180 research outputs found
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 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
A behavioral approach to optimal control
In this paper we consider a formulation of the optimal control problem in which the controller is not viewed as an operator that transforms measurements to controls. Instead, the controller is assumed to be a device that constrains a set of a-priori specified interconnection variables so as to achieve a controlled system whose manifest variables have a free component and satisfy an upperbound on the norm of its impulse response. We formalize and solve this problem in a behavioral setting, that is, without reference to system representations and input-output structures. The equivalance between the control problem, the generalized control problem and the LQ optimal control problem are established
Model reduction for linear parameter-varying systems through parameter projection
For affine linear parameter-varying (LPV) systems, this paper develops two
parameter reduction methods for reducing the dimension of the parameter space.
The first method achieves the complexity reduction by transforming the affine
LPV system into a parameter-ordered form and establishing an affine upper bound
of the system Gramians, which is extended to time-varying rate-bounded
parameters. The second method is based on considering the sensitivity function
of the transfer function and time evolution equations. Both methods are applied
to an academic example and a thermal model. Simulation results together with
some analysis are given.Comment: This paper has been accepted by 58th IEEE Conference on Decision and
Control (CDC 2019, Nice, France
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
Affine Parameter-Dependent Lyapunov Functions for LPV Systems with Affine Dependence
This paper deals with the certification problem for robust quadratic
stability, robust state convergence, and robust quadratic performance of linear
systems that exhibit bounded rates of variation in their parameters. We
consider both continuous-time (CT) and discrete-time (DT) parameter-varying
systems. In this paper, we provide a uniform method for this certification
problem in both cases and we show that, contrary to what was claimed
previously, the DT case requires a significantly different treatment compared
to the existing CT results. In the established uniform approach, quadratic
Lyapunov functions, that are affine in the parameter, are used to certify
robust stability, robust convergence rates, and robust performance in terms of
linear matrix inequality feasibility tests. To exemplify the procedure, we
solve the certification problem for -gain performance both in
the CT and the DT cases. A numerical example is given to show that the proposed
approach is less conservative than a method with slack variables.Comment: 8 pages, 3 figure
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