Florin Stoican

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.

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.

Necessary and sufficient conditions for sensor recovery in a multisensor control scheme

Abstract The present paper deals with a multisensor scheme based on a switching control strategy. Fault tolerance guarantees were obtained in this framework lately upon the characterization of invariant sets for state estimations in healthy and faulty functioning. A source of conservativeness of this approach is related to the issue of sensor recovery. Indeed, in the previous work, it was supposed that the sensors are functioning under healthy dynamics for a long enough time, in order to enter the respective invariant sets, before being considered for feedback. In the current paper we present necessary and sufficient conditions for the acknowledgement of sensor recovery and the reintegration of sensors in the closed-loop decision making mechanism.

Zonotopic ultimate bounds for linear systems with bounded disturbances

Abstract This paper deals with robust invariant sets construction for discrete-time linear time-invariant dynamics. The case of a zonotopic disturbance set is analysed in detail by exploiting the properties of these geometrical structures. A constructive method is provided for diminishing the conservatism of ultimate bound invariant sets. It is shown that the resulting zonotopic set is related to the minimal robust positively invariant set in the sense that their boundaries have common points.

On the design of exact penalty functions for MPC using mixed integer programming

Abstract Soft constraints and penalty functions are commonly used in MPC to ensure that the optimization problem has a feasible solution, and thereby avoid MPC controller failure. On the other hand, soft constraints may allow for unnecessary violations of the original constraints, i.e., the constraints may be violated even if a valid solution that does not violate any constraints exists. The paper develops procedures for the minimizing (according to some norm) of the Lagrange multipliers associated with a given mp-QP problem, assumed to originate from an MPC problem formulation. To this end the LICQ condition is exploited in order to efficiently formulate the optimization problem, and thereby improve upon existing mixed integer formulations and enhance the tractability of the problem. The results are used to design penalty functions such that corresponding soft constraints are made exact, that is, the original (hard) constraints are violated only if there exists no solution where all constraints are satisfied.

Persistently Exciting Model Predictive Control for SISO systems

Abstract A formulation of Persistently Exciting Model Predictive Control (PE-MPC) for Single-Input Single-Output (SISO) systems is presented. PE-MPC is an extension of a conventional model predictive control where a Persistence of Excitation Condition (PEC) is included as inequality constraint, to allow for adaptive implementation and on-line tuning of the model. The PEC makes the PE-MPC feasible region non-convex. For SISO systems the non-convex region can be represented as the union of two convex regions. Therefore an ad-hoc solution of the PE-MPC optimization problem can be efficiently computed. This is done by exploiting the particular structure of the PEC constraint. Finally a numerical example of SISO sytem is given and several scenarios are simulated to analyze the PE-MPC properties.

Enhancements on the hyperplane arrangements in mixed integer techniques

The current paper addresses the problem of optimizing a cost function over a non-convex and possibly non-connected feasible region. A classical approach for solving this type of optimization problem is based on Mixed integer technique. The exponential complexity as a function of the number of binary variables used in the problem formulation highlights the importance of reducing them. Previous work which minimize the number of binary variables is revisited and enhanced. Practical limitations of the procedure are discussed and a typical control application, the control of Multi-Agent Systems is exemplified.

Reference governor for tracking with fault detection capabilities

This paper presents a fault tolerant multisensor strategy for feedback control of a class of nonlinear systems upon a geometrical approach. A key point to ensure fault tolerance is the separation between healthy and faulty closed-loop behavior. Here we achieve this through set theoretic operations upon sets describing the healthy/faulty behavior of the system. The results rely both on an appropriate choice for the exogenous signals and on fixed point conditions for a nonlinear mapping which describes the gap between the nonlinear system and a linearized model in the functioning interval. A reference governor is employed such that, under a receding horizon technique, only feasible exogenous signals are provided to the system.