On Barriers in State and Input Constrained Nonlinear Systems

In this paper, the problem of state and input constrained control is addressed, with multidimensional constraints. We obtain a local description of the boundary of the admissible subset of the state space where the state and input constraints can be satisfied \emph{for all times}. This boundary is made of two disjoint parts: the subset of the state constraint boundary on which there are trajectories pointing towards the interior of the admissible set or tangentially to it; and a barrier, namely a semipermeable surface which is constructed via a minimum-like principle.Comment: 36 pages, 8 figures, submitte

Symmetry between constrained reference tracking and constrained state estimation

This paper exposes a symmetry relationship between constrained output reference tracking and constrained state estimation problems. The symmetry, which is different from the traditional duality relationship between control and estimation, is provided by means of two tables that give a complete translation of all variables of one problem into the variables of the other. An example is provided to illustrate the behaviour of the optimal solutions to the reference tracking and state estimation problems. The symmetry relationship leads to interesting interpretations of several of the resulting trajectories

Fault tolerant control using virtual actuators and invariant-set based fault detection and identification

In this paper we combine an invariant-set approach to fault detection and identification (FDI), recently proposed by the authors, with the virtual actuator approach to controller reconfiguration of Steffen, Lunze and co-authors. The FDI approach is based on the separation of invariant sets that characterise healthy system operation from invariant sets that characterise faulty operation. The derivation of these sets takes into account the closed-loop system reconfigured by means of the virtual actuator under all considered fault situations. We provide analytic conditions, in terms of closed-loop system parameters and bounds on external signals, which guarantee the aforementioned set separation and, thus, closed-loop stability of the scheme under all considered fault situations

Robust actuator fault compensation accounting for uncertainty in the fault estimation

We propose a fault tolerant control scheme that compensates for actuator faults by adjusting the controller gain based on an estimate of the fault magnitude. The scheme consists of a plant in closed loop with an observer-based feedback tracking controller, which is adapted to the fault situation diagnosed by a fault detection and isolation algorithm. We give conditions for correct fault detection and isolation and for robust closed-loop stability accounting for possible errors in the fault estimation

Actuator fault tolerant multi-controller scheme using set separation based diagnosis

We present a fault tolerant control strategy based on a new principle for actuator fault diagnosis. The scheme employs a standard bank of observers which match the different fault situations that can occur in the plant. Each of these observers has an associated estimation error with distinctive dynamics when an estimator matches the current fault situation of the plant. Based on the information from each observer, a fault detection and isolation (FDI) module is able to reconfigure the control loop by selecting the appropriate control law from a bank of controllers, each of them designed to stabilise and achieve reference tracking for one of the given fault models. The main contribution of this article is to propose a new FDI principle which exploits the separation of sets that characterise healthy system operation from sets that characterise transitions from healthy to faulty behaviour. The new principle allows to provide pre-checkable conditions for guaranteed fault tolerance of the overall multi-controller scheme

An Introduction to Constrained Control

An ubiquitous problem in control system design is that the system must operate subject to various constraints. Although the topic of constrained control has a long history in practice, there have been recent significant advances in the supporting theory. In this chapter, we give an introduction to constrained control. In particular, we describe contemporary work which shows that the constrained optimal control problem for discrete-time systems has an interesting geometric structure and a simple local solution. We also discuss issues associated with the output feedback solution to this class of problems, and the implication of these results in the closely related problem of anti-windup. As an application, we address the problem of rudder roll stabilization for ships

Robust MPC multicontroller design for actuator fault tolerance of constrained systems

In this paper, we present a robust actuator fault-tolerant control strategy for constrained linear systems, in the presence of bounded state and output disturbances. The scheme is based on a bank of state estimators which match different fault situations that can occur in the system. A fault detection and isolation (FDI) unit verifies that suitable residual variables lie inside pre-computed sets and selects the estimate that matches the current plant behaviour. A bank of robustly stabilising tube-based MPC control laws is designed, each associated to a fault scenario and the appropriate controller is selected among them using the information provided by the FDI module. By means of "tubes" of trajectories, we ensure robust closed-loop exponential stability of the constrained system and good performance in the fault-free case and under the occurrence of abrupt actuator faults

ROBUST MULTISENSOR FAULT TOLERANT MODEL–FOLLOWING MPC DESIGN FOR CONSTRAINED SYSTEMS

In this paper, a robust fault-tolerant control strategy for constrained multisensor linear systems, subject to sensor faults and in the presence of bounded state and output disturbances, is proposed. The scheme verifies that, for each sensors–estimator combination, suitable residual variables lie inside pre-computed sets and selects a more appropriate combination based on a chosen criterion. An active fault tolerant output feedback controller yields an MPC-based control law and, by means of the notion of a “tube ” of trajectories, we ensure robust closed-loop exponential stability and good performance in the fault-free case and under the occurrence of abrupt sensor faults

Robust MPC design for fault tolerance of constrained multisensor linear systems

In this paper, a robust fault-tolerant control strategy for constrained multisensor linear systems, subject to sensor faults and in the presence of bounded state and output disturbances is proposed. The scheme verifies that for each sensors estimator combination, suitable residual variables lie inside precomputed sets and selects the more appropriate combination based on a chosen criterion. An active fault tolerant output feedback controller yields an MPC-based control law and by means of the notion of “tube” of trajectories, we ensure robust closed-loop exponential stability and good performance in the fault-free case and under the occurrence of abrupt sensor faults

Multisensor fusion fault tolerant control

In this paper, a multisensor fusion fault tolerant control system with fault detection and identification via set separation is presented. The fault detection and identification unit verifies that for each sensor–estimator combination, the estimation tracking errors lie inside pre-computed sets and discards faulty sensors when their associated estimation tracking errors leave the sets. An active fault tolerant controller is obtained, where the remaining healthy estimates are combined using a technique based on the optimal fusion criterion in the linear minimum-variance sense. The fused estimates are then used to implement a state feedback tracking controller. We ensure closed-loop stability and performance under the occurrence of abrupt sensor faults. Experimental validation, illustrating the multisensor fusion fault tolerant control strategy is included