Bounded Error Identification of Systems With Time-Varying Parameters

This note presents a new approach to guaranteed system identification for time-varying parameterized discrete-time systems. A bounded description of noise in the measurement is considered. The main result is an algorithm to compute a set that contains the parameters consistent with the measured output and the given bound of the noise. This set is represented by a zonotope, that is, an affine map of a unitary hypercube. A recursive procedure minimizes the size of the zonotope with each noise corrupted measurement. The zonotopes take into account the time-varying nature of the parameters in a nonconservative way. An example has been provided to clarify the algorithm

Enlarging the domain of attraction of MPC controllers

This paper presents a method for enlarging the domain of attraction of nonlinear model predictive control (MPC). The usual way of guaranteeing stability of nonlinear MPC is to add a terminal constraint and a terminal cost to the optimization problem such that the terminal region is a positively invariant set for the system and the terminal cost is an associated Lyapunov function. The domain of attraction of the controller depends on the size of the terminal region and the control horizon. By increasing the control horizon, the domain of attraction is enlarged but at the expense of a greater computational burden, while increasing the terminal region produces an enlargement without an extra cost. In this paper, the MPC formulation with terminal cost and constraint is modified, replacing the terminal constraint by a contractive terminal constraint. This constraint is given by a sequence of sets computed off-line that is based on the positively invariant set. Each set of this sequence does not need to be an invariant set and can be computed by a procedure which provides an inner approximation to the one-step set. This property allows us to use one-step approximations with a trade off between accuracy and computational burden for the computation of the sequence. This strategy guarantees closed loop-stability ensuring the enlargement of the domain of attraction and the local optimality of the controller. Moreover, this idea can be directly translated to robust MPC.Ministerio de Ciencia y Tecnología DPI2002-04375-c03-0

Computationally efficient min-max MPC

2005 IFAC 16th Triennial World Congress, Prague, Czech RepublicMin-Max MPC (MMMPC) controllers (Campo and Morari, 1987) suffer from a great computational burden that is often circumvented by using upper bounds of the worst possible case of a performance index. These upper bounds are usually computed by means of LMI techniques. In this paper a more efficient approach is shown. This paper proposes a computationally efficient MMMPC control strategy in which the worst case cost is approximated by an upper bound which can be easily computed using simple matrix operations. This implies that the algorithm can be coded easily even in non mathematical oriented programming languages such as those found in industrial embedded control hardware. Simulation examples are given in the paper

Enlarging the domain of attraction of MPC controller using invariant sets

2002 IFAC15th Triennial World Congress, Barcelona, SpainThis paper presents a method for enlarging the domain of attraction of nonlinear model predictive control (MPC). The useful way of guaranteeing stability of nonlinear MPC is to add a terminal constraint and a terminal cost in the optimization problem. The terminal constraint is a positively invariant set for the system and the terminal cost is an associated Lyapunov function. The domain of attraction of the controller depends on the size of the terminal region and the prediction horizon. By increasing the prediction horizon, the domain of attraction is enlarged but at expense of a greater computational burden. A strategy to enlarge the domain of attraction of MPC without increasing the prediction horizon is presented. The terminal constraint is replaced by a contractive terminal constraint which is given by a sequence of control invariant sets for the system. This strategy guarantees closed loop stability under the same assumptions

Robust stability of min-max MPC controllers for nonlinear systems with bounded uncertainties

Sixteenth International Symposium on Mathematical Theory of Networks and Systems 05/07/2004 Leuven, BélgicaThe closed loop formulation of the robust MPC has been shown to be a control technique capable of robustly stabilize uncertain nonlinear systems subject to constraints. Robust asymptotic stability of these controllers has been proved when the uncertainties are decaying. In this paper we extend the existing results to the case of uncertainties that decay with the state but do not tend to zero. This allows us to consider both plant uncertainties and external disturbances in a less conservative way. First, we provide some results on robust stability under the considered kind of uncertainties. Based on these, we prove robust stability of the min-max MPC. In the paper we show how the robust design of the local controller is translated to the min-max controller and how the persistent term of the uncertainties determines the convergence rate of the closed-loop system.Ministerio de Ciencia y Tecnología DPI-2001-2380-03-01Ministerio de Ciencia y Tecnología DPI-2002-4375-C02-0

Computational burden reduction in Min-Max MPC

Min–max model predictive control (MMMPC) is one of the strategies used to control plants subject to bounded uncertainties. The implementation of MMMPC suffers a large computational burden due to the complex numerical optimization problem that has to be solved at every sampling time. This paper shows how to overcome this by transforming the original problem into a reduced min–max problem whose solution is much simpler. In this way, the range of processes to which MMMPC can be applied is considerably broadened. Proofs based on the properties of the cost function and simulation examples are given in the paper

Probabilistic reachable and invariant sets for linear systems with correlated disturbance

In this paper a constructive method to determine and compute probabilistic reachable and invariant sets for linear discrete-time systems, excited by a stochastic disturbance, is presented. The samples of the disturbance signal are not assumed to be uncorrelated, only a bound on the correlation matrices is supposed to be known. The concept of correlation bound is introduced and employed to determine probabilistic reachable sets and probabilistic invariant sets. Constructive methods for their computation, based on convex optimization, are given

Probabilistic reachable and invariant sets for linear systems with correlated disturbance

In this paper a constructive method to determine and compute probabilistic reachable and invariant sets for linear discrete-time systems, excited by a stochastic disturbance, is presented. The samples of the disturbance signal are not assumed to be uncorrelated, only a bound on the correlation matrices is supposed to be known. The concept of correlation bound is introduced and employed to determine probabilistic reachable sets and probabilistic invariant sets. Constructive methods for their computation, based on convex optimization, are given

A Prediction approach to introduce dead-time process control in a basic control course

7TH IFAC SYMPOSIUM ON ADVANCES IN CONTROL EDUCATION. 21/06/2006. MADRIDThis paper presents a methodology to introduce the control of dead-time processes using a simple and intuitive predictive approach. A trivial solutionfor the control of a process with a dead-time is first proposed. From this strategythe idea of the predictor based controller is derived. Open-loop predictors andclosed-loop ones are then used to analyze the obtained solution. A simple tuningof the proposed structure for a first order plus dead-time process together with apolynomial approximation of the dead-time allows to derive apidcontroller. Thus,the approach based on the idea of prediction can be used to interpret the use of apidto control a dead-time process. It is illustrated how the performance of thepidcontroller is limited by the modelling error introduced in the approximation. Thepresented approach gives a measurement of the achievable performance. Severalsimulation examples illustrate the results.Ministerio de Ciencia y Tecnología DPI 2005-0456