Robust Fault Diagnosis by Optimal Input Design for Self-sensing Systems

This paper presents a methodology for model based robust fault diagnosis and a methodology for input design to obtain optimal diagnosis of faults. The proposed algorithm is suitable for real time implementation. Issues of robustness are addressed for the input design and fault diagnosis methodologies. The proposed technique allows robust fault diagnosis under suitable conditions on the system uncertainty. The designed input and fault diagnosis techniques are illustrated by numerical simulation.Comment: Accepted in IFAC World Congress 201

Optimal control of linear, stochastic systems with state and input constraints

In this paper we extend the work presented in our previous papers (2001) where we considered optimal control of a linear, discrete time system subject to input constraints and stochastic disturbances. Here we basically look at the same problem but we additionally consider state constraints. We discuss several approaches for incorporating state constraints in a stochastic optimal control problem. We consider in particular a soft-constraint on the state constraints where constraint violation is punished by a hefty penalty in the cost function. Because of the stochastic nature of the problem, the penalty on the state constraint violation can not be made arbitrary high. We derive a condition on the growth of the state violation cost that has to be satisfied for the optimization problem to be solvable. This condition gives a link between the problem that we consider and the well known $H_\infty$ control problem

Stochastic disturbance rejection in model predictive control by randomized algorithms

In this paper we consider model predictive control with stochastic disturbances and input constraints. We present an algorithm which can solve this problem approximately but with arbitrary high accuracy. The optimization at each time step is a closed loop optimization and therefore takes into account the effect of disturbances over the horizon in the optimization. Via an example it is shown that this gives a clear improvement of performance although at the expense of a large computational effort

Control refinement for discrete-time descriptor systems: a behavioural approach via simulation relations

The analysis of industrial processes, modelled as descriptor systems, is often computationally hard due to the presence of both algebraic couplings and difference equations of high order. In this paper, we introduce a control refinement notion for these descriptor systems that enables analysis and control design over related reduced-order systems. Utilising the behavioural framework, we extend upon the standard hierarchical control refinement for ordinary systems and allow for algebraic couplings inherent to descriptor systems.Comment: 8 pages, 3 figure

A Generalized LMI Formulation for Input-Output Analysis of Linear Systems of ODEs Coupled with PDEs

In this paper, we consider input-output properties of linear systems consisting of PDEs on a finite domain coupled with ODEs through the boundary conditions of the PDE. This framework can be used to represent e.g. a lumped mass fixed to a beam or a system with delay. This work generalizes the sufficiency proof of the KYP Lemma for ODEs to coupled ODE-PDE systems using a recently developed concept of fundamental state and the associated boundary-condition-free representation. The conditions of the generalized KYP are tested using the PQRS positive matrix parameterization of operators resulting in a finite-dimensional LMI, feasibility of which implies prima facie provable passivity or L2-gain of the system. No discretization or approximation is involved at any step and we use numerical examples to demonstrate that the bounds obtained are not conservative in any significant sense and that computational complexity is lower than existing methods involving finite-dimensional projection of PDEs

Stability of hybrid model predictive control

In this paper we investigate the stability of hybrid systems in closed-loop with Model Predictive Controllers (MPC) and we derive a priori sufficient conditions for Lyapunov asymptotic stability and exponential stability. A general theory is presented which proves that Lyapunov stability is achieved for both terminal cost and constraint set and terminal equality constraint hybrid MPC, even though the considered Lyapunov function and the system dynamics may be discontinuous. For particular choices of MPC criteria and constrained Piecewise Affine (PWA) systems as the prediction models we develop novel algorithms for computing the terminal cost and the terminal constraint set. For a quadratic MPC cost, the stabilization conditions translate into a linear matrix inequality while, for an 1-norm based MPC cost, they are obtained as 1-norm inequalities. It is shown that by using 1-norms, the terminal constraint set is automatically obtained as a polyhedron or a finite union of polyhedra by taking a sublevel set of the calculated terminal cost function. New algorithms are developed for calculating polyhedral or piecewise polyhedral positively invariant sets for PWA systems. In this manner, the on-line optimization problem leads to a mixed integer quadratic programming problem or to a mixed integer linear programming problem, which can be solved by standard optimization tools. Several examples illustrate the effectiveness of the developed methodology

Finite-time behavior of inner systems

In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer function. The relation between nonminimum phase zeros and Hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance. The results are used to solve various tracking problems both on finite as well as on infinite time horizons. A typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller

Non-smooth model predictive control: stability and applications to hybrid systems

In this report we investigate the stability of hybrid systems in closed-loop with Model Predictive Controllers (MPC) and we derive a priori sufficient conditions for Lyapunov asymptotic stability and exponential stability. A general theory is presented which proves that Lyapunov stability is achieved for both terminal cost and constraint set and terminal equality constraint hybrid MPC, even though the considered Lyapunov function and the system dynamics may be discontinuous. For particular choices of MPC criteria and constrained Piecewise Affine (PWA) systems as the prediction models we develop novel algorithms for computing the terminal cost and the terminal constraint set. For a quadratic MPC cost, the stabilization conditions translate into a linear matrix inequality while, for an ∞-norm based MPC cost, they are obtained as ∞-norm inequalities. It is shown that by using ∞-norms, the terminal constraint set is automatically obtained as a polyhedron or a finite union of polyhedra by taking a sublevel set of the calculated terminal cost function. New algorithms are developed for calculating polyhedral or piecewise polyhedral positively invariant sets for PWA systems. In this manner, the on-line optimization problem leads to a mixed integer quadratic programming problem or to a mixed integer linear programming problem, which can be solved by standard optimization tools. Several examples illustrate the effectiveness of the developed methodology

End-point parametrization and guaranteed stability for a model predictive control scheme

In this paper we consider the closed-loop asymptotic stability of the model predictive control scheme which involves the minimization of a quadratic criterion with a varying weight on the end-point state. In particular, we investigate the stability properties of the (MPC-) controlled system as function of the end-point penalty and provide a useful parametrization of the class of end-point penalties for which stability of the controlled system can be guaranteed. The results are successfully applied for the implementation of an MPC controller of a binary distillation proces