant economic MPC

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