Sorin Olaru

Positive invariant sets for fault tolerant multisensor control schemes

This article deals with fault tolerant multisensor control schemes for systems with linear dynamics. Positive invariance is a common analysis and control design tool for systems affected by bounded constraints and disturbances. This article revisits the construction of ε-approximations of minimal robust positive invariant sets for linear systems upon contractive set-iterations. The cases of switching between different sets of disturbances and the inclusion of a predefined region of the state space are treated in detail. All these results are used in multisensor control schemes which have to deal with specific problems originated by the switching between different estimators and by the presence of faults in some of the sensors. The construction of positive invariant sets for different operating regimes provides, in this context, effective fault detection information. Within the same framework, global stability of the switching strategies can be assured if the invariant sets topology allows the exclusive selection of estimates obtained from healthy sensors.

Technical communique: On polytopic inclusions as a modeling framework for systems with time-varying delays

One of the important issues in networked control systems is the appropriate handling of the nonlinearities arising from uncertain time-varying delays. In this paper, using the Cayley-Hamilton theorem, we develop a novel method for creating discrete-time models of linear systems with time-varying input delays based on polytopic inclusions. The proposed method is compared with existing approaches in terms of conservativeness, scalability and suitability for controller synthesis.

Predictive control for linear systems with delayed input subject to constraints

Abstract The paper deals with the moving horizon control of systems subject to input delays and affected by input and state and/or output constraints. The robustness of the control law with respect to the uncertainties introduced by the discretization is considered. The stability of the closed-loop system is guaranteed by forcing the state trajectories to attain a robust positively invariant terminal set on the prediction horizon. Illustrative examples complete the paper.

A parameterized polyhedra approach for explicit constrained predictive control

The elaboration of an explicit description for the constrained model based predictive control laws is a useful alternative to the usually time-consuming on-line optimization methods. The paper presents a geometrical approach in this direction based on parameterized polyhedra. Subdomains in the parameters space and the correspondent linear affine laws are defined based on the parameterized vertices and their validity domains. The theoretical insight for the overall control law is brought through a double description (constraints-generators) of the feasible domain. The gain in computational effort is due to a hierarchic organization of the piecewise affine controllers.

Implicit improved vertex control for uncertain, time-varying linear discrete-time systems with state and control constraints

The problem of regulating an uncertain and/or time-varying linear discrete-time system with state and control constraints to the origin is addressed. It is shown that feasibility and a robustly asymptotically stable closed loop can be achieved using an interpolation technique. The design method can be seen as an alternative to optimization-based control schemes such as Robust Model Predictive Control. Especially for problems requiring complex calculations to find the optimal solution, the present method can provide a straightforward suboptimal solution. A simulation demonstrates the performance of this class of constrained controllers.

Avoiding constraints redundancy in predictive control optimization routines

This note concentrates on removing redundancy in the set of constraints for the multiparametric quadratic problems (mpQP) related with the constrained predictive control. The feasible domain is treated as a parameterized polyhedron with a focus on its parameterized vertices. The goal is to find a splitting of the parameters (state) space corresponding to domains with regular shape (nonredundant constraints), resulting in a table of regions where the constraints have a minimal representation, so that the online optimization routines can act with better performances. The procedure can be seen as a preprocessor either for the classical QP methods or for the routines based on explicit solutions. For important degrees of redundancy, the proposed technique may bring computational gains for real-time application or on the complexity of the positioning mechanism for evaluating the explicit solution.

Fault Tolerant Control Allowing Sensor Healthy-to-Faulty and Faulty-to-Healthy Transitions

In this paper, we present a new sensor fault tolerant control scheme for linear, discrete-time systems. The scheme consists of a bank of estimators, each associated with a sensor or group of sensors, a mechanism for the detection and identification of sensor transitions from healthy-to-faulty and faulty-to-healthy operation, an estimate reconfiguration module, and an estimate-based feedback controller with reference tracking. The detection and identification approach is based on the separation of “healthy” and “faulty” sets, where appropriately selected residual variables remain under healthy or faulty operation, from “after-fault” and “after-recovery” sets, towards which the residual variables “jump” when abrupt sensor faults or recoveries occur in one or more groups of sensors. This “set-separation” approach provides pre-checkable fault tolerance guarantees whenever certain conditions, given in terms of systems known data such as plant and estimator dynamics and bounds on reference and disturbance signals, are satisfied.

Adaptation of set theoretic methods to the fault detection of a wind turbine benchmark

Abstract The last decade has seen the emergence of set-theoretic methods in fault detection and identification mechanisms. These techniques are seen as restrictive and mathematically challenging due to the strict conditions (e.g. signal boundedness) imposed for reactivity to faults by means of set separation. The present paper aims at implementing such methods to a practical application proposed by a wind turbine benchmark setup. It is shown that strict boundedness conditions can be adjusted in order to obtain robust fault detection.

Enhancements on the Hyperplanes Arrangements in Mixed-Integer Programming Techniques

This paper is concerned with improvements in constraints handling for mixed-integer optimization problems. The novel element is the reduction of the number of binary variables used for expressing the complement of a convex (polytopic) region. As a generalization, the problem of representing the complement of a possibly not connected union of such convex sets is detailed. In order to illustrate the benefits of the proposed improvements, a typical control application, the control of multiagent systems using receding horizon optimization techniques, is considered.

On the hyperplanes arrangements in mixed-integer techniques

This paper is concerned with the improved constraints handling in mixed-integer optimization problems. The novel element is the reduction of the number of binary variables used for expressing the complement of a convex (polytopic) region. As a generalization, the problem of representing the complement of a possibly non-connected union of such convex sets is detailed. In order to illustrate the benefits of the proposed improvements, a practical implementation, the problem of obstacle avoidance using receding horizon optimization techniques is considered.